Design method of plug-in feed-forward odd repetitive controller and plug-in feed-forward odd repetitive controller

Abstract

The invention discloses a design method of a plug-in feed-forward odd repetition controller and the controller. The design method comprises the following steps: S1, determining a transfer function P (s) of a controlled object; s2, constructing a plug-in feed-forward odd repetition controller, and calculating an error transfer function E (z) of a plug-in feed-forward odd repetition control system so as to obtain a stable condition of the control system; s3, designing plug-in feed-forward odd-number repetition control parameters, not only enabling all roots of [1 + P (z) Gpi (z)] = 0 to be in a unit circle, but also meeting # imgabs0 # so as to ensure that a plug-in feed-forward odd-number repetition control system is stable; according to the invention, the plug-in repetitive controller has higher gain and wider harmonic broadband under the odd harmonic frequency through the plug-in feed-forward odd repetitive control technology, so that the odd harmonic current in the single-phase inverter can be effectively suppressed.

Description

Technical Field

[0001] The invention relates to the technical field of industrial control, and more particularly to a design method for an insertion-type feedforward odd-order repetitive controller and a controller thereof. Background Art

[0002] With the rapid development of renewable energy, including the widespread application of distributed energy systems such as solar and wind power, the use of grid-connected inverters in power systems is becoming increasingly popular. However, the harmonic currents generated by the inverter may have serious effects on the power grid and surrounding equipment, including grid voltage distortion, equipment failure and even damage. Therefore, it is an urgent problem to study how to effectively suppress the current harmonics output by the grid-connected inverter. Current research focuses on developing new control strategies and filtering technologies to reduce the harmonic content of the inverter current, improve the current quality of the power grid and the stability of the system, thereby promoting the effective integration of clean energy and traditional power grids.

[0003] Repetitive control (RC) is widely used in inverter current controllers because it can accurately track fundamental signals and eliminate multi-frequency harmonic signals. However, due to the inherent fundamental cycle delay of the RC internal model, its transient response is relatively slow; in order to improve the dynamic response speed of RC, a method combining RC and proportional-integral (PI) control is usually adopted. Common repetitive controller structures include parallel structure and plug-in structure; parallel repetitive controller can improve current dynamic response, effectively suppress current harmonics, and enhance system robustness. Considering the complexity of parameter design in the parallel structure and the coupling between the outputs of the two controllers (i.e., RC and PI controllers).

[0004] In order to solve the problem of high odd harmonic content in the output current harmonics of single-phase inverters, the insertion-type odd harmonic RC control strategy is widely used to suppress these odd harmonics. However, due to the inherent delay of repetitive control (RC), the dynamic performance of PORC is limited. Moreover, the change of grid frequency will greatly reduce the control accuracy of PORC. Summary of the invention

[0005] The object of the present invention is to provide a plug-in feedforward odd-order repetitive controller design method and its controller, which can achieve higher gain and wider resonant bandwidth at fundamental frequency and odd harmonic frequencies, thereby solving the deficiencies in the above-mentioned prior art.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A plug-in feedforward odd-order repetitive controller design method comprises the following steps:

[0008] S1. Determine the transfer function P(s) of the controlled object;

[0009] S2, construct an insertion feedforward odd-order repetitive controller, the discrete transfer function G of the internal model of the insertion feedforward odd-order repetitive controller forc (z) is:

[0010]

[0011] Where S(z) is a low-pass filter that attenuates high-frequency harmonics, z m is the phase advance compensation; k r is the repetitive control gain; Q(z) is the internal model coefficient, a constant between 0 and 1;

[0012] The steady-state error E(z) of the system of the plug-in feedforward odd-order repetitive controller is:

[0013]

[0014] In the above formula, G pi (z)P(z) is the open-loop transfer function, where P(z) is the controlled object and P(z) is converted from P(s) using the zero-order hold method; G pi (z) is the PI controller; i ref (z) is the reference current; d g (z) is the harmonic disturbance current;

[0015] The characteristic polynomial of the insertion-type feedforward odd-order repetitive control system is:

[0016] 1+[G forc (z)+G pi (z)]P(z)=[1+G pi (z)P(z)][1+G forc (z)P0(z)] (3)

[0017] Where P0(z)=P(z)G pi (z) / (1+P(z)G pi (z)), P0(z) is the equivalent controlled object; and according to formula (3), (1) is substituted into (2) to obtain the steady-state error E(z);

[0018]

[0019] Wherein, S(z) is a filter; let the characteristic equation of the steady-state error E(z) be [1+P(z)G pi All roots of [z] = 0 are inside the unit circle and Make the insertion feedforward odd-order repetitive control system stable;

[0020] S3, design the insertion feedforward odd-number repetition control parameters, not only [1+P(z)G pi All roots of (z)] = 0 are inside the unit circle and also satisfy

[0021] Furthermore, the controlled object in step S1 includes: an inductor L1, an inductor L2 and a capacitor C, and the transfer function P(s) of the controlled object is:

[0022]

[0023] Among them, H ic is the capacitor current feedback coefficient.

[0024] Further, in the step S2, the i ref (z) and d g The angular frequency ω of (z) is close to ω a =2π(2a+1) / (NT s ), then a=0,1,2,…,A; when N is an even number, A=N / 2, when N is an odd number, A=(N-1) / 2; when z -N / 2 =e -jπ(2a+1) = -1, we get |z -N / 2 |=1; and |Q(z)|≤1, if the stability condition of the insertion feedforward odd-order repetitive control system is met, the following inequality must be guaranteed to hold:

[0025]

[0026] Furthermore, it is assumed that the amplitude-frequency and phase-frequency characteristics of P0(z) and S(z) in formula (4) are as follows:

[0027]

[0028] Since the phase of Q(z) is 0, combining the above equations, we get:

[0029]

[0030] Furthermore, in the formula (7) And through Euler's formula, k r >0, Therefore, formula (7) can be written as:

[0031]

[0032] The conditions for making formula (7) and formula (8) stable are:

[0033]

[0034] Furthermore, the inserted feedforward odd-number repetition control parameters in step S3 include: the open-loop transfer function P(z)G pi (z)Satisfy 10f g <f c <0.1f s , where f g is the grid frequency, f c is the cutoff frequency, f c =650Hz, H ic =10, k p =14, k i =7000, open loop basic gain T fo The gain margin is 24.6dB, the phase margin is 48°, and the open-loop basic gain T fo If it is greater than 20dB, the calculation result of the discrete transfer function of the equivalent controlled object P0(z) is as follows:

[0035]

[0036] Assume the internal model coefficient Q(z) of the plug-in feedforward odd-order repetitive control system and the low-pass filter S(z) for attenuating high-frequency harmonics; Assume Q(z) = 0.95, set the dominant odd harmonic frequency of the grid-connected inverter to within 1000Hz, S(z) is the low-pass filter for attenuating high-frequency harmonics, then the discrete expression of S(z) is:

[0037]

[0038] In the above formula, z m It is phase advance compensation;

[0039] Assume that the repetitive control gain k r ; When the phase advance link z m When m=8, the angle of γ(ω) is between 0° and 17.3°, so the minimum value of cosγ(ω) is 0.9547, then z m The maximum gain of S(z)P0(z) is 3.23dB. The maximum value of is 1.0104. In order to obtain a stable closed-loop feedback control system, set k r is 0.46;

[0040] And let

[0041] According to formula (13), we know that k r The maximum value is 0.6414.

[0042] Furthermore, the control object is an industrial device whose output voltage / current signal is composed of odd characteristic power harmonics, including a programmable AC power supply, a power converter and a servo motor.

[0043] The present invention also provides an insertion-type feedforward odd-order repetitive controller, and the controller is implemented by a design method of an insertion-type feedforward odd-order repetitive controller.

[0044] Furthermore, the control object of the controller is an industrial device whose output voltage / current signal is composed of odd characteristic power harmonics, including a programmable AC power supply, a power converter and a servo motor.

[0045] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: the present invention mainly suppresses odd harmonic currents in single-phase inverter applications through plug-in feedforward odd-order repetitive control technology, and has excellent harmonic suppression capability; the introduction of the feedforward channel also enables the PFORC to have a higher gain at odd harmonic frequencies, with excellent dynamic performance and super adaptability to changes in grid frequency.

[0046] Based on the feedforward channel, the PFORC has a wider resonance bandwidth at odd harmonic frequencies, and can provide high-quality output current even when the grid frequency fluctuates, with strong robustness.

[0047] The present invention is also applicable to all industrial facilities that require periodic signal processing capabilities, including but not limited to inverters, servo motors, steering gears and other devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0049] The following further describes the design method of the plug-in feedforward odd-order repetitive controller and the controller thereof in conjunction with the accompanying drawings;

[0050] Figure 1 It is a structural diagram of an insertion-type feedforward odd-order repetitive control system provided by the present invention;

[0051] Figure 2 is a frequency characteristic comparison diagram of the plug-in odd-order harmonic repetitive control internal model and the plug-in feedforward odd-order repetitive control internal model provided by the present invention; wherein, Figure 2 (a) is the amplitude-frequency response curve; Figure 2 (b) is the detail diagram of the amplitude-frequency response curve;

[0052] Figure 3 It is a structural diagram of a single-phase three-level grid-connected inverter in a design method based on an insertion-type feedforward odd-order repetitive controller provided by the present invention;

[0053] Figure 4 It is a structure diagram of the grid current closed-loop control of the grid-connected inverter in the design method of the plug-in feedforward odd-order repetitive controller provided by the present invention;

[0054] Figure 5 It is a block diagram of the discrete domain inner model structure in the plug-in feedforward odd-order repetitive controller provided by the present invention;

[0055] Figure 6 The present invention provides an inverter output waveform and a grid-connected current THD diagram when the lower grid frequency is 50Hz in an insertion-type feedforward odd-order repetitive control system; wherein, Figure 6 (a) is the inverter output waveform when the grid frequency is 50Hz; Figure 6 (b) is the grid-connected current THD diagram;

[0056] Figure 7 It is the inverter output waveform and grid-connected current THD diagram when the lower grid frequency is 49.6Hz and 50.4Hz in the plug-in feedforward odd-order repetitive controller design method provided by the present invention;

[0057] Figure 8 This is a waveform diagram of the inverter output when the lower reference current suddenly changes from 10A to 5A in the design method based on the insertion-type feedforward odd-order repetition technology provided by the present invention. DETAILED DESCRIPTION

[0058] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0059] In order to better understand the purpose, structure and function of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings.

[0060] The present invention selects a plug-in RC (PRC), in which the designs of the repetitive controller and the PI controller are independent of each other to ensure the fast performance of the PRC structure and effectively suppress current harmonics. Considering that the odd harmonic content in the output current of the single-phase inverter is high, it is proposed to adopt a PORC strategy to suppress odd harmonics. Compared with PRC, the inherent delay of PORC is only 0.5 fundamental cycle, which can shorten the dynamic response time. However, due to the inherent delay of RC, the dynamic performance of PORC is also limited. Therefore, it is still necessary to develop a new RC strategy with faster dynamic response.

[0061] The present invention provides a design method of an insertion-type feedforward odd-order repetitive controller, comprising the following steps:

[0062] S1. A single-phase three-level grid-connected inverter is constructed, and based on the single-phase three-level grid-connected inverter, a transfer function P(s) of a controlled object is obtained; the single-phase three-level grid-connected inverter includes 8 power switches and an LCL filter; the LCL filter includes an inductor L1, an inductor L2 and a capacitor C; the controlled object is the LCL filter;

[0063]

[0064] Among them, H ic is the capacitor current feedback coefficient.

[0065] It should be noted that the single-phase three-level grid-connected inverter model with LCL filter is as follows: Figure 3 As shown, the inverter has 8 power switches, represented by Q1~Q8, and its input voltage is U dc The LCL filter is composed of L1, L2 and C. g and i g are the grid voltage and grid current respectively. ic is the capacitor current feedback factor, which is used to eliminate the resonance peak of the LCL filter. The effective value of the reference current I ref Use i ref The phase angle and frequency of the power grid are provided to the current controller G by the phase-locked loop. i (z). Compared with the analog control system, the closed-loop system characteristics will change due to the 1.5-cycle digital control delay, which includes 1 cycle of sampling calculation delay and 0.5 cycle of PWM delay. Figure 3 Based on the above, considering the delay of 1.5 cycles, the grid current control block diagram is as follows Figure 4 As shown. Figure 2 In, T s Represents the sampling period, and the controlled object can be obtained.

[0066] The system parameters are shown in the following table:

[0067] Table 1. Inverter system parameters

[0068] parameter Numeric Inverter side filter inductor L1 / mH 4.4 Grid-side filter inductor L2 / mH 0.2 Filter capacitor C / μF 4.7 <![CDATA[DC-side input voltage u dc / V]]> 380 <![CDATA[Grid voltage u g / V]]> 220 <![CDATA[Grid voltage frequency f g / Hz]]> 50 Sampling frequency fs / kHz 10

[0069] S2, construct an insertion feedforward odd-order repetitive controller and insert it into the inverter model. The discrete transfer function G of the internal model of the insertion feedforward odd-order repetitive control system is forc (z) is:

[0070]

[0071] Where S(z) is a low-pass filter that attenuates high-frequency harmonics, z m is the phase advance compensation; k r is the repetitive control gain; Q(z) is the internal model coefficient, a constant between 0 and 1;

[0072] The steady-state error E(z) of the insertion-type feedforward odd-order repetitive control system is:

[0073]

[0074] In the above formula, G pi (z)P(z) is the open-loop transfer function, where P(z) is the controlled object and P(z) is converted from P(s) using the zero-order hold method; G pi (z) is the PI controller; i ref (z) is the reference current; d g (z) is the harmonic disturbance current;

[0075] The characteristic polynomial of the insertion-type feedforward odd-order repetitive control system is:

[0076] 1+[G forc (z)+G pi (z)]P(z)=[1+G pi (z)P(z)][1+G forc (z)P0(z)] (3)

[0077] Where P0(z)=P(z)G pi (z) / (1+P(z)G pi (z)), P0(z) is the equivalent controlled object; and according to formula (3), (1) is substituted into (2) to obtain the steady-state error E(z);

[0078]

[0079] Wherein, S(z) is a low-pass filter for attenuating high-frequency harmonics;

[0080] Let the characteristic equation of the steady-state error E(z) be [1+P(z)G pi All roots of [z] = 0 are inside the unit circle and Make the insertion feedforward odd-order repetitive control system stable;

[0081] S3, design the insertion feedforward odd-number repetition control parameters to form a stable control system, which not only satisfies [1+P(z)G pi All roots of (z)] = 0 are inside the unit circle and also satisfy

[0082]

[0083] In step S2, if the i ref (z) and d g The angular frequency ω of (z) is close to ω a =2π(2a+1) / (NT s ), then a=0,1,2,…,A; when N is an even number, A=N / 2, when N is an odd number, A=(N-1) / 2; when z -N / 2 =e -jπ(2a+1) = -1, we can get |z -N / 2 |=1; and |Q(z)|≤1, the stability condition of the insertion feedforward odd-order repetitive control system is met, and the following inequality must be guaranteed to hold:

[0084]

[0085] Assume that the amplitude-frequency and phase-frequency characteristics of P0(z) and S(z) are as follows:

[0086]

[0087] Since the phase of Q(z) is 0, combining the above equations, we get:

[0088]

[0089] In the formula (7) And through Euler's formula, k r >0, Therefore, formula (7) can be written as:

[0090]

[0091] The stability condition of formula (8) becomes:

[0092]

[0093] It should be noted that formulas (9) and (10) can be used as parameters m and k r Selection basis. By further analyzing the system stability conditions, equations (9) and (10) can be used as the basis for the design of the PFORC composite controller parameters. First, the value of parameter m is determined according to equation (9), and then substituted into equation (10) to further determine k r The value of can ensure the stability of the PFORC system.

[0094] The inserted feedforward odd-number repetition control parameters in step S3 include: the open-loop transfer function P(z)G pi (z)Satisfy 10f g <f c <0.1fs , where f g is the grid frequency, f c is the cutoff frequency, f c =650Hz, H ic =10, k p =14, k i =7000, open loop basic gain T fo The gain margin is 24.6dB, the phase margin is 48°, and the open-loop basic gain T fo If it is greater than 20dB, the calculation result of the discrete transfer function of the equivalent controlled object P0(z) is as follows:

[0095]

[0096] It should be noted that the design proportional gain k p , integral gain k i , active damping coefficient H ic ; The pi controller is to meet the stability condition ①, in order to reduce the switching noise, the open-loop transfer function P(z)G pi (z) Need to meet 10f g <f c <0.1f s The requirement, where f g is the grid frequency, f c is the cutoff frequency. Therefore, choose f c =650Hz. The gain margin (GM) should be greater than 3dB, and the phase margin (PM) should be within the range of [30°, 60°]. In addition, the open-loop basic gain T fo Should be greater than 20dB.

[0097] Combined with Matlab, we conducted precise trials and finally selected H ic =10k p =14k i =7000. At this time, the open-loop basic gain T fo It is 24.6dB, GM=9.75dB, PM=48°, all of which meet the design standards.

[0098] Design the internal model coefficient Q(z) of the plug-in feedforward odd-order repetitive control system and the low-pass filter S(z) for attenuating high-frequency harmonics; set Q(z) = 0.95 to set the dominant odd harmonic frequency of the grid-connected inverter within 1000Hz, S(z) is a low-pass filter for attenuating high-frequency harmonics, and the discrete expression of S(z) is:

[0099]

[0100] Phase lead compensation z m: Wherein m=8. The low-pass filter S(z) for attenuating high-frequency harmonics is specifically: a fourth-order Butterworth low-pass filter.

[0101] It should be noted that: the internal mode coefficient Q(z) and the low-pass filter S(z) for attenuating high-frequency harmonics are designed: when Q(z) is constant, the open-loop gain of the RC internal mode decreases as Q(z) decreases, while the resonant bandwidth increases. The present invention selects Q(z)=0.95. S(z) is used to filter out high-frequency interference and enhance stability. Since the dominant odd harmonic frequency of the grid-connected inverter is within 1000Hz.

[0102] Design gain k r ; When the phase advance link z m When m=8, the angle of γ(ω) is between 0° and 17.3°, so the minimum value of cosγ(ω) is 0.9547, then z m The maximum gain of S(z)P0(z) is 3.23dB. The maximum value of is 1.0104. In order to obtain a stable closed-loop feedback control system, set k r is 0.46;

[0103]

[0104] According to formula (13), we know that k r The maximum value is 0.6414.

[0105] It should be noted that: Design phase advance link z m :Adding a low-pass filter S(z) to attenuate high-frequency harmonics will further reduce the high-frequency gain of P2(z), but it will also cause the phase to lag further. Phase lag will affect the dynamic response speed and control accuracy of the system. Therefore, the phase advance link z m The design is necessary. In the 1000Hz frequency range, when the phase lead beat m takes different values, the compensated z k The phase-frequency curve of P0(z)S(z) is between [-90°, 90°], which satisfies the stability of the system. Then, a suitable m is selected so that the phase-frequency curve after compensation is closest to the 0dB line. The present invention selects m=8.

[0106] The present invention also establishes a simulation model to verify the controller;

[0107] A 1.5 kW single-phase three-level grid-connected inverter simulation model was established, and the proposed control strategy was verified by simulation experiments. The parameters of the inverter are shown in Table 1. Odd harmonics with a frequency below 1000 Hz are added to the grid to accurately simulate the background harmonics of the grid. Table (2) gives the values ​​of each odd harmonic. The grid voltage u g The THD value is 4.9%. Figure 2 The simulation model shown

[0108] Table 2. Power grid background harmonic content

[0109]

[0110] Simulation Results

[0111] (1) When the grid frequency becomes 50 Hz, the inverter output waveform and grid-connected current THD analysis of the PFORC-based control system are as follows: Figure 6 As shown, the results show that when the background harmonic of the power grid is 5.7%, the proposed new PFORC based on repetitive control equivalent can still output a relatively high-quality grid-connected current.

[0112] (2) When the grid frequency fluctuates between 49.6 Hz and 50.4 Hz, the output waveform and current THD analysis of the PFORC system are as follows: Figure 7 Obviously, the proposed PFORC based on the new design method can still have good performance when the frequency fluctuates.

[0113] (3) When the reference current suddenly changes from 10A to 5A, the output waveform of the PFORC system is as follows Figure 8 As shown. g The waveform tends to be stable within about 1.5 cycles (30 milliseconds), and the PFORC system has a fast response speed.

[0114] It should be noted that the discrete domain internal model structure diagram of the plug-in feedforward odd-number repetitive control system (PFORC) is as follows: Figure 5 As shown. The input signal is represented by E(z), the output signal is represented by Y(z), Q(z) is a constant between 0 and 1, and the variable N is defined as the sampling frequency f s With the fundamental frequency f o ratio. Figure 5 It can be seen that both the PORC internal model and the PFORC internal model have an inherent delay of 1 / 2 fundamental wave period, that is, the memory unit required for digital implementation is N / 2.

[0115] like Figure 5 As shown, the present invention provides a method based on the insertion feedforward odd-order repetitive controller design method with a greater gain and a wider resonant bandwidth:

[0116] The discrete domain transfer function expression of the inner model of the plug-in feedforward odd-order repetitive control system is:

[0117]

[0118] The continuous domain transfer function of the inner model of the inserted feedforward odd-order repetitive control system can be expressed as follows:

[0119]

[0120] When the reference current i ref (z) Harmonic disturbance signal d g The angular frequency ω of (z) approaches ω n =2π(2n+1) / T0, where x=0,1,2,..., then

[0121]

[0122] According to the above two formulas (15) and (16), G forc (s) can be expanded to:

[0123]

[0124] In the above formula: ω0 = 2π / T0, ω0 is the resonant angular frequency. It can be seen from the above formula that the PFORC internal mode has infinite gain at odd harmonic frequencies, thereby eliminating odd harmonics and achieving static-free tracking of the reference input signal.

[0125] When Q(z) = 1, it can be seen from formulas (15) and (16) that G forc (s) The frequency domain expression is as follows:

[0126]

[0127] When Q=1,ω=2π(2n+1)f0(n=0,1,2,3,...,), the frequency domain expressions of PRC internal mode and PORC internal mode are as follows:

[0128]

[0129] From formulas (18), (19), and (20), we can see that:

[0130]

[0131] According to formulas (21) and (22), when the RC gain k r At the same time, at odd harmonic frequencies, the gain of the PFORC internal model is twice that of the PORC internal model, and is four times that of the PRC internal model structure. Therefore, theoretically, the error convergence speed of the PFORC internal model for odd harmonics is twice that of the PORC internal model and four times that of the PRC internal model.

[0132] Figure 2 The frequency response plots of the PRC, PORC, and PFORC internal modes are shown. Figure 2 (b) Figure 2 (a) is a detail of the amplitude-frequency response curve. Figure 2 It is obvious from (a) that the internal modes of PFORC and PORC have high resonant peaks only at the fundamental and odd harmonic frequencies. However, the internal mode of PFORC introduces a zero at the even harmonic frequencies, which creates an anti-resonant peak at these frequencies. Due to the effect of Bode sensitivity integration, this peak weakens the error signal near the even harmonic frequencies while increasing the error signal near the odd harmonic frequencies. Therefore, the internal mode of PFORC exhibits higher gain at the odd harmonic frequencies. From Figure 2 (b) It can be seen that the PFORC inner mode has a larger gain and a wider resonant bandwidth at the fundamental frequency and odd harmonic frequencies. Therefore, this indicates that the PFORC is less sensitive to frequency fluctuations in the power system.

[0133] The control object is an industrial device whose output voltage / current signal is composed of odd-order characteristic power harmonics, including a programmable AC power supply, a power converter and a servo motor.

[0134] The present invention also provides an insertion-type feedforward odd-order repetitive controller, and the controller is implemented by a design method of an insertion-type feedforward odd-order repetitive controller.

[0135] The control object of the controller is an industrial device whose output voltage / current signal is composed of odd-order characteristic power harmonics, including a programmable AC power supply, a power converter and a servo motor.

[0136] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A design method for an insertion-type feedforward odd-order repetitive controller, characterized in that: The following steps are involved: S1. Determine the transfer function P(s) of the controlled object; S2, construct an insertion feedforward odd-order repetitive controller, the discrete transfer function G of the internal model of the insertion feedforward odd-order repetitive controller forc (z) is: Where S(z) is a low-pass filter that attenuates high-frequency harmonics, z m is the phase advance compensation; k r is the repetitive control gain; Q(z) is the internal model coefficient, a constant between 0 and 1; The steady-state error E(z) of the system of the plug-in feedforward odd-order repetitive controller is: In the above formula, G pi (z)P(z) is the open-loop transfer function, where P(z) is the controlled object and P(z) is converted from P(s) using the zero-order hold method; G pi (z) is the PI controller; i ref (z) is the reference current; d g (z) is the harmonic disturbance current; The characteristic polynomial of the insertion-type feedforward odd-order repetitive control system is: 1+[G forc (z)+G pi (z)]P(z)=[1+G pi (z)P(z)][1+G forc (z)P0(z)] (3) Where P0(z)=P(z)G pi (z) / (1+P(z)G pi (z)), P0(z) is the equivalent controlled object; and according to formula (3), (1) is substituted into (2) to obtain the steady-state error E(z); Wherein, S(z) is a low-pass filter for attenuating high-frequency harmonics; let the characteristic equation of the steady-state error E(z) be [1+P(z)G pi All roots of [z] = 0 are inside the unit circle and Make the insertion feedforward odd-order repetitive control system stable; S3, design the insertion feedforward odd-number repetition control parameters, not only [1+P(z)G pi All roots of (z)] = 0 are inside the unit circle and also satisfy 2. The design method of an insertion-type feedforward odd-order repetitive controller according to claim 1, characterized in that: The controlled object in step S1 includes: inductor L1, inductor L2 and capacitor C, and the transfer function P(s) of the controlled object is: Among them, H ic is the capacitor current feedback coefficient.

3. The design method of an insertion-type feedforward odd-order repetitive controller according to claim 1, characterized in that: In the step S2, the i ref (z) and d g The angular frequency ω of (z) is close to ω a =2π(2a+1) / (NT s ), then a=0,1,2,…,A; when N is an even number, A=N / 2, when N is an odd number, A=(N-1) / 2; when z -N / 2 =e -jπ(2a+1) = -1, we get |z -N / 2 |=1; and |Q(z)|≤1, if the stability condition of the insertion feedforward odd-order repetitive control system is met, the following inequality must be guaranteed to hold:

4. The design method of an insertion-type feedforward odd-order repetitive controller according to claim 1 is characterized in that The amplitude-frequency and phase-frequency characteristics of P0(z) and S(z) in formula (4) are as follows: Since the phase of Q(z) is 0, combining the above equations, we get:

5. The design method of an insertion-type feedforward odd-order repetitive controller according to claim 4, characterized in that: In the formula (7) And through Euler's formula, k r >0, Therefore, formula (7) can be written as: The conditions for making formula (7) and formula (8) stable are:

6. The design method of an insertion-type feedforward odd-order repetitive controller according to claim 1, characterized in that: The inserted feedforward odd-number repetition control parameters in step S3 include: the open-loop transfer function P(z)G pi (z)Satisfy 10f g <f c <0.1f s , where f g is the grid frequency, f c is the cutoff frequency, f c =650Hz, H ic =10, k p =14, k i =7000, open loop basic gain T fo The gain margin is 24.6dB, the phase margin is 48°, and the open-loop basic gain T fo If it is greater than 20dB, the calculation result of the discrete transfer function of the equivalent controlled object P0(z) is as follows: Assume the internal model coefficient Q(z) of the plug-in feedforward odd-order repetitive control system and the low-pass filter S(z) for attenuating high-frequency harmonics; Assume Q(z) = 0.95, set the dominant odd harmonic frequency of the grid-connected inverter to within 1000Hz, S(z) is the low-pass filter for attenuating high-frequency harmonics, then the discrete expression of S(z) is: In the above formula, z m It is phase advance compensation; Assume that the repetitive control gain k r ; When the phase advance link z m When m=8, the angle of γ(ω) is between 0° and 17.3°, so the minimum value of cosγ(ω) is 0.9547, then z m The maximum gain of S(z)P0(z) is 3.23dB. The maximum value of is 1.0104. In order to obtain a stable closed-loop feedback control system, set k r is 0.46; And let According to formula (13), we know that k r The maximum value is 0.6414.

7. The design method of an insertion-type feedforward odd-order repetitive controller according to claim 1, characterized in that: The control object is an industrial device whose output voltage / current signal is composed of odd-order characteristic power harmonics, including a programmable AC power supply, a power converter and a servo motor.

8. An insertion-type feedforward odd-order repetitive controller, characterized in that: The controller is implemented by the insertion-type feedforward odd-order repetitive controller design method described in any one of claims 1-7.

9. The plug-in feedforward odd-order repetitive controller according to claim 8, characterized in that: The control object of the controller is an industrial device whose output voltage / current signal is composed of odd-order characteristic power harmonics, including a programmable AC power supply, a power converter and a servo motor.

Images