Integral sliding mode based linear oscillatory motor resonant frequency control method and system

Abstract

The application discloses a linear oscillation motor resonant frequency control method and system based on integral sliding mode, and belongs to the technical field of linear oscillation motor resonant frequency tracking control. The method adopts the cross-correlation function method to obtain the resonant frequency of the system according to the characteristics that the displacement current phase difference is 90 degrees when the linear oscillation motor works at the resonant frequency point; the integral sliding mode surface and a novel sliding mode approaching law are introduced; an improved integral sliding mode observer is designed to observe the motor back electromotive force signal; and according to the characteristics that the back electromotive force is proportional to the speed signal, the piston speed signal is obtained; the estimated speed signal is filtered by adopting the second-order generalized integral to obtain the piston stroke signal which has almost no amplitude and phase offset. Compared with the traditional open-loop back electromotive force method for estimating the piston stroke signal to realize the resonant frequency tracking without the position sensor, the method has higher resonant frequency tracking precision.

Description

Technical Field

[0001] This invention belongs to the field of linear oscillating motor resonant frequency tracking control technology, and more specifically, relates to a linear oscillating motor resonant frequency control method and system based on integral sliding mode. Background Technology

[0002] Linear oscillating motors are a new type of motor that directly converts electromagnetic force into linear motion, and they have broad application prospects in the field of refrigeration compressors. Compared with traditional rotary motor-driven compressor systems, linear compressors driven by linear oscillating motors eliminate the crank-connecting rod device, and have advantages such as simple structure, low noise, and adjustable stroke.

[0003] In the operation of a linear oscillating motor, it is often necessary to operate at the system's resonant frequency to achieve maximum output efficiency. Because the piston stroke-to-current amplitude ratio reaches its maximum when the linear oscillating motor operates at the system resonant frequency, researchers have proposed a perturbation search method based on this characteristic. This method continuously changes the motor frequency and compares the magnitudes of the piston stroke and current. When the ratio of piston stroke to current reaches its maximum, the motor's operating frequency at this point can be considered the system resonant frequency. However, the resonant frequency obtained using this method experiences severe oscillations, and the response speed is affected by the adjustment step size, making it difficult to achieve good control results. Furthermore, researchers have found that when the linear oscillating motor operates at the resonant frequency, the phase difference between the piston stroke and current is 90°. Based on this characteristic, some researchers have proposed a waveform fitting phase detection algorithm, using the least squares method to fit the sinusoidal signal parameters and then directly calculate the phase difference. However, this type of method requires extremely large data storage space and computational load, placing extremely high demands on the computing performance of the control chip, making it impractical for real-world engineering applications.

[0004] By controlling the piston stroke of a linear oscillating motor, the exhaust volume can be freely adjusted. However, when the piston stroke exceeds the cylinder's maximum allowable value, piston collision will occur. Therefore, to ensure the safe and reliable operation of the control system, precise control of the piston stroke signal is required. Traditional methods often use position sensors to obtain the piston stroke signal for closed-loop stroke control, but this method suffers from problems such as difficult sensor installation, high cost, and difficult maintenance. Using a precise sensorless algorithm to obtain the piston stroke signal can effectively solve the problems caused by position sensors. Currently, research on sensorless algorithms for linear oscillating motors mainly adopts the open-loop back electromotive force integration method. This method calculates the motor's back electromotive force using voltage and current signals, and calculates the piston speed signal based on the proportional relationship between the back electromotive force and piston speed. Finally, integrating the piston speed signal yields the piston stroke signal. However, this method is an open-loop calculation method without feedback correction, and its calculation accuracy is severely affected by motor parameters, making it impossible to obtain a precise piston stroke signal. In summary, the control effects of traditional resonant frequency tracking control strategies and sensorless control strategies are difficult to meet the requirements of engineering practice, and their control performance needs improvement. Summary of the Invention

[0005] To address the shortcomings and improvement needs of existing technologies, this invention provides a method and system for controlling the resonant frequency of a linear oscillating motor based on integral sliding mode. The aim is to improve the accuracy of resonant frequency estimation and simultaneously achieve resonant frequency tracking and sensorless stroke closed-loop control.

[0006] To achieve the above objectives, the present invention provides a method for controlling the resonant frequency of a linear oscillating motor based on integral sliding mode, comprising the following steps: S1. Perform cross-correlation calculation on the piston stroke signal of the linear oscillating motor and the current signal collected by the current sensor to obtain the cross-correlation function of the piston stroke-current signal; S2. Adjusting the obtained cross-correlation function value to 0 ensures that the phase difference between the piston stroke signal and the current signal is 90°. By adding the frequency change during the adjustment process to the original operating frequency of the motor, the system resonant frequency can be obtained. S3. Based on the motor voltage equation, an improved integral sliding mode observer is designed to observe the back electromotive force information of the motor. The improved integral sliding mode observer selects the integral sliding surface and the designed approaching law to construct the sliding mode control law. S4. Based on the proportional relationship between the back electromotive force of the motor and the piston speed, the estimated piston speed signal is obtained, and a second-order generalized integrator is used to filter the piston speed signal to obtain a piston stroke signal with almost no amplitude and phase shift. S5. The estimated piston stroke signal is used for cross-correlation function calculation and piston stroke closed-loop control to achieve sensorless resonant frequency tracking control.

[0007] Further, the method described in step S1 includes: The expressions for the piston stroke signal and current signal of the linear oscillating motor are as follows:

[0008]

[0009] in, The acquired current signal, The current amplitude, For motor frequency, The initial phase of the current. This is the piston stroke signal. This represents the amplitude of the piston stroke.

[0010] The cross-correlation function between piston stroke and current signal is:

[0011] Further, the method described in step S2 includes: The cross-correlation function value is adjusted to 0 using a P controller, i.e.:

[0012] At this time, the phase difference between the piston stroke signal and the current signal is... It is exactly 90°.

[0013] Furthermore, by adding the frequency change controlled by the P controller to the original operating frequency of the motor, the system resonant frequency can be obtained.

[0014] Further, the method described in step S3 includes: The voltage equation for a linear oscillating motor is:

[0015] in, For resistance, For inductance, For output voltage, For sampling current, This is the back electromotive force of the motor.

[0016] Rewriting the voltage equation as a current state equation, we get:

[0017] Furthermore, based on the current state equation, an improved integral sliding mode observer is designed as follows:

[0018] in, To observe the current, This is a sliding mode control law.

[0019] The integral sliding surface selected in the sliding mode control law is:

[0020] in, For integral sliding surfaces, To observe the current and sampling current Current error, This is the integral gain.

[0021] The convergence law of design is:

[0022] in, , , , It is a constant, satisfying , , , ; and It is an odd number, satisfying .

[0023] Based on the aforementioned integral sliding surface and novel reaching law, a construction is made... The specific expression is:

[0024] Therefore, the back electromotive force information can be estimated using an integral sliding mode observer.

[0025] Further, the method described in step S4 includes: The relationship between the back electromotive force and the piston speed of a linear oscillating motor is as follows:

[0026] in, This is the thrust coefficient.

[0027] Therefore, the velocity signal estimated by the improved sliding mode observer can be obtained as follows: .

[0028] Furthermore, considering that in practical engineering, the voltage and current signals acquired by voltage and current sensors always contain a certain DC component, and for a linear oscillating motor, the piston stroke signal is obtained by integrating the piston speed. During pure integration, the DC component accumulates continuously, leading to integral drift and affecting the accuracy of piston stroke estimation. To solve the pure integration saturation problem, a second-order generalized integrator is used to filter the estimated speed signal. Its transfer function expression is:

[0029] in, for Independent variables, For input signal, For filtered signals, This is the cutoff frequency of the second-order generalized integrator. is the filter constant.

[0030] A second-order generalized integrator can retain the fundamental frequency information of the input signal while filtering out harmonic signals other than the fundamental frequency signal, exhibiting strong filtering capabilities. Using a second-order generalized integrator to filter the estimated speed signal yields a smooth speed-filtered signal with almost no amplitude or phase shift. Because a large number of harmonic signals are filtered out, integrating the speed signal again will not cause pure integration saturation, resulting in an accurate piston stroke signal.

[0031] Furthermore, the stroke signal obtained using the second-order generalized integrator in step S5 is not only used for calculating the piston stroke-current cross-correlation function, but also for piston stroke closed-loop control. Therefore, the method proposed in this paper can realize sensorless resonant frequency tracking control of a linear oscillating motor.

[0032] The present invention also provides a resonant frequency control system for a linear oscillating motor based on integral sliding mode, comprising: a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the above-described linear oscillating motor resonant frequency control method based on integral sliding mode.

[0033] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art: (1) Compared with the traditional search method and waveform fitting phase detection method, the linear oscillating motor resonant frequency tracking control method provided by the present invention has the advantages of small computational load and high tracking accuracy.

[0034] (2) The present invention employs an integral sliding surface and a novel approaching law to construct a sliding mode control law, which greatly reduces the influence of sliding mode chattering. Compared with the traditional open-loop back EMF method, the improved sliding mode observer designed has greatly improved the observation accuracy due to the introduction of a current error feedback loop.

[0035] (3) This invention combines an improved integral sliding mode observer with a cross-correlation function resonant frequency tracking method to achieve high-performance sensorless resonant frequency tracking control of a linear oscillating motor. Attached Figure Description

[0036] Figure 1 Block diagram of a linear oscillating motor resonant frequency control method based on integral sliding mode; Figure 2 A piston stroke estimation method based on an improved sliding mode observer and a second-order generalized integrator; Figure 3 Piston stroke signal estimation results based on the improved sliding mode observer; Figure 4 Resonant frequency tracking results based on the cross-correlation function method. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0038] This invention provides a method for controlling the resonant frequency of a linear oscillating motor based on integral sliding mode, and its control system structure block diagram is shown below. Figure 1 As shown, it includes the following steps: S1. Perform cross-correlation calculation on the piston stroke signal of the linear oscillating motor and the current signal collected by the current sensor to obtain the cross-correlation function of the piston stroke-current signal.

[0039] Specifically, the expressions for the piston stroke signal and current signal of the linear oscillating motor are as follows:

[0040]

[0041] in, The acquired current signal, The current amplitude, For motor frequency, The initial phase of the current. This is the piston stroke signal. This represents the amplitude of the piston stroke.

[0042] The cross-correlation function between piston stroke and current signal is:

[0043] S2. Adjusting the obtained cross-correlation function value to 0 ensures that the phase difference between the piston stroke and the current signal is 90°. By adding the frequency change during the adjustment process to the original operating frequency of the motor, the system resonant frequency can be obtained.

[0044] S3. Based on the motor voltage equation, an improved integral sliding mode observer is designed to observe the back electromotive force information of the motor. The sliding mode control law is constructed by selecting the integral sliding mode surface and a new approaching law, and the sliding mode chattering is weakened by using the integral filtering characteristics, thereby improving the observation accuracy.

[0045] Specifically, the voltage equation for the linear oscillating motor is:

[0046] The voltage equation can be rewritten as the current state equation as follows:

[0047] The improved integral sliding mode observer is designed based on the current state equation as follows:

[0048] The integral sliding surface selected in the sliding mode control law is:

[0049] The novel convergence law designed is as follows:

[0050] Sliding mode control law for:

[0051] S4. Based on the relationship that the back electromotive force of the linear oscillating motor is proportional to the piston speed, the estimated speed signal is obtained, and a second-order generalized integrator is used to filter the piston signal to obtain a piston stroke signal with almost no amplitude and phase shift.

[0052] Specifically, the relationship between the back electromotive force and the speed of the linear oscillating motor is as follows:

[0053] The transfer function of the second-order generalized integrator is:

[0054] The piston stroke estimation method based on the improved sliding mode observer and the second-order generalized integrator constructed by S3-S4 is as follows: Figure 2 As shown.

[0055] S5. The estimated piston stroke signal is used for cross-correlation function calculation and piston stroke closed-loop control to achieve sensorless resonant frequency tracking control.

[0056] The present invention also provides a resonant frequency control system for a linear oscillating motor based on integral sliding mode, comprising: a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the above-described linear oscillating motor resonant frequency control method based on integral sliding mode.

[0057] Example: This embodiment uses a stator permanent magnet type dual-stator linear oscillating motor as an example to simulate and verify the above method. The rated power is set to 120W, the system resonant frequency to 22.1Hz, the stator resistance to 18.4Ω, the stator inductance to 0.755H, the thrust coefficient to 47.08N / A, and the mover piston mass to 1.03kg. The actual equivalent damping coefficient of the system is 20N / (m / s), and the actual equivalent spring constant is 30kN / m.

[0058] like Figure 3 As shown, the proposed piston stroke estimation method based on the improved sliding mode observer can accurately estimate the actual stroke signal of the motor. Figure 4 As shown, by using the resonant frequency tracking method based on cross-correlation function proposed in this invention, the motor operating frequency can quickly converge to the system resonant frequency.

[0059] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for controlling the resonant frequency of a linear oscillating motor based on integral sliding mode, characterized in that, Includes the following steps: S1. Calculate the cross-correlation function of the piston stroke signal of the linear oscillating motor and the current signal acquired by the current sensor to obtain the cross-correlation function of the piston stroke-current signal; the expressions for the piston stroke signal and current signal of the linear oscillating motor are as follows: in, The acquired current signal, The current amplitude, For motor frequency, This represents the initial phase of the current. This is the piston stroke signal. This represents the magnitude of the piston stroke. The cross-correlation function of the piston stroke-current signal is: in, T One cycle time; S2. Adjust the obtained cross-correlation function value to 0 to ensure that the phase difference between the piston stroke signal and the current signal is 90°. Add the frequency change during the adjustment process to the original operating frequency of the motor to obtain the system resonant frequency. S3. Based on the motor voltage equation, an improved integral sliding mode observer is designed to observe the motor back electromotive force information. This involves selecting the integral sliding surface and a reaching law to construct the sliding mode control law, and utilizing integral filtering characteristics to weaken sliding mode chattering, thereby improving observation accuracy. The voltage equation is: in, For resistance, For inductance, For output voltage, For sampling current, This is the back electromotive force of the motor; Rewrite the voltage equation as a current state equation: The improved integral sliding mode observer is designed based on the current state equation as follows: in, To observe the current, This is a sliding mode control law; The integral sliding surface selected in the sliding mode control law is: in, For integral sliding surfaces, To observe the current and sampling current Current error, This is the integral gain; The convergence law of design is: in, , , , It is a constant, satisfying , , , ; and It is an odd number, satisfying ; Based on the aforementioned integral sliding surface and novel reaching law, a sliding mode control law is constructed. for: ； S4. Based on the proportional relationship between the back electromotive force of the linear oscillating motor and the piston speed, the estimated speed signal is obtained, and a second-order generalized integrator is used to filter the piston signal to obtain a piston stroke signal without amplitude and phase shift. S5. The piston stroke signal is used for cross-correlation function calculation and piston stroke closed-loop control to achieve sensorless resonant frequency tracking control.

2. The control method according to claim 1, characterized in that, By using a P controller to adjust the cross-correlation function value to 0, ensuring that the phase difference between the piston stroke and the current signal is 90°, and accumulating the frequency change controlled by the P controller to the original operating frequency of the motor, the system resonant frequency can be obtained, thus achieving resonant frequency tracking control.

3. The control method according to claim 1, characterized in that, The relationship between the motor back electromotive force and the piston speed in step S4 is as follows: in, For thrust coefficient, v Piston speed; Therefore, the estimated velocity signal is obtained as follows: .

4. The control method according to claim 3, characterized in that, The estimated piston velocity signal is filtered using a second-order generalized integrator, and its transfer function expression is as follows: in, for Independent variables, For input signal, For filtered signals, This is the cutoff frequency of the second-order generalized integrator. is the filter constant.

5. A resonant frequency control system for a linear oscillating motor based on integral sliding mode, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the linear oscillating motor resonant frequency control method based on integral sliding mode as described in any one of claims 1 to 4.

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