Advanced adjustment method for mitigating RF load impedance fluctuations due to periodic disturbances

Abstract

A radio frequency (RF) power generation system includes an RF power supply that generates an RF output signal to be transmitted to a load. An RF power controller is configured to generate control signals that vary the RF output signal. The controller adjusts parameters associated with the RF output signal, which are controlled by trigger signals. The parameters are adjusted across a predetermined number of bins. The parameters are adjusted according to a cost function, which is determined by introducing perturbations for each bin into actuators that affect the cost function. The actuators may control an external RF output signal. The trigger signals may vary according to the external RF output signal. The perturbations are determined according to a basis set having fewer dimensions than the number of bins.

Description

【Technical Field】 【0001】 Cross-references to related applications This application claims priority to U.S. Patent Application No. 18 / 302,141, filed on April 18, 2023. The entire disclosure of the above application is incorporated herein by reference. 【0002】 field This disclosure relates to RF generator systems and the control of RF generators. 【Background Art】 【0003】 background Plasma processing is commonly used in semiconductor manufacturing. In plasma processing, ions are accelerated by an electric field to etch material from the surface of a substrate or deposit material on the surface of the substrate. In one basic example, an electric field is generated based on an RF or DC power signal generated by each radio frequency (RF) or direct current (DC) generator of a power transmission system. The power signal generated by the generator must be accurately controlled to effectively perform plasma etching. 【0004】 The description of the background provided herein is generally for the purpose of illustrating the background of the present disclosure. Aspects of the description that may not be the achievements of the inventors currently named within the scope described in this background section and may not be eligible as prior art at the time of filing are not admitted as prior art to the present disclosure, either expressly or implicitly. 【Summary of the Invention】 【0005】 overview A system comprising one or more computers may be configured to perform a particular operation or action by installing software, firmware, hardware, or a combination thereof on the system and causing the system to perform the operation during operation. One or more computer programs may be configured to perform a particular operation or action by including instructions that cause the data processing device to perform the operation when executed by the data processing device. One general aspect includes an RF power generation system. The controller includes an RF power controller coupled to an RF power source, the RF power controller being configured to generate a control signal that varies an RF output signal having a plurality of bins from the RF power source. The RF power controller is configured to adjust at least one parameter that determines a characteristic of the RF output signal in response to a synchronization signal. The parameter is perturbed according to a hopping pattern associated with the plurality of bins, and the parameter is adjusted by either minimizing or maximizing a cost function in response to the perturbation of the at least one parameter by the hopping pattern. The hopping pattern is adjusted by a basis set having a plurality of dimensions, the number of dimensions being less than the number of bins. Other embodiments of this aspect include corresponding computer systems, devices, and computer programs recorded on one or more computer storage devices, each configured to perform the operation of the method. 【0006】 The embodiment may include one or more of the following features: The RF power controller iterates through the dimensions to adjust the hopping pattern with each iteration. The hopping pattern can be adjusted by applying either an offset or a scaling factor to the hopping pattern. Perturbation of at least one of the parameters for the plurality of bins determines the hopping pattern. The basis set includes at least one of sinusoidal functions, spline functions, polynomial functions, exponential functions, and radial basis functions. The first dimension of the basis set is orthogonal to the second dimension of the basis set. Each bin has a width, and the width of a selected bin may be the same as or different from the widths of the other bins. The plurality of dimensions of the basis set are determined according to the Fast Fourier Transform (FFT) of the hopping pattern. The plurality of dimensions of the basis set are determined from data analysis. The plurality of dimensions of the basis set are determined according to singular value decomposition (SVD) or principal component analysis (PCA). The RF power controller adjusts the above parameters according to the synchronization signal, which indicates the relative position of the external RF output signal. The above parameters are either frequency or frequency offset, and include a plurality of frequencies introduced by the RF power controller to the RF output signal in a predetermined order and timing according to the synchronization signal, or the above parameters are either reactance or reactance offset, and include a plurality of reactances controlled by the RF power controller in a predetermined order and timing according to the synchronization signal, where the reactance is at least one of capacitance or inductance. The hopping pattern can be adjusted by applying either an offset or a scaling factor to the hopping pattern, and the offset is adjusted by perturbing the offset to determine its effect on the cost function, generating a composite gradient according to the cost function, and adjusting the offset by either minimizing or maximizing the cost function.The scaling factor is adjusted by perturbing the current scaling factor to determine its effect on the cost function, generating a composite gradient according to the cost function, and adjusting the scaling factor by either minimizing or maximizing the cost function. The scaling factor is adjusted by perturbing the current scaling factor to determine its effect on the cost function, generating a composite gradient according to the cost function, and adjusting the scaling factor by either minimizing or maximizing the cost function, and the hopping pattern is adjusted by applying the scaling factor to the hopping pattern. Embodiments of the described techniques may include hardware, methods or processes, or computer software on a computer-accessible medium. 【0007】 One general embodiment includes a non-transient computer-readable medium for storing instructions. The non-transient computer-readable medium stores instructions for controlling a first power supply to output a first output signal having multiple bins to a load. The instructions also include generating a control signal to change the first output signal from the power supply to adjust at least one parameter that determines the characteristics of the first output signal in response to a synchronization signal. The instructions also include perturbing the parameter according to a hopping pattern associated with the multiple bins, the parameter being adjusted by either minimizing or maximizing a cost function in response to the perturbation of the at least one parameter by the hopping pattern. The instructions also include adjusting the hopping pattern by applying either an offset or a scaling factor to the hopping pattern, or by adjusting the hopping pattern by a basis set having multiple dimensions, the number of dimensions being less than or equal to the number of bins. Other embodiments of this embodiment include corresponding computer systems, devices, and computer programs recorded on one or more computer storage devices, each configured to perform the operation of the method. 【0008】 The embodiment may include one or more of the following features: The instruction on the non-transient computer-readable medium includes iterating through the dimensions to adjust the hopping pattern with each iteration. Two or more of the plurality of bins are adjusted during each iteration. The basis set may include basis functions including at least one of the following basis sets: sine curves, splines, polynomials, exponentials, and radial basis sets. Perturbation of at least one parameter for the plurality of bins determines the hopping pattern. Each bin has a width, and the width of a selected bin may be the same as or different from the widths of the other bins. The instruction on the non-transient computer-readable medium may include determining the plurality of dimensions of the basis set according to the Fast Fourier Transform (FFT) of the hopping pattern. The instruction on the non-transient computer-readable medium may include determining the plurality of dimensions of the basis set using data analysis. The instructions for the non-transient computer-readable medium described above may include determining the multiple dimensions according to singular value decomposition (SVD) or principal component analysis (PCA). The power controller adjusts the parameters according to the synchronization signal, which indicates the relative position of the external output signal. The parameters are either frequency or frequency offset, and include multiple frequencies introduced to the output signal in a predetermined order and timing according to the synchronization signal, or the parameters are either reactance or reactance offset, and include multiple reactances introduced in a predetermined order and timing according to the synchronization signal, where the reactance is at least one of capacitance or inductance. The instructions for the non-transient computer-readable medium include adjusting the hopping pattern by applying either an offset or a scaling factor to the hopping pattern, where the offset is adjusted by perturbing the offset to determine its effect on the cost function, generating a composite gradient according to the cost function, and adjusting the basis set by either minimizing or maximizing the cost function.Instructions on the non-transient computer-readable medium described above may include perturbing the current scaling factor to determine its effect on the cost function, generating a composite gradient according to the cost function, and adjusting the scaling factor by either minimizing or maximizing the cost function. Embodiments of the described techniques may include hardware, methods, or processes, or computer software on a computer-accessible medium. 【0009】 One general embodiment includes a power generator system comprising a power supply that generates an output signal having variable amplitude and frequency and a plurality of bins. The system also includes a power controller coupled to the power supply, configured to generate a control signal that changes the output signal and to adjust at least one parameter that determines the characteristics of the output signal in response to a synchronization signal. The parameter is perturbed according to a hopping pattern associated with the plurality of bins, and the parameter is adjusted by either minimizing or maximizing a cost function in response to the perturbation of the at least one parameter by the hopping pattern. The hopping pattern is adjusted by a basis set having multiple dimensions, the number of dimensions being less than the number of bins. Other embodiments of this embodiment include corresponding computer systems, devices, and computer programs recorded on one or more computer storage devices, each configured to perform the operation of the method. 【0010】 An embodiment may include one or more of the following features: Two or more of the above multiple bins are adjusted during each iteration. The basis set may include basis functions that include at least one of the following: sine curves, splines, polynomials, exponentials, and radial basis sets. The first dimension of the basis set is orthogonal to the second dimension of the basis set. The above multiple dimensions of the basis set are determined from data analysis. The above multiple dimensions of the basis set are determined according to singular value decomposition (SVD) or principal component analysis (PCA). The power controller adjusts the above parameters according to the synchronization signal, which indicates the relative position of the external output signal. Embodiments of the described technique may include hardware, methods or processes, and computer software on a computer-accessible medium. 【0011】 Further scope of the applicable nature of this disclosure will become apparent from the detailed description, claims, and drawings. The detailed description and specific examples are for illustrative purposes only and are not intended to limit the scope of this disclosure. [Brief explanation of the drawing] 【0012】 Brief explanation of the drawing [Figure 1] Figure 1 shows one representation of an inductively coupled plasma processing system. 【0013】 [Figure 2] Figure 2 shows one representation of a capacitively coupled plasma processing system. 【0014】 [Figure 3] Figure 3 shows a generalized representation of a plasma system arranged in various configurations of this disclosure. 【0015】 [Figure 4] Figure 4 is an illustrative plot of intermodulation distortion (IMD) resulting from applying two signals of different frequencies to a nonlinear reactor. 【0016】 [Figure 5] Figure 5 shows the voltage and power waveforms for a system with two RF signals applied to a load, and the effect of intermodulation distortion on power transmission to the load. 【0017】 [Figure 6] Figure 6 shows the voltage and power waveforms for a system with two RF signals applied to a load, and the power transmission when there is no intermodulation distortion between the two signals. 【0018】 [Figure 7] Figure 7 is a schematic block diagram of a power transmission system having multiple power supply units arranged in various configurations of the present disclosure. 【0019】 [Figure 8] Figure 8 shows the waveform of the RF signal and the pulses that modulate this RF signal. 【0020】 [Figure 9] Figure 9 shows the voltage and power waveforms for a system with two RF signals applied to a load when periodic disturbance compensation is not applied. 【0021】 [Figure 10] Figure 10 shows the voltage and power waveforms for a system with two RF signals applied to a load when periodic disturbance compensation is applied. 【0022】 [Figure 11] Figure 11 shows a waveform subdivided into bins to illustrate the periodic disturbance compensation system described herein. 【0023】 [Figure 12] Figure 12 shows a flowchart of the periodic disturbance compensation system. 【0024】 [Figure 13]Figure 13 shows a functional block diagram of the periodic disturbance compensation system. 【0025】 [Figure 14] Figure 14 shows the voltage and power waveforms for a system having two RF signals applied to a load when the periodic disturbance compensation described herein is applied. 【0026】 [Figure 15] Figure 15 shows the voltage and power waveforms of the system in Figure 14 when periodic disturbance compensation includes smooth transitions between each compensation value. 【0027】 [Figure 16] Figure 16 shows an RF generator configured to compensate for periodic system disturbances. 【0028】 [Figure 17] Figure 17 shows a functional block diagram of an example control module arranged in various configurations. 【0029】 [Figure 18] Figure 18 shows a flowchart illustrating the operation of a control system arranged according to the principles of this disclosure. 【0030】 [Figure 19] Figure 19 shows a partial functional block diagram of a periodic disturbance compensation system, including actuation values ​​for each bin in a 20-bin system. 【0031】 [Figure 20] Figure 20 shows the waveforms of the upward and downward fluctuations of the squared reflection coefficient in response to the perturbation. 【0032】 [Figure 21] Figure 21 shows the relationship between the normalization coefficient for each bin and the normalization coefficient in the one-to-one correspondence full profile. 【0033】 [Figure 22] Figure 22 shows the relationship between the normalization coefficients for each bin in the full profile and the Fourier series basis for many-to-few correspondences between each bin and the basis function index. 【0034】 [Figure 23] Figure 23 shows a functional block diagram of the periodic disturbance compensation system provided for in this disclosure. 【0035】 [Figure 24] Figure 24 shows the relationship between the learned hopping pattern and the singular values ​​of the frequency offset matrix obtained using singular value decomposition (SVD). 【0036】 [Figures 25A-25E] Figures 25A–25E show individual basis vectors for an example of a 5-dimensional basis vector for a periodic disturbance compensation system arranged in this disclosure. 【0037】 In drawings, reference numbers may be reused to identify similar and / or identical elements. [Modes for carrying out the invention] 【0038】 Detailed explanation A power system may include a DC or RF power generator, or a DC or RF generator, a matching network, and a load (such as a process chamber, plasma chamber, or reactor with fixed or variable impedance). The power generator produces a DC or RF power signal, which is received by the matching network or an impedance-optimizing controller or circuit. The matching network or impedance-optimizing controller or circuit converts the load impedance to the characteristic impedance of the transmission line between the power generator and the matching network. Impedance matching helps maximize the amount of power delivered to the load ("forward power") and minimize the amount of power reflected back from the load to the power generator ("reverse power" or "reflected power"). Power delivered to the load can be maximized by minimizing reflected power when the input impedance of the matching network matches the characteristic impedance of the transmission line and the generator. 【0039】 In the field of power sources or power supply, there are typically two approaches to applying a power signal to a load. The first, more traditional approach is to apply a continuous power signal to the load. In continuous mode or continuous wave mode, the continuous power signal is typically a constant DC power signal or sinusoidal RF power signal continuously output to the load by the power source. In the continuous mode approach, the power signal exhibits a constant DC output or sinusoidal output, and the amplitude and / or frequency (of the RF power signal) of the power signal can be varied to change the output power applied to the load. 【0040】 A second approach to supplying a power signal to a load is to pulse the RF signal rather than supplying a continuous RF signal to the load. In pulsed or pulsed mode of operation, the RF signal is modulated by a modulation signal to define an envelope for the modulated power signal. The RF signal can be, for example, a sinusoidal RF signal or other time-varying signal. The power supplied to the load is typically changed by changing the modulation signal. 【0041】 In a typical power supply configuration, the output power applied to the load is determined using sensors that measure forward power and reflected power, or the voltage and current of the RF signal applied to the load. These signal sets are analyzed in a control loop. This analysis typically determines the power values ​​used to adjust the output of the power supply to change the power applied to the load. In power transmission systems where the load is a process chamber or other nonlinear or time-varying load, the applied power is partly a function of the load impedance; therefore, a change in the load impedance causes a corresponding change in the power applied to the load. 【0042】 In systems where the manufacturing of various devices relies on introducing power into a load to control the manufacturing process, power is typically delivered by one of two configurations. In the first configuration, power is capacitively coupled to the load. Such systems are called capacitively coupled plasma (CCP) systems. In the second configuration, power is inductively coupled to the load. Such systems are typically called inductively coupled plasma (ICP) systems. Power coupling to the plasma can also be achieved via wave coupling at microwave frequencies. Such approaches typically use electron cyclotron resonance (ECR) or microwave sources. Helicon sources are another form of wave-coupled source and typically operate at RF frequencies similar to conventional ICP and CCP systems. The power transmission system may include at least one bias power and / or source power applied to one or more electrodes of the load. The source power typically generates the plasma and controls the plasma density. The bias power modulates ions in sheath formation. Depending on various design considerations, the bias and source may share the same electrode or use separate electrodes. 【0043】 When a power transmission system drives a time-varying or nonlinear load, such as a process chamber or plasma chamber, the power absorbed by the bulk plasma and plasma sheath creates an ion density in the range of ion energy. One characteristic criterion for ion energy is the ion energy distribution function (IEDF). The ion energy distribution function (IEDF) can be controlled by bias power or bias voltage. One way to control the IEDF for a system in which multiple RF power signals are applied to a load is to vary the multiple RF signals, which are associated by at least one of amplitude, frequency, and phase. At least one of the associated amplitude, frequency, and phase of the multiple RF power signals is also associated by a Fourier series and associated coefficients. The frequencies between the multiple RF power signals may be locked, and the relative phases between the multiple RF power signals may also be locked. Examples of such systems can be found in U.S. Patents 7,602,127, 8,110,991, and 8,395,322. All of these patents have been assigned to the assignee of this application and are incorporated by reference into this application. 【0044】 Time-varying or nonlinear loads can exist in various applications. In some applications, a plasma processing system may also include components for plasma generation and control. One such component is a nonlinear load implemented as a process chamber, such as a plasma chamber or reactor. As an example, a typical plasma chamber or reactor used in a plasma processing system for thin-film manufacturing can utilize a dual power system. One power generator (source) controls the generation of plasma, and another power generator (bias) controls the ion energy. Examples of dual power systems include those described in U.S. Patents 7,602,127, 8,110,991, and 8,395,322, which were referenced above. The dual power systems described in the above patents adapt the power supply operation to control the ion density and its corresponding ion energy distribution function (IEDF) using a closed-loop control system. 【0045】 For example, there are several approaches to controlling a process chamber that can be used to generate plasma. For instance, in an RF power transmission system, the phases and frequencies of multiple drive RF signals operating at the same or nearly identical frequencies can be used to control plasma generation. For RF-driven plasma sources, periodic waveforms that affect plasma sheath dynamics and corresponding ion energy are commonly known and controlled by the frequency and associated phase interactions of these periodic waveforms. Another approach in RF power transmission systems involves dual-frequency control, where two RF frequency sources operating at different frequencies are used to power the plasma chamber to allow substantially independent control of ion and electron densities. 【0046】 Another approach utilizes a broadband RF power supply to drive the plasma chamber. However, broadband approaches present several challenges. One challenge is coupling the power to the electrodes. A second challenge is that, in order to support material surface interactions, the transfer function from the generated waveform for the desired IEDF to the actual sheath voltage must be formulated over a wide process space. One approach addressing this in an inductively coupled plasma system involves controlling the plasma density by controlling the power supplied to the source electrode, while controlling the IEDF by controlling the power supplied to the bias electrode to modulate ions and control the etching rate and etching feature profile. By controlling the source and bias electrodes, the etching rate and various other etching characteristics are controlled via ion density and energy. 【0047】 As the manufacturing of integrated circuits and integrated devices continues to evolve, the power requirements for controlling the manufacturing process also evolve. For example, in the manufacturing of memory devices, the requirements for bias power continue to increase. As power increases, more high-energy ions are generated for increased directivity or anisotropic etching feature profiles and faster surface interactions, which increases the etching rate and allows etching of features with higher aspect ratios. In RF systems, the increase in ion energy can sometimes be accompanied by a decrease in bias frequency requirements, along with an increase in the power and number of bias power supplies coupled to the plasma sheath generated within the plasma chamber. The increase in power and the number of bias power supplies at low bias frequencies results in intermodulation distortion (IMD) from sheath modulation. IMD radiation can significantly reduce the power supplied by the source from which the plasma generation originates. U.S. Patent No. 10,821,542, issued on November 3, 2020, and assigned to the assignee of this application, describes a method for pulse synchronization by monitoring power in another frequency band, which is incorporated herein by reference. In the aforementioned U.S. patent application, pulse generation of the second RF generator is controlled in response to detection of pulse generation of the first RF generator in the second RF generator, thereby synchronizing pulse generation between the two RF generators. 【0048】 Figure 1 shows one representation of an inductively coupled plasma (ICP) system 110. The ICP system 110 includes a nonlinear load such as a reactor, plasma reactor, or plasma chamber 112 (used interchangeably herein) for generating plasma 114. Power in the form of voltage or current is supplied to the plasma chamber 112 via a pair of coils, including a coil assembly that includes one or more coils arranged in various configurations. In one non-limiting configuration shown in Figure 1, the plasma chamber 112 includes one or both of a first coil 116 and a second coil 118. In various configurations, the coils may be arranged concentrically, entangled, or in a helical configuration. Power is supplied to the first coil 116 via an RF power generator or power supply 120, and to the second coil 118 via an RF power generator or power supply 122. Coils 116 and 118 are arranged to supply power to the plasma chamber 112. The dielectric window 124 provides a vacuum seal while allowing power to be coupled to the plasma. A substrate 126 is placed inside the plasma chamber 112, which typically forms the workpiece to be plasma-treated. An RF power generator, power supply, or power supply 128 (these terms may be used interchangeably herein) supplies power to the plasma chamber 112 via the substrate 126. 【0049】 In various configurations, power supplies 120 and 122 provide a source voltage or current to ignite or generate the plasma 114 and control the plasma density. Also in various configurations, power supply 128 provides a bias voltage or current to modulate ions to control the ion potential or ion energy of the plasma 114. In various configurations, power supplies 120 and 122 are locked to operate at the same frequency, voltage, and current, with a fixed or variable relative phase. In other various configurations, power supplies 120 and 122 may operate at different frequencies, voltages, and currents, as well as with different relative phases. 【0050】 Figure 2 shows one representation of a capacitively coupled plasma (CCP) system 210. The CCP system 210 includes a plasma chamber 212 for generating plasma 214. A pair of electrodes 216, 218 placed within the plasma chamber 212 are connected to DC (ω=0) or RF power generators or power supplies 220, 228, respectively. In various configurations, power supply 220 provides a source voltage or current to ignite or generate the plasma 214 or to control the plasma density, although a bias power supply may also be used to ignite the plasma. In various configurations, power supply 228 provides a bias voltage or current to modulate ions in the plasma to control the ion potential, ion energy, or ion density of the plasma 214. In various CCP configurations, bias power and source power may be applied to an upper electrode such as electrode 216 and a lower electrode such as electrode 226 in various combinations. In other non-limiting examples, bias power and source power may be applied to a lower electrode such as electrode 226, and the upper electrode such as electrode 216 may be grounded or floating. In various RF configurations, power supplies 220 and 228 operate in relative phase when the power supplies are in a harmonic relationship. In various other configurations, power supplies 220 and 228 operate at different frequencies, voltages, and currents with fixed or variable relative phase. Also in various configurations, power supplies 220 and 228 may be connected to the same electrode, but a counter electrode may be provided, or they may be further connected to a third DC (ω=0) or RF power generator (not shown). In addition to sinusoidal bias waveforms, in various configurations, non-sinusoidal bias waveforms may control the ion energy. As a non-limiting example, the bias waveform may be a pulsed rectangular waveform or a piecewise linear waveform, as described in U.S. Patent No. 10,396,601, entitled "Piecewise RF Power Systems and Methods for Supplying Pre-Distorted RF Bias Voltage Signals to an Electrode in a Processing Chamber," issued on 27 August 2019 and assigned to the assignee of this application. That patent is incorporated herein by reference. 【0051】 Figure 3 shows a cross-sectional view of a generalized representation of a dual-power input plasma system 310. The plasma system 310 includes a first electrode 312 connected to ground 314 and a second electrode 316 spaced apart from the first electrode 312. A first DC(ω=0) or RF power supply 318 generates a first RF power supplied to the second electrode 316 at a first frequency f=ω1. A second power supply 320 generates a second DC(ω=0) or RF power supplied to the second electrode 316. In various configurations, the second power supply 320 operates at a second frequency f=ω2, where ω2=nω, i.e., the nth harmonic of the frequency of the first power supply 318. In other various configurations, the second power supply 320 operates at a frequency that is not a multiple of the frequency of the first power supply 318. 【0052】 The coordinated operation of the respective power supplies 318 and 320 enables the generation and control of the plasma 322. As shown in the schematic diagram of Figure 3, the plasma 322 is formed within the asymmetric sheath 330 of the plasma chamber 324. The sheath 330 includes a ground or earth sheath 332 and a power supply side sheath 334. The sheath is generally described as a surface region surrounding the plasma 322. As can be seen from the schematic diagram of Figure 3, the ground sheath 332 has a relatively large surface region 326. The power supply side sheath 334 has a small surface region 328. Since each sheath 332 and 334 acts as a dielectric between the conductive plasma 322 and each electrode 312 and 316, each sheath 332 and 334 forms a capacitance between the plasma 322 and each electrode 312 and 316. 【0053】 As will be described in more detail herein, in systems with a high-frequency voltage source such as a second power supply 320 and a low-frequency voltage source such as a first power supply 318, intermodulation distortion (IMD) products are introduced. IMD products arise from changes in the thickness of the plasma sheath, which changes the capacitance between the plasma 322 and electrode 312 through the ground sheath 332 and the capacitance between the plasma 322 and electrode 316 through the power supply side sheath 334. The variation in the capacitance of the power supply side sheath 334 causes IMD. The variation in the power supply side sheath 334 has a greater effect on the capacitance between the plasma 322 and electrode 316 and, therefore, a greater effect on the inverse IMD emitted from the plasma chamber 324. In some plasma systems, the ground sheath 332 functions as an RF short circuit and is not considered to have an effect on the inverse IMD. 【0054】 Figure 4 shows a plot of amplitude against frequency for an exemplary power transmission system having a low-frequency source such as a first power source 318 and a high-frequency source such as a second power source 320. Figure 4 shows the amplitude of the reflected power spectrum against frequency for power source 320. Figure 4 includes a central peak 410 indicating the center frequency of operation of the high-frequency power source such as the second power source 320 in Figure 3. On either side of the central peak 410, Figure 4 also shows IMD components 412,414 representing the IMD introduced by the power supply from the low-frequency power source such as the first power source 318 in Figure 3. As a non-limiting example, if the second power source 320 operates at a frequency of 60 MHz and the low-frequency power source 318 operates at 400 kHz, the IMD components are found at 60 MHz ± n × 400 kHz, where n is an arbitrary integer. Thus, peaks 412,414 represent the high frequency ± low frequency of each power source. As shown in Figure 3, driving the electrodes with multiple harmonics provides an opportunity to electrically control the DC self-bias and adjust the energy level of the ion density. 【0055】 Figure 5 shows the waveforms of the forward voltage 512 and the reverse or reflected voltage 514 for the high-frequency side or source RF generator. As a non-limiting example, the source RF generator may operate at 60 MHz. Also, as a non-limiting example, Figure 5 shows the voltage waveform 516 representing the output voltage of the low-frequency side or bias RF generator operating at 400 kHz. As can be seen from Figure 5, the reflected voltage 514 of the source RF generator changes in accordance with the voltage fluctuations of the voltage waveform 516 of the bias RF generator. Also, as can be seen from Figure 5, as the reflected voltage 514 increases, the voltage sent to the load or reactor (the difference between the forward voltage 512 and the reflected voltage 514) decreases. 【0056】 In Figure 6, the voltage 616 output by the bias RF generator has zero amplitude. When voltage 616 has a nearly constant value, the reverse or reflected voltage 614 is virtually constant. Therefore, when there is no fluctuation in the reflected voltage 614, the forward voltage 612 sent to the load is relatively constant and has a high amplitude. In various configurations, when the bias RF generator is off, voltage 616 can be maintained constant without fluctuation. 【0057】 As can be seen from Figures 5 and 6, fluctuations in the voltage waveform 516 of the bias RF generator cause the resulting IMD at the load. The resulting IMD causes fluctuations in the reverse voltage 514, which negatively affects the transmission of the forward voltage 512. By minimizing IMD, a higher amplitude and more consistent forward voltage can be delivered to the load or process chamber. Although the waveforms described in Figures 5 and 6 are voltage waveforms, it should be understood that the principles described here are equally applicable to power detection as well as voltage detection. 【0058】 As shown in Figure 5, various approaches to responding to load fluctuations associated with IMD include configuring the source RF generator to supply a higher output voltage to the load. Increasing the voltage does not improve the efficiency of the system and requires the selection of components that operate at higher voltage levels. When operating at such higher voltage levels, other RF generator components must be selected not only to provide a larger forward voltage but also to withstand higher reflected voltage levels. For this reason, increasing the voltage results in an increase in RF generator costs. 【0059】 Other approaches to address load fluctuations associated with IMD include implementing a disturbance cancellation system that adjusts the frequency actuator of a source RF generator in synchronization with the operation of a bias RF generator. Because the operation of a bias RF generator is typically periodic, the adjustment of the frequency actuator of the source RF generator can be synchronized with the frequency of a lower frequency generator. An example of such an approach can be found in U.S. Patent No. 9,947,514, published on 17 April 2018 and assigned to the assignee of this application, which is incorporated herein by reference. 【0060】 Other disturbance cancellation systems are implemented by controlling actuators that affect the harmonic network reactance. An example of this can be found in U.S. Patent No. 11,232,931, titled "Intermodulation Distortion Mitigation Using Electronic Variable Capacitor," issued on 25 January 2022 and assigned to the assignee of this application, which is incorporated herein by reference. Further approaches can be found concerning the control of actuators, such as power amplifier drive control. An example of this can be found in U.S. Patent No. 11,158,488, titled "High Speed ​​Synchronization of Plasma Source / Bias Power Delivery," issued on 26 October 2021 and assigned to the assignee of this application, which is incorporated herein by reference. 【0061】 Returning to the disturbance cancellation system achieved by adjusting the frequency actuator of the source RF generator described above, disturbance cancellation requires adjusting the profile of the frequency actuator. Since the frequency of the source RF generator changes in synchronization with the frequency of the bias RF generator, such a profile can generally be described as a hopping pattern, adjustment pattern, or compensation pattern. This approach can generally be described as frequency hopping. 【0062】 Traditionally, frequency hopping or tuning patterns were obtained by manually adjusting frequency profiles via an iterative approach using a graphical user interface. Such approaches are inefficient because the patterns are adjusted prior to the manufacturing process occurring in the process chamber or plasma chamber, and they do not allow for response to disturbances that occur during normal system operation. 【0063】 Figure 7 shows an RF generator or power supply system 710. The power supply system 710 includes a pair of radio frequency (RF) generators or power supply devices 712a, 712b, matching networks 718a, 718b, and a load 732 such as a nonlinear load, which may be a plasma chamber, plasma reactor, process chamber, etc. In various configurations, the RF generator 712a is called the source RF generator or power supply device, and the matching network 718a is called the source matching network. Also in various configurations, the RF generator 712b is called the bias RF generator or power supply device, and the matching network 718b is called the bias matching network. It will be understood that the components can be referred to individually using reference numbers with or without subscripts or prime symbols. In various configurations, for example, a matching network receiving a pulsed DC or non-sinusoidal signal may be considered, but one or both of the matching networks 718a, 718b may be implemented as RF blocking filters rather than impedance matching. In various other configurations, one or both of the harmonized networks 718a and 718b may be omitted. 【0064】 In various configurations, the source RF generator 712a receives a control signal 730 from the matching network 718b and the generator 712b, or from the bias RF generator 712b. The control signal 730 or 730' represents an input signal to the source RF generator 712a that represents one or more operating characteristics or parameters of the bias RF generator 712b. In various configurations, the synchronous bias detector 734 detects the RF signal output from the matching network 718b to the load 732 and outputs a synchronous or trigger signal 730 to the source RF generator 712a. In various configurations, a synchronous or trigger signal, rather than a trigger signal 730, may be output from the bias RF generator to the source RF generator. The difference between the trigger or synchronous signals 730, 730' may arise from the influence of the matching network 718b, thereby adjusting the phase between the input signal to the matching network and the output signal from the matching network. Signals 730 and 730' contain information about the operation of the bias RF generator 712b, which in various configurations enables a predictive response to address periodic fluctuations in the impedance of the plasma chamber 732 caused by the bias RF generator 712b. In the absence of control signals 730 or 730', the RF generators 712a and 712b operate autonomously. 【0065】 The RF generators 712a and 712b each include an RF power supply or amplifier 714a and 714b, an RF sensor 716a and 716b, and a processor, controller, or control module 720a and 720b, respectively. The RF power supplies 714a and 714b generate RF power signals 722a and 722b, respectively, which are output to the sensors 716a and 716b. The RF power signals 722a and 722b pass through the sensors 716a and 716b and are supplied to the matching network 718a and 718b as RF power signals f1 and f2, respectively. The sensors 716a and 716b output signals that vary depending on various parameters detected from the load 732. Although the sensors 716a and 716b are shown as being located within the respective RF generators 712a and 712b, the RF sensors 716a and 716b may be located outside the RF generators 712a and 712b. Such external detection can be performed at the output of the RF generator, at the input of an impedance matching device located between the RF generator and the load, or between the output of the impedance matching device (including the inside of the impedance matching device) and the load. 【0066】 Sensors 716a and 716b detect various operating parameters and output signals X and Y. Sensors 716a and 716b may include voltage sensors, current sensors, and / or directional coupler sensors. Sensors 716a and 716b receive (i) voltage V and current I and / or (ii) forward power P output from their respective power amplifiers 714a, 714b and / or RF generators 712a and 712b. FWD And the reverse power or reflected power P received from the respective matching networks 718a, 718b or load 732 connected to the respective sensors 716a, 716b. REV It can detect voltage V, current I, and forward power P. FWD , and reverse power P REVThe actual voltage, current, forward power, and reverse power associated with each power supply 714a, 714b may be scaled, filtered, or scaled and filtered. Sensors 716a, 716b may be analog or digital sensors, or a combination thereof. In the digital embodiment, sensors 316a, 316b may include an analog-to-digital (A / D) converter and a signal sampling component having a corresponding sampling rate. Signals X and Y are voltage V and current I or forward (or source) power P FWD and the reverse (or reflected) power P REV It can represent either of the following: 【0067】 Sensors 716a and 716b generate sensor signals X and Y, which are received by their respective controllers or control modules 720a and 720b. Power control modules 720a and 720b process the respective X and Y signals 724a, 726a, and 724b and 726b, respectively, and generate one or more feedforward or feedback control signals 728a and 728b for their respective power supplies 714a and 714b. Power supplies 714a and 714b adjust the RF power signals 722a and 722b based on the received feedforward or feedback control signals. In various configurations, power control modules 720a and 720b may, for example, control the respective matched networks 718a and 718b via control signals 729a and 729b, respectively, based on the X and Y signals 724a, 726a, and 724b and 726b. The power control modules 720a and 720b may include one or more proportional integral (PI), proportional-integral-derivative (PID), linear quadratic regulator (LQR) controllers or subsets thereof, and / or one or more direct digital synthesis (DDS) components and / or modules, as described below. 【0068】 In various configurations, the power control modules 720a, 720b may include multiple functions, multiple processes, multiple processors, or multiple submodules. The control signals 728a, 728b may be control or actuator drive signals and may communicate DC offset or rail voltage, voltage or current values, frequency, and phase components. In various configurations, the feedback control signals 728a, 728b can be used as inputs to one or more control loops. In various configurations, the multiple control loops may include proportional-integral (PI), proportional-integral-derivative (PID) controllers, linear secondary regulator (LQR) control loops, or subsets thereof, for RF drive and power rail voltage. In various configurations, the control signals 728a, 728b can be used in one or both of single-input-single-output (SISO) or multiple-input-multiple-output (MIMO) control schemes. An example of a MIMO control scheme can be found by referring to U.S. Patent No. 10,546,724, titled "Pulsed Bidirectional Radio Frequency Source / Load," issued on 28 January 2020 and assigned to the assignee of this application. That patent is incorporated herein by reference. In other configurations, signals 728a and 728b can provide feedforward control as described in U.S. Patent No. 10,049,857, titled "Adaptive Periodic Waveform Controller," issued on 14 April 2018 and assigned to the assignee of this application. That patent is incorporated herein by reference. 【0069】 In various configurations, the power supply system 710 may include a controller 720'. The controller 720' may be located outside of either one or both of the RF generators 712a, 712b, and may be referred to as the external or common controller 720'. In various configurations, the controller 720' may implement one or more functions, processes, or algorithms described herein with respect to either or both of the controllers 720a, 720b. Thus, the controller 720' communicates with each of the RF generators 712a, 712b via a pair of links 736, 738 that allow for the exchange of data and control signals between the controller 720' and the RF generators 712a, 712b, where appropriate. In various configurations, the controllers 720a, 720b, and 720' can perform distributive and collaborative analysis and control of the RF generators 712a, 712b. In various other configurations, controller 720' controls the RF generators 712a and 712b, eliminating the need for their respective local controllers 720a and 720b. 【0070】 In various configurations, the RF power supply 714a, sensor 716a, controller 720a, and matching network 718a can be referred to as the source RF power supply 714a, source sensor 716a, source controller 720a, and source matching network 718a, respectively. Similarly, in various configurations, the RF power supply 714b, sensor 716b, controller 720b, and matching network 718b can be referred to as the bias RF power supply 714b, bias sensor 716b, bias controller 720b, and bias matching network 718b, respectively. In various configurations, as described above, the term "source" refers to the RF generator that generates plasma, and the term "bias" refers to the RF generator that adjusts the ion potential and ion energy distribution function (IEDF) of the plasma. In various configurations, the source and bias RF power supplies operate at different frequencies. In various configurations, the source RF power supply operates at a higher frequency than the bias RF power supply. In various configurations, the source and bias RF power supplies operate at the same or substantially the same frequency. 【0071】 Depending on the configuration, the source RF generator 712a and the bias RF generator 712b include multiple ports for communication with the outside. The source RF generator 712a includes a pulse envelope synchronous output port 740, a digital communication port 742, an RF output port 744, and a control signal port 760. The bias RF generator 712b includes an RF input port 748, a digital communication port 750, and a pulse synchronous input port 752. The pulse envelope synchronous output port 740 outputs a pulse synchronous signal 756 to the pulse synchronous input port 752 of the bias RF generator 712b. The digital communication port 742 of the source RF generator 712a and the digital communication port 750 of the bias RF generator 712b communicate via a digital communication link 757. The control signal port 760 of the source RF generator 712a receives one or both of the control signals 730, 730'. The RF output port 744 generates an RF control signal 758 which is input to the RF input port 748. In various configurations, the RF control signal 758 is substantially identical to the RF control signal that controls the source RF generator 712a. In other various configurations, the RF control signal 758 is identical to the RF control signal that controls the source RF generator 712a, but is phase-shifted within the source RF generator 712a by the required phase shift generated by the bias RF generator 712b. Thus, in various configurations, the source RF generator 712a and the bias RF generator 712b are driven by substantially identical RF control signals, or by substantially identical RF control signals that are phase-shifted by a predetermined amount. 【0072】 In various configurations, the power supply system 710 may include multiple RF source generators 712a and multiple RF bias generators 712b. As a non-limiting example, multiple source RF generators 712a, 712a', 712a'', ..., 712a may be used to supply multiple output power signals to one or more source electrodes of a load 732. n Similarly, multiple bias RF generators 712b, 712b', 712b'', ..., 712b can be arranged to supply multiple output power signals to multiple bias electrodes of the load 732. nA source RF generator 712a and a bias RF generator 712b are configured to include multiple source RF generators or bias RF generators, where each RF generator outputs a separate signal to a corresponding multiple matching networks 718a, 718b, which are configured to operate in a one-to-one correspondence as described above. In various other configurations, there may be no one-to-one correspondence between each RF generator and the matching network. In various configurations, multiple source electrodes may mean multiple electrodes cooperating to define a composite source electrode. Similarly, multiple bias electrodes may mean multiple connections to multiple electrodes cooperating to define a composite bias electrode. 【0073】 Figure 8 shows a voltage-over-time plot illustrating a pulse or pulse operation mode for supplying power to a load such as the load 732 in Figure 7. More specifically, Figure 8 shows two multi-state pulses P1 and P2 of a pulse signal 812 having multiple states S1-S4 and S1-S3. In Figure 8, the RF signal 810 is modulated by pulses P1 and P2. When the pulse is ON, as shown in states S1-S3 of P1 and states S1-S2 of P2, the RF generator 732 outputs the RF signal 810 having an amplitude defined by the pulse value in each state. Conversely, between state S4 of P1 and state S3 of P2, the pulse is OFF, and the RF generator 732 does not output the RF signal 810. Pulses P1 and P2 can repeat with a constant or variable duty cycle, and each pulse P1 and P2 state S1-S4, S1-S3 may have the same or variable amplitude and width. 【0074】 In various configurations, the RF signal 810 does not need to be realized as a sinusoidal waveform as shown in Figure 8. As referenced above with respect to Figure 2, in addition to a sinusoidal waveform, in various configurations, the signal 810 may be a non-sinusoidal waveform. As an unrestricted example, the waveform 810 may be a repeatedly or intermittently pulsed rectangular waveform or a piecewise linear waveform as described in U.S. Patent No. 10,396,601. In various configurations, the pulsed signal 812 may be a shape other than a square wave as shown in Figure 8. Furthermore, as an unrestricted example, the envelope of the pulsed signal 812 may be rectangular, trapezoidal, triangular, sawtooth, Gaussian, or other shapes that define the envelope or modulated envelope of the underlying modulated RF signal. In various configurations, the pulsed signal may occur or occur again within a fixed or variable period or time. In other various configurations, the shape of the pulsed signal may change between each occurrence. In other various configurations, the pulsed signal may occur or occur again within a fixed or variable time, and its shape may change between each occurrence. Furthermore, pulses P1, P2 may have multiple states S1, ..., Sn, with varying amplitude, duration, and shape. States S1, ..., Sn may repeat within a fixed or variable period and may include all or some of the various shapes described above. Also, as shown in Figure 8, the RF signal 810 may operate at a frequency that varies between multiple states or within a single state. 【0075】 This disclosure is directed toward compensating for periodic disturbances caused by changes in the electrical parameters of RF power transmission systems. In RF generator applications, the RF frequency of the signal applied to the load affects the load's impedance. In various configurations, frequency is used as a control actuator to minimize the power reflected back from the load to the RF generator. The RF frequency is varied to minimize reflected power and maximize forward power delivered to the load. 【0076】 As described above, the application of a second RF signal, such as a bias RF generator applying a low-frequency RF signal to the load, can typically affect the power transmitted by a first RF generator or source RF generator that applies a high RF frequency to the load. In various disturbance cancellation systems, the period of the low-frequency generator is divided into a selected number of bins or more. In the source RF generator, the RF frequency of the signal output by the source RF generator is adjusted according to the expected disturbance from the periodic signal output by the low-frequency generator. Furthermore, the RF frequency of the source RF generator is adjusted according to each bin or more of the RF signals output by the low-frequency generator or bias RF generator. The frequency offset applied to the RF frequency signal output by the high-frequency generator or source RF generator defines a hopping pattern intended to reduce or minimize the effects of load fluctuations caused by IMD from the RF signal output by the low-frequency generator or bias RF generator. This approach provides feedforward correction to the RF source frequency actuator, where the frequency hopping pattern per bin provides the correction value or offset. 【0077】 Figure 9 discloses waveforms corresponding to the voltage and power of an RF generator that generates an RF signal applied to a common load such as a plasma chamber or reactor. Waveform 912 represents the signal associated with the RF signal output by the bias RF generator. As a non-limiting example, the bias RF generator operates at 400 kHz. Waveform 914 is generally a square wave synchronous pulse that changes in response to the RF signal output by the bias RF generator. Waveform 916 represents the forward power from the source RF generator output to a load such as load 732 in Figure 7. Waveform 918 shows the power reflected back from the load. As a non-limiting example, the source RF generator operates at 60 MHz. 【0078】 Referring to FIG. 10, FIG. 10 shows a waveform similar to that of FIG. 9 when the RF signal output by the source RF generator 712a of FIG. 7 is adjusted using, for example, frequency hopping or a correction pattern. As described above, the waveform 1012 indicates, for example, the forward voltage output by the bias RF generator 712b of FIG. 7. Similar to FIG. 9, the waveform 1014 represents a synchronization pulse related to the output of an RF signal from a bias RF generator such as the RF generator 712b. As can be seen from FIG. 10, the application of a frequency offset to the output from the RF generator 712a significantly reduces the reverse power 1018 and increases the power transmitted to the load or reactor (the difference between the forward power 1016 and the reverse power 1018). Thus, by using the interference cancellation described herein, the reflected power 1018 is reduced and the transmitted power is increased. 【0079】 In various configurations, the challenge for interference cancellation is how to determine the frequency offset, adjustment, or correction actuations required to implement the frequency hopping, adjustment, or correction pattern. Various approaches have been described for the extremum search iterative learning control (ILC) that determines a frequency activation profile or hopping pattern to mitigate the effect of IMD from periodic impedance variations. 【0080】 FIG. 11 shows a voltage-versus-time waveform 1112 for an RF signal output by a high-frequency generator or source RF generator such as the RF generator 712a of FIG. 7. The waveform 1112 includes a first section 1124 and a second section 1126. In various perspectives, the sections 1124, 1126 can be further divided into bins, where x comprehensively represents any bin among a plurality of bins, as bin b x can be further divided. As shown in FIG. 11, the section 1124 is subdivided into bins such as bin b a1 , b a2 , …, b an . Similarly, the section 1126 is divided into bins such as bin b b1 , bb2 ,…,b bn It can be subdivided into sections. In various configurations, the width and number of bins within each section 1124, 1126 and between each section 1124, 1126 can all vary. The width of each bin within section 1124 may be the same or may vary. Similarly, the width of each bin in section 1126 may be the same or may vary. Furthermore, the number of bins including section 1124 and the number of bins including section 1126 can vary. In pulsed embodiments, the bin width may be narrow in bins near the pulse edge and wide in the relatively steady-state portion of the pulse. 【0081】 In various configurations, bin b x Any one or any of these may, as an unrestricted example, define a pattern of electrical parameter hops, adjustments, or corrections to control the frequency of the source RF generator, or other electrical parameter actuations that mitigate or reduce IMD or improve the operation of the RF generator system. Such parameters may include the frequency, amplitude, and phase of the RF signal output by an RF generator such as RF generator 712a in Figure 7, matching network control parameters, and other control parameters. Other parameters may include various actuators in the RF power transmission system, such as reactances including inductance and capacitance in the matching network. Control of such reactances may be achieved using electronically variable capacitance or inductance. In various configurations, bin b x The bin width can be selected such that the bin spacing is small compared to the fastest rate of change in the reflected power profile generated by IMD. If the bins are too wide, only the low-frequency components in the IMD profile may be adequately compensated. In some configurations, the bin width may be selected based on hardware or software requirements that limit the number of bin values ​​that can be treated and written as frequency offsets from the generator. 【0082】 In various configurations, the width of section 1124 or 1126 is determined according to the periodic nature of the signal that causes fluctuations in the reflected power at the load driven by waveform 1112. As a non-limiting example, in an RF generator system including a source RF generator operating at 60 MHz and a bias RF generator operating at 400 kHz, the width of sections 1124, 1126 may be set according to the period of the output signal of the 400 kHz bias RF generator. Since the output signal of the bias RF generator causes periodic disturbances at the load in the form of IMD, bin b in sections 1124, 1126 x The adjustment pattern formed by this process corrects the IMD when the pattern is applied to the source RF signal in relation to the operation of the bias RF generator. In the example described herein, where the source RF generator operates at 60 MHz and the bias RF generator operates at 400 kHz, there are approximately 150 cycles of source RF waveforms for a single bias RF waveform. For this reason, sections 1124 and 1126 are not shown to scale with respect to waveform 1112. 【0083】 As described herein, each bin is assigned an offset frequency or frequency adjustment (also called a hopping, adjustment, or correction parameter) that is applied to the RF signal output by the source RF generator 712a in synchronization with the bias RF waveform 1112 in Figure 11. The offset or correction associated with each bin defines the frequency hopping pattern. The frequency offset or adjustment associated with each bin is determined as a calibration step and can be stored in memory or continuously updated. Thus, in various configurations, the frequency hopping or adjustment of the source RF frequency is feedforward control, and the feedforward value in a bin is updated based on measurements taken over one or more previous bias cycles for the corresponding bin. 【0084】 Each bottle b xThis can define the hopping frequency, frequency offset, adjustment, or correction parameters of the RF signal output by the RF generator 712a. The frequency may be selected to control the power transmitted to the load by changing the impedance matching between the RF generator 712a and the load 732. Furthermore, in various embodiments, bin b in Figure 11 can be used. x This can specify the tuning of various electrical parameters of the source RF generator of a matched network, such as matched network 718. 【0085】 Figure 12 shows flowchart 1210, and Figure 13 shows functional block diagram 1310 showing the determination of electrical parameters for each bin in Figure 11 in order to determine the adjustment of relevant electrical parameters and the adjustment values ​​of the electrical parameters in order to improve the operation of the RF generator system. Generally speaking, describing the operation of Figures 12 and 13, electrical parameter adjustment or correction profiles, such as frequency hopping profiles, are determined by perturbing the actuator values ​​independently in each iteration. In embodiments, the electrical parameter may be frequency. The independent perturbation involves either increasing or decreasing the actuator associated with the electrical parameter in each iteration. In each iteration, bin b described in Figure 11 x One or more bins related to electrical parameters such as are perturbed, and the effect of the perturbation on one or more output evaluation metrics of interest is determined. In various configurations, one or more output evaluation metrics of interest may be one or more of the following: average reflected power, transmitted power, or the average value of the reflection coefficient over the operating period of a bias generator such as the RF generator 712b in Figure 7. The evaluation metric of interest is also called a cost function, which is optimized to indicate the point in time when a sufficient adjustment pattern has been determined. In various embodiments, the perturbed actuator includes one or more of the following: frequency, amplitude, or phase of the signal applied to the load, or reactance such as inductance or capacitance that affects power transmission to the load. 【0086】 Referring to Figure 12, the control begins in block 1212 and proceeds to block 1214. In block 1214, the perturbation of each bin in the profile is determined to determine the effect of each bin on the cost function. x The bin b is perturbed. Referring to Figure 11, each bin b x One or more actuators corresponding to are perturbed, increased, or decreased by a set amount to produce a change corresponding to the output evaluation index of interest. In block 1214, bin b in Figure 11. x Each of these is modified in a similar manner, and the output metric of interest is analyzed to determine the effect of the perturbation on the cost function associated with the metric of interest. 【0087】 Referring to Figure 13, the functional block diagram 1310 includes a signal conditioning module 1312. The signal conditioning module 1312 receives one or more (n) input signals. In various embodiments, the one or more (n) input signals include one or more signals that are tuned by a tuning pattern, such as an RF output from a source RF generator. The signal conditioning module 1312 also includes one or more (n) perturbation signals from a perturbation generator 1314. The signal conditioning module outputs one or more (n) perturbation signals in response to the one or more (n) inputs and the one or more (n) perturbation signals. The signal conditioning module 1312 can mix, combine, or process the one or more (n) input signals and the one or more (n) perturbation signals to generate one or more (n) perturbation signals that are input to the power amplifier module 1315. The power amplifier module outputs one or more power signals in response to multiple (n) perturbation signals. One or more (n) power signals are input to one or more (n) sensors of the sensor module 1316 and output to the plant or system 1318. The perturbation signals applied to the plant or system 1318 may cause a change in one or more output evaluation metrics of interest, determined by one or more sensors of the sensor module 1316. The sensor module 1316 outputs one or more (n) detected values ​​to the cost module 1320. The cost module 1320 determines one or more (n) costs, as described herein. Figures 12 and 13 illustrate an extreme-search iterative learning control (ILC) approach for learning a frequency actuation profile or hopping pattern required to mitigate periodic load fluctuations. 【0088】 Returning to Figure 12, the control proceeds to block 1216, which determines the composite gradient for the change in the cost function. Referring to Figure 12, the composite gradient module 1322 receives one or more (n) costs and determines the composite gradient in block 1218. Actuator update u i(k+1) is determined based on the gradients of one or more (n) cost functions. The actuator update u is performed using the gradient descent method described below for equation (1). i (k+1) can be determined. u i (k+1) = u i (k) - μG i (1) Here, u i This is frequency actuation at bin i, G i This is the measured cost gradient arising from the perturbed bin i. μ is a variable learning rate. k is the repetition exponent. That is the case. The measurement cost gradient is the gradient of change from the baseline due to the injection of a perturbation signal. That is, the measurement cost gradient is the difference between the output from the sensor module 1316 when no perturbation signal is applied to the signal conditioning module 1312 and the output from the sensor module 1316 when a perturbation input signal is applied to the signal conditioning module 1312, divided by the actuator change. Since the gradient indicates an increasing direction, the negative sign in equation (1) ensures that the iteration is moving in the direction that minimizes cost. 【0089】 Referring to block 1216 in Figure 12, we can use various approaches to obtain G in equation (1). i This can be determined. In one approach, the bin actuator values, such as one or more (n) perturbation signals output by the signal adjustment module 1312, can be adjusted in a certain direction, and the difference in the cost metric between the baseline (unperturbed) value and the perturbed value is used to determine the local gradient for the actuator response slope as described in equation (2) below. It is possible to predict TIFF2026519931000002.tif9170. TIFF2026519931000003.tif10170 Here, C pert The cost when a perturbation is injected, C baseThe cost when perturbation is not administered, U pert is perturbation amplitude That is the case. The measurement cost gradient is calculated by dividing the difference between the unperturbed output evaluation index and the perturbed output evaluation index by the amount of perturbation. 【0090】 In other approaches, the actuator is adjusted in an increasing direction, then in a decreasing direction, or in a first direction and in opposite directions to create a local gradient. TIFF2026519931000004.tif9170 can be predicted as shown in equation (3) below. TIFF2026519931000005.tif11170 Here, C up This is the cost of a bin actuator that has been increased (perturbed) by a fixed amount. C down The cost of a bin actuator that has been reduced (perturbed) by the same fixed amount, U pert This is the magnitude of the actuator change. That is the case. The approach of equation (3) is more robust to local nonlinearities such as the shape of the quadratic cost function than the unidirectional perturbation method described above for equation (2). 【0091】 Other methods may be used to predict local gradients. In non-restrictive examples, the baseline, C up , and C down A quadratic polynomial can be fitted to the output value or cost using the cost values ​​used in the relevant bin actuations. The predicted slope at the central actuator value can then be calculated using this quadratic polynomial. If the quadratic polynomial suggests a local minimum of the cost function occurs, the actuator value associated with that minimum can be directly predicted. 【0092】 Returning to Figure 12, the control is performed using the gradient information acquired in block 1216. The control proceeds to block 1218, which determines a hopping pattern in the direction of lower costs based on TIFF2026519931000006.tif9170. The adjustment or hopping pattern is adjusted according to equation (1) above. The control then proceeds to block 1220, which determines whether the cost is below a predetermined threshold. If the cost is above the predetermined threshold, the control proceeds to block 1214 to perform another iteration consisting of perturbation in block 1214, cost gradient determination in block 1216, and parameter adjustment or adjustment of the correction pattern in block 1218. If it is determined in block 1220 that the cost is below the predetermined threshold, the control proceeds to the end of block 1222. 【0093】 Following the determination of the composite gradient, we return to the cost module 1322 in Figure 13, where the composite gradient is output to the update module 1334, which determines the actuator update according to equation (1) based on the composite gradient determined in the composite gradient module 1332. Composite gradient TIFF2026519931000007.tif7170 can be represented as a vector associated with bin actuator i. Here, The file is TIFF2026519931000008.tif8170. The update module 1334 outputs a parameter adjustment pattern or hopping pattern to one or more adjustment patterns, such as those shown in memory 1336a, a look-up table (LUT) 1336b, or dynamically in 1336c. The parameter adjustment pattern can adjust one or more (n) actuators to control one or more costs according to a MIMO approach to parameter adjustment. The parameter adjustment values ​​in the parameter correction pattern may indicate parameter offset values ​​or parameter values. 【0094】 Returning to block 1214 in Figure 12 and cost module 1320 in Figure 13, the cost function can be determined using various approaches. In one approach, the cost is the average of measured values, such as reflected power, over the period of a low-frequency generator. In various other approaches, the evaluation metric for the cost function may be the average magnitude of the reflection coefficient over the period of a low-frequency generator, such as the low-frequency generator or bias generator 712b in Figure 7. In various other approaches, the cost may vary depending on the magnitude of the transmitted power or the reflection coefficient. In addition to averaging, other evaluation metrics can be used for the average reflected power or magnitude, including maximum, minimum, or other statistical analysis values ​​of those values. 【0095】 One generalized representation of the cost function may include terms weighted individually for different cost components, as shown in equation (4) below. TIFF2026519931000009.tif12170 Here, C j and W j The values ​​represent the cost components and the individual weights assigned to each of these cost components. That is, C total The cost can be expressed as the sum of various weighted cost components, such as the magnitude of the measured reflected power or reflection coefficient at the negative and positive zero crossings of a low-frequency signal or biased RF signal, and can be summed up to form a cost function. That is, a first weight may be assigned to the magnitude of the reflected power or reflection coefficient measured at the negative zero crossing. A first value may also be assigned to the magnitude of the reflected power and reflection coefficient measured at the negative zero crossing. A second cost value may be assigned with a second weight to the magnitude of the reflected power or reflection coefficient measured at the positive zero crossing. 【0096】 Furthermore, the cost function may include additional terms to improve the smoothness of the actuator profile across a fully corrected or hopping pattern, as described in equation (5) below. Total = W avg C avg + W neg C neg+ W pos C pos + W smooth C smooth (5) Here, C avg This is the average cost, W avg This is the weight assigned to the average cost. C neg This is the cost at the negative zero crossing of a periodic disturbance or bias RF signal. W neg This is the weight assigned to the cost of the negative zero crossing of the bias RF signal. C pos This is the cost at the forward zero crossing of a periodic disturbance or bias RF signal. W pos This is the weight assigned to the cost of the positive zero crossing of the bias RF signal. C smooth The cost of the smoothness evaluation index, W smooth This is the weight assigned to the cost of the smoothness evaluation metric. The evaluation index for smoothness is C. smooth It can take many forms. In one form, the smoothness metric includes an output metric or the derivative of the cost difference between consecutive bin actuations. In another form, the smoothness metric C smooth This is the sum of squared quadratic differences in the bin actuation or output evaluation index between consecutive bin actuations. 【0097】 Figures 14 and 15 show the difference in system responsiveness between the cost function without smoothing (Figure 14) and the cost function with smoothing (Figure 15). Waveform 1412 represents a periodic synchronization signal associated with a low-frequency source or bias RF source, such as RF generator 712b in Figure 7. Waveform 1414 represents the frequency of a high-frequency generator or source RF generator, such as RF generator 712a in Figure 7. Waveform 1414 represents the frequency of the source RF generator over time and represents the adjustment pattern, correction pattern, or hopping pattern of RF generator 712a. Figure 15 shows waveforms similar to those described for Figure 14, where waveform 1512 represents the synchronization signal associated with bias RF generator 712b in Figure 7, and waveform 1514 represents the actual RF frequency of source RF generator 712a in Figure 7. Waveform 1514 shows a correction or hopping pattern used by a disturbance cancellation system approach to minimize the effects of IMD. As can be seen by comparing Figures 14 and 15, waveform 1514 has a smoother appearance than waveform 1414. With respect to both Figures 14 and 15, the reflected powers 1418 and 1518 are generally similar. However, the additional smoothness in waveform 1514, obtained by applying the smoothing aspect to the cost function, makes the actuation profile smoother. Such smoothness in the hopping profile increases uniformity in the customer process. 【0098】 Figure 16 shows an extended block diagram of an RF generator, such as the RF generator 712a in Figure 7, in which the controller 1620a includes an amplitude parameter control section 1636. The parameter control section 1636 includes a regeneration module 1640, a parameter adjustment module 1642, and an update module 1644. Each module 1640, 1642, and 1644 can be implemented comprehensively or individually as a process, processor, module, or submodule. Furthermore, each module 1640, 1642, and 1644 can be implemented as one of the various components described below in relation to the module. The regeneration module 1640 monitors trigger events or signals to synchronize with the application of parameter correction, adjustment, or offset to the RF signal f1. Parameter adjustment may include frequency correction, adjustment, or offset in the frequency hopping pattern described above. The correction, adjustment, or offset corresponds to n bins. When the regeneration module 1640 detects a trigger event or signal, it begins applying parameter adjustments or offsets to the RF signal f1. The regeneration module 1640 works in cooperation with the parameter adjustment module 1642. The parameter adjustment module 1642 provides the parameter adjustments to the update module 1644, which then adjusts the application of the parameter adjustments or offsets to the RF signal f1. Alternatively, the parameter adjustments may be one or more electrical parameters, such as frequency, power, amplitude, phase, impedance matching network settings, etc. 【0099】 In various embodiments, the parameter tuning module 1642 may be implemented as a lookup table (LUT). Parameter tuning is determined, for example, according to timing or synchronization with respect to a trigger event or signal. Given the periodic nature of the bias RF signal f2 in Figure 7 and the predicted periodic impedance fluctuations that occur in response to the application of the RF signal f2 to the load 732, the LUT for tuning or offsetting the RF signal f1 is determined as described above with respect to Figure 13. The parameter tuning, offset, or hop added to the RF signal f1 is generated to match the dynamic effect on the load 732 introduced by the RF generator 12b, improve efficiency through selective and coordinated frequency tuning by the RF source generator 1612a, and at least partially offset the IMD induced by the periodic bias signal. In various embodiments, the LUT may be predetermined and static during operation, or it may be dynamically tuned by an update process, for example by an update module 1644 that implements the ILC approach described above. In various other embodiments, parameter tuning may be determined dynamically. 【0100】 Figure 17 shows the control module 1710. The control module 1710 combines various components from Figures 2-16. The control module 1710 may include a power generation module 1712, an impedance matching module 1714, a parameter control section 1716, and an iterative learning control section 1718. The parameter control section 1712 includes a regeneration module 1720, a parameter adjustment module 1722, and a parameter update module 1724. The iterative learning control section 1718 includes a perturbation module 1730, a cost module 1732, a gradient module 1734, and an actuator pattern update module 1736. In various embodiments, the control module 1710 includes one or more processors that execute code associated with the module sections or modules 1712, 1714, 1716, 1718, 1720, 1722, 1724, 1730, 1732, 1734, and 1736. The operation of the module section or modules 1712, 1714, 1716, 1718, 1720, 1722, 1724, 1730, 1732, 1734, and 1736 is described below in relation to the method shown in Figure 18. 【0101】 For a more detailed structure of the controllers 720a, 720b, 720', and 1612a in Figures 7 and 16, please refer to the flowchart in Figure 18 shown below and the definition of the term "module" shown below. The systems disclosed herein can be operated using a number of methods, examples, and various control system methods shown in Figure 18. The following operations are mainly described with respect to the embodiments in Figures 12, 13, and 16, but these operations can be easily modified to be applied to other embodiments of this disclosure. The following operations are shown and mainly described as being performed sequentially, but one or more of the following operations may be performed while one or more of the other operations are being performed. 【0102】 Figure 18 shows the flowchart 1810 of the IMD mitigation system described above. Control begins in block 1812, where various parameters are initialized. Control proceeds to block 1814, which monitors trigger events. A trigger event can be any event that allows for parameter adjustment, compensation, or hopping pattern to be suitably matched to the RF signal f1 output by the RF generator 1612a. Block 1814 continues to monitor whether a trigger event has occurred and loops back in a standby state until such an event occurs. Upon detecting a trigger event, control proceeds to block 1816, which begins regenerating a parameter compensation pattern synchronized with the occurrence of the trigger event. 【0103】 When playback begins, control proceeds to block 1818. In block 1818, parameter adjustments are obtained from block A 1824. The parameter adjustments that form a correction pattern are determined in various embodiments by predicted impedance fluctuations referencing events such as the sequence of RF signals output from bias RF generator 712b in Figure 7. Once the parameter adjustments or corrections are obtained, typically with respect to a trigger event, control proceeds to block 1820, where the parameter adjustments are applied, for example, by applying the parameter adjustments or offsets in the pattern to the RF signal output from RF generator 1612a. One or more adjustments or corrections may include frequencies. Control proceeds to block 1826, returning to control to monitor the next trigger. 【0104】 Figure 18 includes block 1824, which invokes the iterative learning control flowchart of Figure 12. Block 1824 is simulated to show that a parameter compensation pattern can be executed before the occurrence of a trigger event, as indicated by the connection to block 1812. The parameter adjustment pattern may remain fixed until updated. Alternatively, the parameter adjustment pattern may be updated dynamically or continuously in background operation, as indicated by the dotted line connection to block 1818. 【0105】 In various embodiments, the trigger event, as described with respect to block 1814, is intended to synchronize the bias RF generator 712b with the source RF generator 712a or 1612a or to allow appropriate parameter adjustments to the bias RF signal, thereby minimizing impedance fluctuations. Synchronization between RF generators 712a or 1612a and 712b can be achieved using control signals 730 or 730', which can provide a synchronization pulse or replicate the RF signal output from RF generator 712b. In various other embodiments, synchronization with RF generator 712b can be achieved without direct connections such as control signals 730 or 730' or other direct connections between RF generators 712a or 1612a and 712b. 【0106】 Synchronization without direct connection can be achieved by analyzing impedance fluctuations and phase-locking the signal representing these impedance fluctuations. For example, a signal representing impedance fluctuations can be generated by analyzing the signals X and Y output from sensors 716a or 1616a. This signal can provide an appropriate trigger event. The signal representing impedance fluctuations can be created by performing a Fast Fourier Transform (FFT) on the impedance fluctuations. In this configuration, the source RF generator 712a or 1612a can effectively operate as a standalone unit without connection to the bias RF generator 712b. 【0107】 The trigger events described in the various embodiments above are typically related to the periodicity of the trigger events. For example, the control signal received from the bias RF generator 712b, the output control signal 730 or 730' may be periodically repeated by the RF signal output from the RF generator 712b. Similarly, the signal exhibiting the impedance fluctuations described above may also have periodicity. 【0108】 In various embodiments, the required gradient information can be predicted using a changing perturbation pattern. As a non-limiting example, bins can be grouped, as shown in sections 1124 and 1126 of Figure 11, and the bins in the group can be perturbed simultaneously to identify local gradients. In various other embodiments, the amplitude of the perturbation signal can be adjusted as a function of the magnitude of the cost metric; that is, as the cost metric approaches zero, the amplitude of the perturbation can be reduced accordingly. 【0109】 In various other embodiments, the number of parameters that need to be optimized can be reduced by using alternating basis functions. That is, with respect to Figures 14 and 15, waveforms 1414 and 1514 can be selected as correction patterns, respectively. Rather than perturbing each bin individually to determine the local gradient and learning independent actuator values ​​for each bin of the correction or hopping pattern, a predetermined adjustment or hopping pattern can be applied, and DC offset and scaling factors can be used to adjust the hopping pattern. In various other embodiments, the shape of the adjustment or hopping pattern may be substantially constant as the operating conditions change. When using a predetermined hopping pattern and varying the DC offset to scale the hopping profile or correction profile, the variations in scaling of the DC offset and hopping profile can be determined using the approach described in Figures 12 and 13. In various other embodiments, additional basis vectors orthogonal to and mutually orthogonal to the DC offset and orthogonal initial hopping pattern or adjustment pattern and the DC shift and initial hopping pattern allow for capturing finer characteristics of the hopping pattern. The orthogonal basis set can be determined before initiating the manufacturing process steps in the reactor, or it can be dynamically learned as a data-dependent basis set. 【0110】 The system and method described above enable constant power transmission from an RF source in the presence of periodic load disturbances, such as a source RF generator that maintains constant power transmission in the presence of a low-frequency bias RF generator. Furthermore, the method and system described above enable a significant reduction in reflected power in the source RF generator by reducing IMD induced by a second low-frequency generator connected to the same load, such as a bias RF generator. The reduction in IMD makes it possible to provide less expensive hardware for the same transmission power output from the source RF generator. 【0111】 Furthermore, the apparatus and methods described herein enable an automated approach to determining the required actuator profile of the generator, such as a frequency hopping pattern or a correction pattern, which is driven synchronously with the period of the low-frequency bias RF generator. The systems and methods described herein also enable the maintenance of constant transmission power through a reduced reflected power profile during semiconductor manufacturing within a nonlinear reactor. This automated adjustment approach improves upon slower, manually implemented approaches that cannot be performed dynamically. 【0112】 Figure 19 shows a functional block diagram of a portion of a periodic disturbance compensation system, including actuation values ​​or signals for each bin of a 20-bin system. In Figure 19, process 1912 receives hopping offset values ​​or signals, which are stored in memory or dynamically generated, corresponding to one of the actuator values ​​or signals corresponding to each pin in the set of 20 bins. The bins and their respective actuator values ​​or signals are shown in waveform or plot 1914. Each bin has an assigned actuator value or signal. It should be understood that the number of bins may vary depending on various design considerations. However, in various non-limiting examples, a set of 20 bins is used for discussion. Each bin represents a base dimension in waveform or plot 1914 and is used to extract gradients to minimize costs. 【0113】 The hopping offset output from the waveform or plot 1914 is input to process 1912, which outputs feedback bin-synchronized readback (BSR) data to a processor or controller (not shown) that generates updates to the waveform or plot 1914. Thus, the actuator values ​​shown in the waveform or plot 1914 are dynamically generated according to the BSR data returned from process 1912. In various configurations, process 1912 represents the generation of output signals from the RF generator (as described above) to perturb the RF output power and frequency from the generator. Furthermore, in various configurations, the RF generator controlled according to the received hopping offset may have a hopping offset applied in response to the output of a second RF generator, as described above. In various configurations, the hopping offset controls the output of the RF source generator and is synchronized to the output of the RF bias generator, as described above. 【0114】 Figure 20 shows the square of the reflection coefficient (|Γ|) for the waveform or plot 2012 of an upward perturbation or the waveform or plot 2014 of a downward perturbation. 2 Figure 20 shows a plot or waveform of performance data illustrating the response of ). Thus, Figure 20 provides a display of the transmitted power corresponding to the perturbation of each of the 20 bins. In various examples, a downward or upward perturbation can cause either an increase or decrease in transmitted power. 【0115】 In various configurations, the actuator value or hopping offset corresponding to each bin shown in the waveform or plot 1914 can be updated according to equation (1). Here, the actuator value to be updated for a selected bin is determined by the current actuation value and the cost gradient resulting from perturbing the selected bin. Although equation (1) represents the update for a single bin, a set of actuator updates u can be applied to a complete set of bins as shown in equation (6). k+1 It is possible to define this. TIFF2026519931000010.tif12170 Here, u k This refers to the current set of actuator values ​​or signals. μ is the learning rate, C is the cost being measured, and the partial derivatives shown are the individual gradients resulting from perturbing the bin j, where j is an integer from 1 to n. T is the transpose of the set of values That is the case. In the examples described herein, n=20, but this will vary depending on the number of bins. 【0116】 The approach described above defines the relationship between the bin approach and the basis function approach. Furthermore, since the bins form a basic basis set as shown below, equation (6) above is a specific example of the basis function method. In the basic basis set described above, each row describes a basis vector, and "1" indicates a specific bin that is perturbed at a particular iteration. To understand that perturbing each bin is done by the approach described above, which involves successive bins (bin 1 to bin 1). 20 This requires 20 iterations in which each of the following is perturbed (up to). After perturbing a particular bin, the cost gradient for that bin is determined, and then the actuator update for that bin is determined. 【0117】 Figure 21 shows the correspondence between the normalization coefficient for each bin and the normalization coefficient in the full profile for the one-to-one correspondence between each bin. The waveform or plot 2112 shows a set of separated, uniformly spaced bins that form a 20-dimensional basic basis set. A one-to-one mapping exists from the bins in the waveform or plot 2112 to the temporal sample points along the output actuator profile shown in the waveform or plot 2114. Thus, the waveform or plot 2114 shows the waveform formed from the individual bins seen in plot 2112. 【0118】 The approach described above provides a flexible approach for adjusting individual bins. However, such an approach can be inefficient for optimizing the hopping pattern because the number of bins or dimensions is adjusted one by one, and the cost gradient and subsequent actuator updates are determined after the adjustment of each bin. Therefore, it is desirable to provide a more efficient approach for updating actuators without circulating through each dimension or bin of waveform or plot 1914 or waveform or plot 2112. 【0119】 Figure 22 shows the relationship between the normalization coefficient for each bin and the normalization coefficient in the full profile for many-to-few correspondences between each bin and basis function index. That is, the number of basis function indices is less than the number of bins. The waveform or plot 2212 is a replica of the waveform or plot 2114 and shows an unrestricted example of a compensated waveform or hopping pattern. The waveform or plot 2214 represents the waveform or plot 2212 reduced from 20 dimensions to 5 dimensions as an unrestricted example. The waveform or plot 2214 represents the normalized magnitude of the Fast Fourier Transform (FFT) of the waveform or plot 2212. To understand, the waveform or plot 2212 shows the relationship between the 20 bins in the full profile and the normalization coefficient corresponding to each of the 20 bins in the full profile. On the other hand, plot 2214 shows the relationship between the basis function indices with 5 dimensions and the normalization coefficient corresponding to each of the 5 dimensions. As seen in plot 2214, basis function indices or dimensions 1-5 correspond to the DC offset, cos(ωt), sin(ωt), cos(2ωt), and cos(2ωt), respectively. It can be seen that more or fewer basis function indices or dimensions can be determined using the FFT. Here, ω is the radian frequency of the synchronization signal, and t represents the period of one cycle of the synchronization signal. In various configurations, t is sampled to correspond to the relevant bin number. 【0120】 Certain relevance can be found when reducing the number of bins or dimensions from 20 in the full profile to fewer. According to this disclosure, each of the five basis function indices or dimensions defines the perturbed basis vector or basis function (DC offset, cos(ωt), sin(ωt), cos(2ωt), sin(2ωt)) compared to perturbing the 20 bins or dimensions in the full profile shown in the waveform or plot 2212. In various configurations, more dimensions can be used to improve accuracy which may affect efficiency, and fewer dimensions can be used to improve efficiency which may affect accuracy. The basis vector or basis function can generally be described as having (1+2n) dimensions, including DC offset, cos(ωt), sin(ωt), cos(2ωt), sin(2ωt), ..., cos(nωt), and sin(nωt). In various configurations, the DC offset dimension may be omitted. In various other configurations, the DC offset dimension may be determined using a separate process, such as the process in a conventional frequency adjustment loop. Furthermore, as shown in the waveform or plot 2214, each dimension, basis vector, or basis function is scaled or weighted by normalization coefficients according to the FFT. 【0121】 Figure 23 shows a functional block diagram of the periodic disturbance compensation system 2310 arranged in this disclosure. The functional block diagram of Figure 23 includes parts of one or more of Figures 7, 13, and 16. The periodic disturbance compensation system 2310 includes a control module 2320 that outputs perturbation and adjustment signals to an output generator module 2322. The output generator module 2322 includes a profile generator module 2324. The profile generator module 2324 stores coefficients such as coefficients referenced in a waveform or plot 2214. These coefficients are used to scale basis functions or basis vectors. Referring to the 5-dimensional example in Figure 22, the basis functions or basis vectors are DC offset, cos(ωt), sin(ωt), cos(2ωt), and sin(2ωt), as described above. The basis functions or basis vectors work together to define an output profile 2326 that defines the offset for each bin. 【0122】 Each basis function or basis vector defines an offset value or signal for each bin of the profile. Compared to the perturbation approach using the basic basis set described above, which does not perturb a single bin and process 20 iterations of perturbing each of the 20 dimensions of the basic basis set, each coefficient of the basis function or basis vector of the 5-dimensional basis is perturbed. The product of the perturbed coefficient and its associated basis function or basis vector is used to perturb each of the 20 bins in each iteration. Each basis function or basis vector, scaled by its associated perturbation coefficient, defines a perturbation that affects each of the 20 bins, and as a result, each of the 20 bins is perturbed through each of the 5 iterations of perturbing the basis function or basis vector by scaling with its associated perturbation coefficient. 【0123】 The output profile 2326 is input to process 2328. Process 2328 controls the output of the RF generator. In various configurations, the normalization coefficients from the waveform or plot stored in or generated by the profile generator module 2324 are used for the inverse FFT (FFT). -1 The output profile 2326 is generated by the following conversion. The output profile 2326 controls the output of the first RF generator. In various configurations, the output profile 2326 controls one or more parameters of the first RF generator, which may be frequency, power, or phase. In various configurations, this one or more parameter is responsive to input from a second RF generator. In various configurations, this one or more parameter adjusts the output frequency of the source RF generator in response to input from a bias RF generator. 【0124】 Various parameters of process 2328 may be monitored and output to cost module 2330. Cost module 2320 determines the cost of one or more monitored parameters. In various configurations, one or more output evaluation metrics of interest are determined as described above. In various configurations, one or more evaluation metrics of interest may be determined according to the monitored parameters and may be one or more of the average reflected power, transmitted power, or average magnitude of the reflection coefficient over the operating period of a bias generator such as RF generator 712b in Figure 7. One or more evaluation metrics of interest is also called a cost function, which, when optimized, indicates when a good tuning pattern has been determined. Cost module 2330 outputs the cost to gradient module 2332, which determines the gradient or change of cost in response to perturbations of one or more selected parameters. Gradient module 2332 outputs a gradient value or signal to control module 2320, which determines perturbation and tuning signals in response to the gradient value or signal received from gradient module 2332. The determination of perturbation and regulating signals is carried out as described above. 【0125】 By using a less dimensional basis space, a considerable increase in tuning speed can be achieved because, rather than perturbing individual bins, groups of bins are perturbed according to a sinusoidal profile defined by the FFT. In various configurations, different basis coefficients corresponding to a particular dimension can be updated at different speeds. In an unrestricted example, in various configurations, the DC offset component can be tuned with each iteration of a controller such as control module 2320. Other basis components can be updated every other iteration of control module 2320. In various other configurations, the DC offset component and the basic (n=1) sine and cosine pairs can be tuned sequentially (DC offset, cos(ωt), and sin(ωt)) in consecutive iterations, for example, in three consecutive iterations as an unrestricted example. At a slower speed, for example, every four iterations as an unrestricted example, higher harmonic sine and cosine components (cos(2ωt) and sin(2ωt)) can be mixed in. Using this approach, the update speed can be a function of the measurement sensitivity of the cost function along the basis dimension. A more sensitive dimension can be adjusted more frequently. 【0126】 Furthermore, in various configurations, various individual basis components can be dynamically adjusted or kept fixed. As a non-restrictive example, the higher harmonic components of the Fourier basis may remain fixed until the cost function falls below a threshold. After the cost function falls below a minimum threshold, the higher harmonic components of the Fourier basis can be adjusted. In such configurations, a coarse adjustment is established while fixing the individual harmonic basis components, and then a fine adjustment is applied by adjusting the higher harmonic components of the Fourier basis. In even more configurations, a gradient descent along a single dimension can be maintained for each iteration. In such configurations, the gradient is established by perturbing the normalization coefficient for one of the basis dimensions, rather than updating the composite gradient encompassing all basis dimensions, and updating the normalization coefficient for that particular basis for each iteration. The basis dimensions for each iteration can be randomly selected in a probabilistic mode or cycle through in a predetermined order. Furthermore, by using orthogonal basis sets such as Fourier bases, Legendre (polynomial) bases, or basic bases, the coefficients for each basis dimension can be updated independently of each other. Moreover, in various configurations, each of the various configurations described herein can be implemented individually or in combination, to the extent possible. 【0127】 Figures 22 and 23 illustrate a generalized approach that uses predetermined basis functions such as sine and cosine to reduce the number of dimensions and generate output profiles, compared to relying on a basic basis set. In various other configurations, data may be collected and analyzed to determine how the process responds. The process response may be used to define data-dependent basis functions or basis vectors. Figure 24 shows the relationship between the learning hopping pattern and the singular values ​​of the frequency offset matrix obtained using data analysis. In Figure 24, the waveform or plot 2412 shows a series of learning hopping patterns following the occurrence of predefined events in a power transmission system. In Figure 24, the waveform or plot 2414 is obtained by Singular Value Decomposition (SVD) analysis. The horizontal axis of the waveform or plot 2414 corresponds to the number of dimensions, and the vertical axis of the waveform or plot 2414 corresponds to the relative variation in the data captured by the added basis dimension. In non-restrictive examples of waveforms or plots 2414, the first five singular values ​​may be used based on the relative variation of the waveform or plot 2414. These five dimensions can then be used to reconstruct or predict the waveform or plot 2412 using fewer input dimensions than the original 20 dimensions (bins) of the waveform or plot 2412. In various configurations, Principal Component Analysis (PCA) may be used instead of SVD to influence the data analysis. Note that when using either SVD or PCA, the coefficients for each basis dimension define an orthogonal basis set and can therefore be updated independently of other basis dimensions. 【0128】 The waveform or plot 2414 shows that the largest variations occur within the first five dimensions. From the waveform or plot 2414, for example, from dimensions 1-5 of the waveform or plot 2414, a set of key basis vectors can be generated. By adding the weighted sum of the selected key basis vectors, an output actuator profile can be generated. As an unrestricted example, the weighted sum of the key basis factors added together may produce an output profile similar to the output profile of the waveform or plot 2212 in Figure 22. Thus, by using a data analysis approach and selecting key basis factors based on relative variations, an output file similar to the output profile generated using FFT can be obtained. 【0129】 Figures 25A–25E show individual basis vectors for an embodiment of the five-dimensional basis vectors of a periodic disturbance compensation system arranged in this disclosure. As a non-limiting example, Figures 25A–25E may be obtained from relative fluctuations in waveforms or plots 2414. Waveform or plot 2510A corresponds to a first basis vector or first dimension (similar to a DC offset), and waveform or plot 2510B corresponds to a second basis factor or second dimension. Similarly, waveform or plot 2510C corresponds to a third basis vector or third dimension, waveform or plot 2510D corresponds to a fourth basis vector or fourth dimension, and waveform or plot 2510E corresponds to a fifth basis factor or fifth dimension. 【0130】 In the configurations of Figures 24 and 25A–25E, the singular vectors in Figures 25A–25B each form an orthonormal basis set. Hopping patterns can be learned as linear combinations of basis vectors. The basis sets are ordered based on changes in the RF generator configuration and the capture of variations between hopping patterns across data acquisition scenarios. In various configurations, subsets of basis vectors may be learned to improve convergence in order to capture selected properties of the hopping pattern. Data-dependent basis sets assume that the data used to derive the basis sets encompass all predicted variations. In various configurations, heuristics may be used to keep basis vector 1 constant in order to apply mean frequency tuning. In various configurations, basis vector 2 is the first singular vector as it captures the primary form of the hopping pattern. Basis vectors 3–5 in Figures 25C–25E provide additional fine-tuning beyond the effects of basis vectors 1 and 2. 【0131】 In various configurations, data-driven basis vectors can be developed for different customer recipes in the plasma manufacturing process. Recipe-specific basis vectors can be developed and applied as plasma manufacturing recipe variations. Alternatively, or in addition to these, data-driven basis vectors can be synthesized into an orthogonal library and used in various recipe steps. In further various configurations, the library of basis vectors can be derived and collected across multiple customer tools to facilitate tool matching. Furthermore, in various configurations, one of the derived basis vectors can realize a complete solution profile from the execution of a preceding recipe in a recipe step, and in the future, similar recipe steps can rely on the saved complete solution from the preceding execution. 【0132】 In various configurations, options for general-purpose basis functions may include sinusoidal functions, spline functions, polynomial functions, exponential functions, and radial basis functions. Each of the above functions may be constructed as an orthogonal function. Furthermore, in various configurations, separate learning rates and sensor amplitudes may be established for each basis dimension, either individually or in combination. In even more various configurations, the basis functions may have different temporal granularities, such as in non-restrictive examples where several bins may be grouped together to move together within a region of the actuator profile. In other various configurations, a hybrid of derived basis functions, such as data-driven basis functions, and general-purpose basis functions, such as FFT or Legendre basis functions, may be used to define the hopping pattern. In other various configurations, the basis functions may be dynamically changed, such as in non-restrictive examples where a Fourier basis function with two harmonics may be used for fast fine-tuning. The additional harmonic dimension of the Fourier function may then be used to fine-tune the hopping pattern. The transition between the coarse and fine adjustments described above may be based on the value of the cost function relative to the number of iterations or a threshold, or a combination of the two. In various other configurations, different cost functions may be used for each basis dimension. As a non-restrictive example, the DC offset basis function may be adjusted with respect to the average reflected power, while the sinusoidal component of the Fourier part of the basis function may vary according to the positive and negative half-cycles and the reflected power envelope. In some configurations of this approach, the cost function may be expressed by equation (5). 【0133】 The above description is purely descriptive and is not intended to limit the Disclosure, its application, or its use. The broad teachings of the Disclosure can be implemented in various forms. Therefore, although the Disclosure includes specific examples, the essential scope of the Disclosure should not be limited, as other variations will become apparent upon consideration of the drawings, specification, and the claims below. It should be understood that one or more steps in the Method may be performed in different orders (or simultaneously) without altering the principles of the Disclosure. Furthermore, although each embodiment is described above as having certain features, one or more of these features described in relation to any embodiment of the Disclosure may be implemented in any feature of any other embodiment, and / or combined with such features, even if such combinations are not explicitly stated. In other words, the embodiments described are not mutually exclusive, and substituting one or more embodiments with each other falls within the scope of the Disclosure. 【0134】 Spatial and functional relationships between elements (e.g., between modules, between circuit elements, between semiconductor layers, etc.) are described using a variety of elements, including “connected,” “engaged,” “linked,” “adjacent,” “next to,” “above,” “below,” and “located.” Unless explicitly stated to be “direct,” where a relationship between a first element and a second element is described in the above disclosure, that relationship may be a direct relationship in which there are no other intervening elements between the first and second elements, or it may be an indirect relationship in which there are one or more intervening elements (spatially or functionally) between the first and second elements. 【0135】 The phrase "at least one of A, B, and C" should be interpreted as meaning a non-exclusive OR (A OR B OR C), and not as meaning "at least one of A, at least one of B, and at least one of C." The term "subset" does not necessarily require a proper subset. In other words, the first subset of the first set may have the same extent (equal) to the first set. 【0136】 In drawings, the direction of an arrow, indicated by its tip, generally represents the flow of information being described (e.g., data or instructions). For example, if elements A and B exchange various types of information, and the information transmitted from element A to element B is relevant to its description, the arrow may point from element A to element B. This unidirectional arrow does not imply that other information is not transmitted from element B to element A. Furthermore, with respect to information transmitted from element A to element B, element B may transmit a request for or acknowledgment of receipt of that information to element A. 【0137】 In this application, the terms “module” or “controller” are interchangeable with the term “circuit,” including the following definitions. The term “module” means, part of, or may include, a combination of some or all of the above, such as an application-specific integrated circuit (ASIC), a digital, analog, or analog / digital mixed discrete circuit, a digital, analog, or analog / digital mixed integrated circuit, a combinational logic circuit, a field-programmable gate array (FPGA), a processor circuit that executes code (shared, dedicated, or grouped), a memory circuit that stores code executed by the processor circuit (shared, dedicated, or grouped), other suitable hardware components that provide the described functionality, or a system-on-a-chip. 【0138】 A module may include one or more interface circuits. In some cases, the (one or more) interface circuits may implement a wired or wireless interface connecting to a local area network (LAN) or a wireless personal area network (WPAN). Examples of LANs include IEEE standard 802.11-2016 (also known as the Wi-Fi wireless networking standard) and IEEE standard 802.3-2015 (also known as the Ethernet wired networking standard). Examples of WPANs include IEEE standard 802.15.4 (including the ZIGBEE standard by the ZigBee Alliance) and Bluetooth wireless networking standards by the Bluetooth Special Interest Group (SIG) (including Bluetooth SIG core specification versions 3.0, 4.0, 4.1, 4.2, 5.0, and 5.1). 【0139】 Modules may communicate with other modules using (one or more) interface circuits. While modules may be shown in this disclosure as communicating logically and directly with other modules, in various embodiments modules may actually communicate via a communication system. The communication system includes physical and / or virtual networking equipment such as hubs, switches, routers, and gateways. In some embodiments, the communication system is connected to or traversed by a wide area network (WAN), such as the Internet. For example, the communication system may include multiple LANs connected to each other over the Internet or point-to-point dedicated lines using technologies including Multiprotocol Label Switching (MPLS) and Virtual Private Networks (VPNs). 【0140】 In various embodiments, the functionality of a module may be distributed among multiple modules connected via a communication system. For example, multiple modules may implement the same functionality distributed by a load balancing system. In further examples, the functionality of a module may be divided between a server module (also known as a remote or cloud) and a client (or user) module. For example, a client module may include a native or web application running on a client device and capable of network communication with the server module. 【0141】 Some or all of the hardware features of a module may be defined using a hardware description language such as IEEE standard 1364-2005 (commonly known as "Verilog") and IEEE standard 1076-2008 (commonly known as "VHDL"). Hardware description languages ​​may be used to manufacture and / or program hardware circuits. In some embodiments, some or all of the module's features may be defined by a language such as IEEE 1666-2005 (commonly known as "SystemC"), which encompasses both code and hardware description as described below. 【0142】 The term "code" as used above may include software, firmware, and / or microcode, and may mean programs, routines, functions, classes, data structures, and / or objects. The term "shared processor circuit" encompasses a single processor circuit that executes some or all of the code from multiple modules. The term "group processor circuit" encompasses a processor circuit, in combination with additional processor circuits, that executes some or all of the code from one or more modules. References to multiple processor circuits include multiple processor circuits on separate dies, multiple processor circuits on a single die, multiple cores in a single processor circuit, multiple threads in a single processor circuit, or a combination of the above. The term "shared memory circuit" encompasses a single memory circuit that stores some or all of the code from multiple modules. The term "group memory circuit" encompasses a memory circuit, in combination with additional memory, that stores some or all of the code from one or more modules. 【0143】 The term "memory circuit" is a subset of the term "computer-readable medium." As used herein, the term "computer-readable medium" does not include transient electrical or electromagnetic signals propagating through a medium (e.g., on a carrier wave). Therefore, the term "computer-readable medium" can be understood as a tangible, non-transient medium. Non-exclusive examples of non-transient computer-readable mediums include non-volatile memory circuits (such as flash memory circuits, erasable programmable read-only memory circuits, or mask read-only memory circuits), volatile memory circuits (such as static random-access memory circuits or dynamic random-access memory circuits), magnetic recording media (such as analog or digital magnetic tape or hard disk drives), and optical recording media (such as CDs, DVDs, or Blu-ray discs). 【0144】 The apparatus and methods described in this application can be partially or completely implemented by a dedicated computer generated by configuring a general-purpose computer to perform one or more specific functions embodied in a computer program. The functional blocks and flowchart elements described above function as software specifications, which can be converted into a computer program by the routine work of a skilled technician or programmer. 【0145】 A computer program includes instructions that can be executed by a processor, stored on at least one non-transient computer-readable medium. A computer program may include, and may depend on, stored data. A computer program may encompass a basic input / output system (BIOS) that interacts with the hardware of a dedicated computer, device drivers that interact with specific devices of the dedicated computer, one or more operating systems, user applications, background services, background applications, and the like. 【0146】 Computer programs may include (i) parsable descriptive text such as HTML (Hypertext Markup Language), XML (Extensible Markup Language), or JSON (JavaScript Object Notation), (ii) assembly code, (iii) object code generated from source code by a compiler, (iv) source code executed by an interpreter, and (v) source code compiled and executed by a just-in-time compiler. As mere examples, source code may be written using syntax from languages ​​including C, C++, C#, Objective C, Swift, Haskell, Go, SQL, R, Lisp, Java®, Fortran, Perl, Pascal, Curl, OCaml, JavaScript (Registered), HTML5 (Hypertext Markup Language, 5th Revision), Ada, ASP (Active Server Pages), PHP (Hypertext Preprocessor), Scala, Eiffel, Smalltalk, Erlang, Ruby, Flash®, Visual Basic®, Lua, MATLAB, SIMULINK, and Python®.

Claims

[Claim 1] A controller for a radio frequency generator, The RF power controller is connected to an RF power supply, and the RF power controller is configured to generate control signals that change an RF output signal having multiple bins from the RF power supply, and the RF power controller is configured to adjust at least one parameter that determines the characteristics of the RF output signal in response to a synchronization signal. The parameters are perturbed according to a hopping pattern associated with the plurality of bins, and the parameters are adjusted by minimizing or maximizing a cost function in response to the perturbation of at least one parameter by the hopping pattern. The hopping pattern is adjusted by a basis set having multiple dimensions, where the number of dimensions is less than the number of bins. controller. [Claim 2] The RF power controller iterates through the dimension to adjust the hopping pattern with each iteration, according to claim 1. [Claim 3] The controller according to claim 2, wherein two or more of the plurality of bins are adjusted during each iteration. [Claim 4] The controller according to claim 1, wherein two or more of the plurality of bins are adjusted during each iteration. [Claim 5] The controller according to claim 1, wherein the hopping pattern can be adjusted by applying either an offset or a scaling factor to the hopping pattern. [Claim 6] The controller according to claim 1, wherein the perturbation of at least one parameter for the plurality of bins determines the hopping pattern. [Claim 7] The controller according to claim 1, wherein the basis set includes at least one of sinusoidal functions, spline functions, polynomial functions, exponential functions, and radial basis functions. [Claim 8] The controller according to claim 1, wherein the first dimension of the basis set is orthogonal to the second dimension of the basis set. [Claim 9] The controller according to claim 1, wherein each bin has a width, and the width of a selected bin may be the same as or different from the width of the other bins. [Claim 10] The controller according to claim 1, wherein the plurality of dimensions of the basis set are determined according to the Fast Fourier Transform (FFT) of the hopping pattern. [Claim 11] The controller according to claim 1, wherein the plurality of dimensions of the basis set are determined from data analysis. [Claim 12] The controller according to claim 1, wherein the plurality of dimensions of the basis set are determined according to singular value decomposition (SVD) or principal component analysis (PCA). [Claim 13] The RF power controller adjusts the parameters according to the synchronization signal, the synchronization signal indicates the relative position of the external RF output signal, according to claim 1. [Claim 14] The parameter is either a frequency or a frequency offset, and the RF power controller includes a plurality of frequencies that are introduced into the RF output signal in a predetermined order and timing according to the synchronization signal, or The parameter is either a reactance or a reactance offset, and includes a plurality of reactances controlled by the RF power controller in a predetermined order and timing according to the synchronization signal, wherein the reactance is at least one of capacitance or inductance. The controller according to claim 1. [Claim 15] The controller according to claim 1, wherein the hopping pattern can be adjusted by applying either an offset or a scaling factor to the hopping pattern, the offset is adjusted by perturbing the offset to determine its effect on a cost function, generating a composite gradient according to the cost function, and adjusting the offset by either minimizing or maximizing the cost function. [Claim 16] The controller according to claim 15, wherein the scaling factor is adjusted by perturbing the current scaling factor to determine its effect on the cost function, generating a composite gradient according to the cost function, and adjusting the scaling factor by either minimizing or maximizing the cost function. [Claim 17] The controller according to claim 1, wherein the scaling factor is adjusted by perturbing the current scaling factor to determine its effect on the cost function, generating a composite gradient according to the cost function, adjusting the scaling factor by either minimizing or maximizing the cost function, and adjusting the hopping pattern by applying the scaling factor to the hopping pattern. [Claim 18] A non-transient computer-readable medium for storing instructions, wherein the instructions are: A first power supply is controlled to output a first output signal having multiple bins to the load. To generate a control signal that changes the first output signal from the power supply in order to adjust at least one parameter that determines the characteristics of the first output signal in response to a synchronization signal. Includes, The parameters are perturbed according to a hopping pattern associated with the plurality of bins, and the parameters are adjusted by minimizing or maximizing a cost function in response to the perturbation of at least one parameter by the hopping pattern. The hopping pattern can be adjusted by applying either an offset or a scaling factor to the hopping pattern, or The hopping pattern is adjusted by a basis set having multiple dimensions, where the number of dimensions is less than or equal to the number of bins. Non-transient computer-readable media. [Claim 19] The non-transient computer-readable medium according to claim 18, wherein the instruction is repeated through the dimension to adjust the hopping pattern with each iteration. [Claim 20] The non-transient computer-readable medium according to claim 19, wherein two or more of the plurality of bins are adjusted during each iteration. [Claim 21] The non-transient computer-readable medium according to claim 18, wherein two or more of the plurality of bins are adjusted during each iteration. [Claim 22] A non-transient computer-readable medium according to claim 18, wherein the perturbation of at least one parameter for the plurality of bins determines the hopping pattern. [Claim 23] The non-transient computer-readable medium according to claim 21, wherein the basis set has basis functions including at least one of sinusoidal functions, spline functions, polynomial functions, exponential functions, and radial basis functions. [Claim 24] The non-transient computer-readable medium according to claim 18, wherein each bin has a width, and the width of a selected bin may be the same as or different from the width of the other bins. [Claim 25] The non-transient computer-readable medium according to claim 18, wherein the instruction includes determining the plurality of dimensions of the basis set according to the Fast Fourier Transform (FFT) of the hopping pattern. [Claim 26] The non-transient computer-readable medium according to claim 18, wherein the instruction includes determining the plurality of dimensions of the basis set using data analysis. [Claim 27] The non-transient computer-readable medium according to claim 18, wherein the instruction includes determining the plurality of dimensions according to singular value decomposition (SVD) or principal component analysis (PCA). [Claim 28] The non-transient computer-readable medium according to claim 18, wherein the instruction includes adjusting the parameter according to the synchronization signal, the synchronization signal indicating the relative position of an external output signal. [Claim 29] The parameter is either a frequency or a frequency offset, and includes a plurality of frequencies introduced into the output signal in a predetermined order and timing according to the synchronization signal, or The parameter is either a reactance or a reactance offset, and includes a plurality of reactances introduced in a predetermined order and timing according to the synchronization signal, wherein the reactance is at least one of capacitance or inductance. The non-transient computer-readable medium according to claim 18. [Claim 30] The non-transient computer-readable medium according to claim 18, wherein the instruction includes adjusting the hopping pattern by applying either an offset or a scaling factor to the hopping pattern, the offset being adjusted by perturbing the offset to determine its effect on a cost function, generating a composite gradient according to the cost function, and adjusting the basis set by either minimizing or maximizing the cost function. [Claim 31] The non-transient computer-readable medium according to claim 18, wherein the instruction includes perturbing the current scaling factor to determine its effect on a cost function, generating a composite gradient according to the cost function, and adjusting the scaling factor by adjusting the scaling factor by either minimizing or maximizing the cost function. [Claim 32] A power supply that generates an output signal having variable amplitude and frequency and multiple bins, A power controller connected to the power supply, configured to generate a control signal that changes the output signal, and configured to adjust at least one parameter that determines the characteristics of the output signal in response to a synchronization signal. Equipped with, The parameters are perturbed according to a hopping pattern associated with the plurality of bins, and the parameters are adjusted by minimizing or maximizing a cost function in response to the perturbation of at least one parameter by the hopping pattern. The hopping pattern is adjusted by a basis set having multiple dimensions, where the number of dimensions is less than the number of bins. Power generator system. [Claim 33] The power generator system according to claim 32, wherein the power controller repeats through the dimension to adjust the hopping pattern with each iteration. [Claim 34] The power generator system according to claim 33, wherein two or more of the plurality of bins are adjusted during each iteration. [Claim 35] The power generator system according to claim 32, wherein two or more of the plurality of bins are adjusted during each iteration. [Claim 36] The power generator system according to claim 32, wherein the basis set has basis functions that include at least one of sinusoidal functions, spline functions, polynomial functions, exponential functions, and radial basis functions. [Claim 37] The power generator system according to claim 32, wherein the first dimension of the basis set is orthogonal to the second dimension of the basis set. [Claim 38] The power generator system according to claim 33, wherein the multiple dimensions of the basis set are determined according to the fast Fourier transform (FFT) of the hopping pattern. [Claim 39] The power generator system according to claim 32, wherein the plurality of dimensions of the basis set are determined from data analysis. [Claim 40] The power generator system according to claim 32, wherein the plurality of dimensions of the basis set are determined according to singular value decomposition (SVD) or principal component analysis (PCA). [Claim 41] The power generator system according to claim 32, wherein the power controller adjusts the parameters according to the synchronization signal, and the synchronization signal indicates the relative position of the external output signal.

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