A Control Method and System for Linear Oscillating Motors Based on Hybrid Terminal Sliding Mode

Abstract

This invention discloses a control method and system for a linear oscillating motor based on hybrid terminal sliding mode, belonging to the field of linear oscillating motor control technology. The method is based on a model reference adaptive approach, using the linear oscillating motor's speed state equation as a reference model to construct an adjustable model. Based on Popov's hyperstability theorem, a parameter adaptive law is derived to adjust the error between the observed speed and the reference speed in real time. A terminal sliding mode observer with stronger parameter robustness is designed as the system reference model, and its estimated speed is used as the reference speed of the adjustable model. A second-order generalized integrator is used to filter the speed signal estimated by the terminal sliding mode observer to obtain a stroke estimation signal, thereby achieving sensorless piston stroke closed-loop control. Through this invention, a relatively accurate resonant frequency tracking signal can be obtained, and sensorless piston stroke and resonant frequency tracking closed-loop control can be simultaneously achieved.

Description

Technical Field

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

[0002] Traditional compressors are typically driven by rotary motors, using a crank-connecting rod structure to convert rotary motion into linear motion. Due to limitations in their mechanical structure, these compressors suffer from low efficiency, high mechanical losses, and non-adjustable piston stroke. To improve the operating efficiency of traditional compressors, linear compressors have attracted widespread attention in recent years. Driven by a linear oscillating motor, a linear compressor can directly convert electrical energy into linear mechanical energy without the need for a crank-connecting rod structure. Compared to traditional rotary compressors, they offer advantages such as simpler structure, lower noise, and controllable piston stroke.

[0003] Because linear oscillating motors contain auxiliary springs in their internal structure, these springs can have a certain impact on the compressor system. The influence of the auxiliary springs is minimized only when the motor operates at its resonant frequency, at which point the system achieves maximum output efficiency. Therefore, it is necessary to implement resonant frequency tracking control for the linear oscillating motor. Furthermore, since the piston stroke of a linear oscillating motor is unrestricted, cylinder collision can occur if the stroke exceeds the rated value. Therefore, to ensure the safe and reliable operation of the compressor system, piston stroke control is also required.

[0004] Traditional resonant frequency tracking control methods are mostly based on the phase angle difference relationship between displacement and current, requiring position sensors or sensorless estimation algorithms to provide piston stroke signals. Under sensorless conditions, the resonant frequency tracking accuracy will decrease due to inaccurate stroke estimation. In recent years, some researchers have applied the model reference adaptive method to linear oscillating motors. Through parameter identification, parameters containing resonant frequency information are identified, thus obtaining the system's resonant frequency. This method does not rely on the motor stroke signal and has advantages such as high identification accuracy and fast convergence speed. However, it uses the traditional open-loop back EMF method to obtain the speed reference signal, which suffers from low estimation accuracy and high dependence on parameters. Inaccurate speed signals provided by the reference model will reduce the system's resonant frequency tracking accuracy. In summary, while the traditional model reference adaptive resonant frequency tracking control method provides a novel approach to resonant frequency tracking, its accuracy is greatly affected by the accuracy of the reference model, and the estimation accuracy needs improvement. Summary of the Invention

[0005] To address the shortcomings and improvement needs of existing technologies, this invention provides a linear oscillating motor control method and system based on hybrid terminal sliding mode, aiming to improve the accuracy of resonant frequency estimation while achieving resonant frequency tracking and sensorless stroke closed-loop control.

[0006] To achieve the above objectives, the present invention provides a linear oscillating motor control method based on hybrid terminal sliding mode, comprising the following steps:

[0007] S1. The mechanical equations of the linear oscillating motor are transformed to obtain the velocity state equations, and an adjustable system model is constructed based on the model reference adaptive method.

[0008] S2. Obtain the first-order velocity error equation through the adjustable model and the reference model, and construct an error feedback system;

[0009] S3. Based on Popov's superstability theorem, the parameter adaptive law is derived, and the estimated resonant frequency is obtained by using the relationship between the identified parameters and the system resonant frequency.

[0010] S4. Rewrite the voltage equation of the linear oscillating motor into a current state equation, construct a terminal sliding mode observer to reconstruct the back EMF information, adopt a second-order non-singular terminal sliding mode surface and introduce an exponential reaching law to design the control law of the observer; use the relationship between the reconstructed back EMF and the velocity to obtain the estimated velocity signal.

[0011] S5. A second-order generalized integrator is used to filter the speed signal estimated by the terminal sliding mode observer. The filtered speed signal is used as the reference speed of the adjustable model, and the filtered orthogonal signal is used for piston stroke closed-loop control.

[0012] Further, the method described in step S1 includes:

[0013] The mechanical equation of the linear oscillating motor is:

[0014]

[0015] Where M is the piston mover mass, x is the piston stroke signal, i is the motor current, and F is the piston stroke signal. e For electromagnetic thrust, K i Let K be the electromagnetic thrust coefficient, K be the equivalent spring constant, and C be the equivalent damping coefficient, and K and C satisfy K = K m +K g C = C m +C g , where K m K is the mechanical elastic coefficient. g C is the equivalent gas force elastic modulus. m C is the mechanical damping coefficient. g This is the equivalent gas force damping coefficient.

[0016] The velocity state equation is:

[0017]

[0018] Where v is the piston speed signal.

[0019] Based on the model reference adaptive method, the velocity state equation is used as the reference model, and the adjustable model is constructed as follows:

[0020]

[0021] Further, the method described in step S2 includes:

[0022] definition K′ and C′ represent respectively Using the adjustable model to subtract the reference model from K / M and C / M, the derivation process of the first-order velocity error equation is as follows:

[0023]

[0024] The transfer function of the linear forward element in the constructed error feedback system is:

[0025]

[0026] Where σ is an independent variable of G(σ).

[0027] Furthermore, the method described in step S3 includes:

[0028] Popov's hyperstability theorem requires the following inequalities to be satisfied:

[0029]

[0030] From the above equation, the adaptive law of parameters can be derived as follows:

[0031]

[0032]

[0033] Where, k pk k ik Parameters Proportional gain and integral gain coefficients, k pc k ic Parameters Proportional gain and integral gain coefficients, and This is the initial value for integration.

[0034] Identified parameters With the estimated resonant frequency The relationship between them is:

[0035]

[0036] Further, the method described in step S4 includes:

[0037] The voltage equation for a linear oscillating motor is:

[0038]

[0039] The current state equation obtained by deformation is:

[0040]

[0041] The constructed terminal sliding mode observer is as follows:

[0042]

[0043] according to The current state error equation is obtained as follows:

[0044]

[0045] Where R i For resistance, L i Let e ​​be the inductance, e be the back electromotive force, and z be the inductance. smo For terminal sliding mode control law;

[0046] Furthermore, the second-order nonsingular terminal sliding surface is:

[0047]

[0048] The exponential law of convergence is:

[0049]

[0050] Based on the second-order nonsingular terminal sliding surface and the exponential reaching law, the terminal sliding mode control law can be constructed as follows:

[0051] z smo =z eq +z n

[0052] Among them, z eq For the equivalent control law, z n To switch control laws, the following must be satisfied:

[0053]

[0054]

[0055] Where p, q, δ, ρ, η, and μ are design parameters. Let η be the first derivative of the back electromotive force e, η > 0, μ > 0, t be the upper bound of the integral, and τ be the integral variable.

[0056] The back electromotive force reconstructed by the hybrid terminal sliding mode control law is:

[0057]

[0058] The observed velocity signal is:

[0059]

[0060] in This is the estimated back electromotive force.

[0061] Furthermore, the method described in step S5 includes:

[0062] The transfer function of the second-order generalized integrator is:

[0063]

[0064] Where a is an independent variable of H(a), υ is the input signal, υ′ is the filtered signal, and ω c γ is the cutoff frequency of the second-order generalized integrator, and γ is the filter constant.

[0065] The present invention also provides a linear oscillating motor control system based on hybrid terminal sliding mode, comprising: a computer-readable storage medium and a processor;

[0066] The computer-readable storage medium is used to store executable instructions;

[0067] The processor is used to read executable instructions stored in the computer-readable storage medium and execute the above-described linear oscillating motor control method based on hybrid terminal sliding mode.

[0068] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0069] (1) The linear oscillating motor control method based on model reference adaptation provided by the present invention can obtain the system resonant frequency through parameter identification without relying on displacement current phase angle information.

[0070] (2) The terminal sliding mode observer is used as the system reference model, which improves the speed estimation accuracy and parameter robustness of the reference model. The estimated speed signal is used as the reference speed of the adjustable model, which further improves the parameter identification accuracy of the adjustable model and can obtain a more accurate resonant frequency estimation value.

[0071] (3) The speed signal estimated by the terminal sliding mode observer is filtered by the second-order generalized integrator. The filtered speed signal is used for resonant frequency tracking control, and the filtered orthogonal signal is used for piston stroke closed-loop control. This can simultaneously realize sensorless piston stroke closed-loop control and resonant frequency tracking control. Attached Figure Description

[0072] Figure 1 This is a control block diagram of a linear oscillating motor provided in an embodiment of the present invention;

[0073] Figure 2 This is a system block diagram of an adjustable model based on a model reference adaptive method provided in an embodiment of the present invention;

[0074] Figure 3 This is a block diagram of a reference model system based on a terminal sliding mode observer and a second-order generalized integrator provided in an embodiment of the present invention.

[0075] Figure 4 This is a simulation result diagram of the linear oscillating motor control method using the open-loop back electromotive force integral method as a reference model, provided in an embodiment of the present invention. (a) shows the velocity observation results of the adjustable model, v ref Provided by the open-loop back electromotive force integration method, (b) is the error diagram of the velocity observation results, and (c) is the parameter... The tracking results are shown in Ref, which represents the parameter identification results obtained by using the velocity signal provided by the real position sensor as the input of the adjustable model; (d) represents the parameter identification error; and (e) represents the resonant frequency. The tracking result is Ref, which is the resonant frequency obtained by using the velocity signal provided by the real position sensor as the input of the adjustable model, and (f) is the resonant frequency tracking error.

[0076] Figure 5 These are simulation results of the linear oscillating motor control method using a terminal sliding mode observer as a reference model provided in this embodiment of the invention, where (a) is the velocity observation result of the adjustable model, v ref Provided by the terminal sliding mode observer, (b) is the error plot of the velocity observation results, and (c) is the parameter... The tracking results are shown in Ref, which represents the parameter identification results obtained by using the velocity signal provided by the real displacement sensor as the input of the adjustable model; (d) represents the parameter identification error; and (e) represents the resonant frequency. The tracking result is given by Ref, which is the resonant frequency obtained by using the velocity signal provided by the real position sensor as the input of the adjustable model, and (f) is the resonant frequency tracking error. Detailed Implementation

[0077] 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.

[0078] This invention provides a linear oscillating motor control method based on hybrid terminal sliding mode, the control block diagram of which is shown below. Figure 1 As shown, it includes the following steps:

[0079] S1. The mechanical equations of the linear oscillating motor are transformed to obtain the velocity state equations, and an adjustable system model is constructed based on the model reference adaptive method.

[0080] Specifically, the mechanical equation of the linear oscillating motor is:

[0081]

[0082] The velocity state equation can be obtained by transforming the mechanical equation:

[0083]

[0084] Based on the model reference adaptive method, the velocity state equation is used as the reference model, and the adjustable model is constructed as follows:

[0085]

[0086] S2. Obtain the first-order velocity error equation through the adjustable model and the reference model, and construct the error feedback system.

[0087] Specifically, define K′ and C′ represent respectively By subtracting the reference model from the adjustable model, the first-order velocity error equation can be derived as follows:

[0088]

[0089] make An error feedback system can be constructed from the velocity error, and the transfer function of its linear forward element is:

[0090]

[0091] S3. Based on Popov's superstability theorem, the parameter adaptive law is derived, and the estimated resonant frequency is obtained by using the relationship between the identified parameters and the system resonant frequency.

[0092] Specifically, Popov's hyperstability theorem requires the following inequality to be satisfied:

[0093]

[0094] Therefore, the adaptive law of parameters can be derived as follows:

[0095]

[0096]

[0097] Identified parameters With the estimated resonant frequency The relationship between them is:

[0098]

[0099] Therefore, the estimated resonant frequency can be obtained as:

[0100]

[0101] The adjustable model based on model reference adaptation constructed from S1-S3 is as follows: Figure 2 As shown.

[0102] S4. Rewrite the voltage equation of the linear oscillating motor into a current state equation, construct a terminal sliding mode observer to reconstruct the back EMF information, adopt a second-order non-singular terminal sliding surface and introduce an exponential reaching law to design the control law of the observer; use the relationship between the reconstructed back EMF and the velocity to obtain the estimated velocity signal.

[0103] Specifically, the voltage equation for the linear oscillating motor is:

[0104]

[0105] The current state equation can be obtained by deformation as follows:

[0106]

[0107] Therefore, the terminal sliding mode observer can be constructed as follows:

[0108]

[0109] make The current state error equation can be obtained as follows:

[0110]

[0111] Specifically, the second-order non-singular terminal sliding surface is:

[0112]

[0113] The exponential law of convergence is:

[0114]

[0115] Based on the second-order nonsingular terminal sliding surface and the exponential reaching law, the terminal sliding mode control law can be constructed as follows:

[0116] z smo =z eq +z n

[0117] satisfy:

[0118]

[0119]

[0120] The back electromotive force reconstructed by the hybrid terminal sliding mode control law is:

[0121]

[0122] The observed velocity signal is:

[0123]

[0124] S5. A second-order generalized integrator is used to filter the speed signal estimated by the terminal sliding mode observer. The filtered speed signal is used as the reference speed of the adjustable model, and the filtered orthogonal signal is used for piston stroke closed-loop control.

[0125] Specifically, the transfer function of the second-order generalized integrator is:

[0126]

[0127] Where a is an independent variable of H(a), υ is the input signal, υ′ is the filtered signal, and ω c γ is the cutoff frequency of the second-order generalized integrator, and γ is the filter constant.

[0128] The reference model constructed from S4-S5, based on the terminal sliding mode observer and the second-order generalized integrator, is as follows: Figure 3 As shown.

[0129] Example:

[0130] This embodiment takes a stator permanent magnet type double stator linear oscillating motor as an example to simulate and verify the above method. The rated power is set to 120W, the rated operating frequency is 22.1Hz, the stator resistance is 18.4Ω, the stator inductance is 0.755H, the thrust coefficient is 47.08N / A, and the mover piston mass is 1.03kg.

[0131] Specifically, Figure 4 The simulation results for linear oscillating motor control using the traditional open-loop back EMF as the reference model are shown, where (a) represents the velocity observation results of the adjustable model, v ref Provided by the open-loop back electromotive force integration method, (b) is the error diagram of the velocity observation results, and (c) is the parameter... The tracking results are shown in Ref, which represents the parameter identification results obtained by using the velocity signal provided by the real position sensor as the input of the adjustable model; (d) represents the parameter identification error; and (e) represents the resonant frequency. The tracking results are shown in Figure 1. Ref represents the resonant frequency obtained using the velocity signal provided by the real position sensor as the input to the adjustable model, and (f) represents the resonant frequency tracking error. It can be seen that the velocity observation error of this method is 0.0351 m / s, and the parameters... Compared to the Ref, the identification error is 0.4056 Nm / s / kg, and the resonant frequency is... The tracking error is 0.1668Hz compared to Ref. Figure 5 Simulation results of a linear oscillating motor control method using a terminal sliding mode observer as the reference model are presented, where (a) shows the velocity observation results of the adjustable model, v ref Provided by the terminal sliding mode observer, (b) is the error plot of the velocity observation results, and (c) is the parameter... The tracking results are shown in Ref, which represents the parameter identification results obtained by using the velocity signal provided by the real displacement sensor as the input of the adjustable model; (d) represents the parameter identification error; and (e) represents the resonant frequency. The tracking results are shown in the figure. Ref represents the resonant frequency obtained by using the velocity signal provided by the real position sensor as the input to the adjustable model, and (f) represents the resonant frequency tracking error. It can be seen that the velocity observation error of this method is 0.0108 m / s, and the parameters... Compared to the Ref, which has an identification error of 0.0393 Nm / s / kg, the resonant frequency... The tracking error is 0.021Hz compared to Ref. The simulation results show that the proposed method has higher parameter identification accuracy and resonant frequency tracking accuracy compared to the resonant frequency tracking control method using the open-loop back EMF method as the reference model. Furthermore, the piston stroke signal obtained using the second-order generalized integrator can be used for piston stroke control, thereby achieving sensorless piston stroke closed-loop control.

[0132] In summary, the resonant frequency tracking control method based on the terminal sliding mode observer provided by this invention has higher resonant frequency tracking accuracy than the traditional resonant frequency tracking control method based on open-loop back electromotive force.

[0133] 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 linear oscillating motor control method based on hybrid terminal sliding mode, characterized in that, Includes the following steps: S1. The mechanical equations of the linear oscillating motor are transformed to obtain the velocity state equation, and an adjustable model is constructed; the constructed adjustable model is as follows: ,in For the piston mover mass, This is the electromagnetic thrust coefficient. The equivalent spring constant is... It is the equivalent damping coefficient, and and satisfy , ,in, The mechanical elasticity coefficient, The equivalent gas force elastic modulus, The mechanical damping coefficient is... This is the equivalent gas force damping coefficient. This is the piston stroke signal. This is the piston speed signal. This refers to the motor current. S2. The first-order velocity error equation is obtained through the adjustable model and the reference model, and an error feedback system is constructed; the transfer function of the linear forward element of the constructed error feedback system is: ,in, for Independent variables, , Represent , ; S3. Based on Popov's superstability theorem, the parameter adaptive law is derived, and the estimated resonant frequency is obtained by utilizing the relationship between the identified parameters and the system resonant frequency; the Popov's superstability theorem satisfies the following inequalities: The derived adaptive law for parameters is: in, , , , Represent , , , , For speed error, , Parameters Proportional gain and integral gain coefficients, , Parameters Proportional gain and integral gain coefficients, and This is the initial value for integration; The estimated resonant frequency for: ; S4. The voltage equation of the linear oscillating motor is rewritten as a current state equation. A terminal sliding mode observer is constructed to reconstruct the back electromotive force (EMF) information. A second-order non-singular terminal sliding mode surface is used, and an exponential reaching law is introduced to design the control law of the observer. The estimated speed signal is obtained by using the relationship between the reconstructed back EMF and the speed. The motor voltage equation is: The current state equation obtained by deformation is: The constructed terminal sliding mode observer is ,according to , The current state error equation is obtained as follows: ,in u This is the motor voltage. For motor resistance, For motor inductance, It is the back electromotive force. For terminal sliding mode control law; The second-order non-singular terminal sliding surface is: The exponential law of convergence is: The constructed terminal sliding mode control law is as follows: in, This is an equivalent control law. To switch control laws, the following must be satisfied: in, For design parameters, , , , This is the upper bound of the integral. For integration variables; The reconstructed back electromotive force is The estimated velocity signal is ,in The estimated back electromotive force; S5. The speed signal is filtered, and the filtered speed signal is used as the reference speed of the adjustable model. The filtered orthogonal signal is used for piston stroke closed-loop control.

2. The control method according to claim 1, characterized in that, The mechanical equation of the linear oscillating motor in step S1 is: in, Electromagnetic thrust; The velocity state equation is: in, This is the piston speed signal. , .

3. The control method according to claim 2, characterized in that, The first-order velocity error equation in step S2 is: .

4. The control method according to claim 1, characterized in that, The transfer function of the second-order generalized integrator in step S5 is: 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 linear oscillating motor control system based on hybrid terminal 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 control method based on hybrid terminal sliding mode as described in any one of claims 1 to 4.

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