Three-closed-loop voice coil motor control method based on sliding mode-active disturbance rejection technology

Abstract

The invention relates to the field of motor control, in particular to a three-closed-loop voice coil motor control method based on a sliding mode-active disturbance rejection technology, and the three-closed-loop voice coil motor control method comprises a position loop, a speed loop and a current loop. Wherein the position loop adopts an active disturbance rejection control (ADRC) method, the internal uncertainty and external disturbance of the system are estimated and compensated in real time through an extended state observer, and meanwhile, control output is quickly adjusted by using an error feedback control strategy, so that high-precision position tracking is realized; the speed ring adopts a sliding mode control strategy, and the speed signal is accurately controlled by using the characteristics of high robustness and quick response of sliding mode control, so that the dynamic performance and the anti-interference capability of speed control are enhanced; the current loop adopts a classic PI control method, so that the current of the motor can be quickly and accurately adjusted; a temperature compensation mechanism is added, electrical parameters in a system state equation are updated through a temperature-parameter model, and errors of three-closed-loop control are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and in particular to a three-closed-loop voice coil motor control method based on sliding mode-auto-disturbance rejection technology. Background Art

[0002] Voice coil motor (VCM) is a motor that converts electrical energy into linear motion using the principle of electromagnetic induction. It has been widely used in industrial automation, precision instruments, medical equipment, aerospace and other fields due to its high speed, high precision, high response speed and other characteristics. Existing motor control methods mainly include open-loop control and closed-loop control. The open-loop control method has a simple structure and low cost, but has low accuracy and cannot effectively deal with nonlinear factors such as load changes and friction. The closed-loop control method measures the actual position, speed or current of the motor and compares it with the expected value, and adjusts the control input according to the error to achieve precise control. However, traditional closed-loop control methods such as PID control are prone to overshoot, oscillation and other problems when facing rapidly changing working conditions and strong interference, affecting the stability and control accuracy of the system.

[0003] Chinese patent CN116345982A discloses a control method for a voice coil motor, which calculates the required incremental voltage value based on the speed deviation of the voice coil motor; then obtains the frequency conversion control parameter based on the incremental voltage value, and further obtains the control signal to drive the motor to rotate.

[0004] Chinese patent CN111478631B discloses a voice coil motor control system and control method for a chip placement machine, which adopts position-current dual closed-loop control for the motor driver, and performs negative feedback control on the position controller and the current controller through position feedback and current detection to achieve dual closed-loop control.

[0005] Chinese patent CN113162512B discloses a control method for a voice coil motor, which determines an inner coil current instruction by compensating a desired force instruction and a force feedback message of an actuator, thereby driving the inner coil to move.

[0006] In order to overcome the shortcomings of traditional control methods, this paper proposes a three-closed-loop voice coil motor control method based on sliding mode-anti-disturbance control technology. ADRC is applied to position loop control to improve the robustness and anti-interference ability of the system; SMC is applied to speed loop control to achieve fast response and stable control; PI control is retained as the control method of the current loop to ensure the stability and accuracy of current control; and a temperature compensation module is added to further reduce the disturbance effect of temperature on the system. The simulation results show that the proposed new method ensures the tracking accuracy of the voice coil motor while making the system more resistant to external interference and robust. Summary of the invention

[0007] The technical problem to be solved by the present invention is how to provide a voice coil motor control method with stronger anti-interference ability and robustness.

[0008] In order to solve the above technical problems, the technical solution adopted by the present invention is: a three-closed-loop voice coil motor control method based on sliding mode-auto-disturbance rejection technology, comprising the following steps:

[0009] Conducting electrical and mechanical analysis on the voice coil motor, obtaining the electrical balance equation and mechanical dynamic balance equation of the voice coil motor respectively, thereby obtaining the state space equation of the voice coil motor;

[0010] Use ADRC control optimization for the position loop, sliding mode control design for the speed loop, PI control for the current loop, and use temperature compensation mechanism to optimize the parameters in the input state equation;

[0011] The voice coil motor is controlled by the output current of the current loop.

[0012] The ADRC control strategy includes a linear differential tracker design, an extended state tracker design and a linear error feedback control rate design.

[0013] The specific design steps of the ADRC control strategy include:

[0014] 1) Design a linear differential tracker and choose a transfer function based on a second-order system:

[0015]

[0016] Where ξ is the damping coefficient, ξ=1, r is the convergence speed of the system, which can be adjusted manually;

[0017] 2) Design an extended state observer and apply it to the position loop. The state space equation of the position loop is:

[0018]

[0019] Among them, x1 and x2 are the transition value and differential value of the target value, u is the control quantity, D is the total disturbance, K is the Ampere force constant, m is the mover mass, and K f is the friction coefficient; introduce the state variable x3 except the control quantity part:

[0020]

[0021] At this time, the state space equation is:

[0022]

[0023] 3) Design a linear error feedback control law, which is expressed as:

[0024]

[0025] Among them, b0, b1, b are gain coefficients, z1, z2, z3 are the estimated values ​​of x1, x2, x3 by the extended state observer, and u1 is the input value v* of the velocity loop.

[0026] The specific steps of optimizing the sliding mode control design of the speed loop are as follows:

[0027] 1) Set the sliding surface, the formula is as follows:

[0028]

[0029] Among them, v* is the input value of the speed loop, v is the actual speed of the motor, and c1 is the control parameter;

[0030] 2) The control law is obtained by calculating the simultaneous exponential reaching laws.

[0031] The specific steps of calculating the control law by the simultaneous exponential reaching law include:

[0032] The acceleration a can be obtained by the state space equation

[0033]

[0034] The exponential approach rate is selected for sliding mode control, in which the sign function sgn(s) is optimized by the saturation function sat(s), and the formula is as follows:

[0035]

[0036] Derivative the sliding surface s and substitute the derivative of a into the calculation to obtain:

[0037]

[0038] Taking the derivative of I as the control rate u, the exponential approach rate is combined with formula (10) to obtain:

[0039]

[0040] Integrating u2 gives the output of the sliding mode controller, which is also the input i of the current loop. * ,

[0041]

[0042] Among them, ε and η are control parameters.

[0043] The current loop PI control design is optimized, and the error value between the current loop input value i* and the actual current value i is input into the PI controller to obtain the control law u3:

[0044]

[0045] Where Kp is the gain coefficient and Ti is the integration time constant.

[0046] The temperature compensation device is set for the model:

[0047] 1), establish a temperature-parameter relationship model;

[0048] 2) Update the electrical parameters in the input state.

[0049] The temperature parameter model is established:

[0050] a. Data acquisition: The temperature sensor is used to obtain electrical parameter data points at a fixed temperature difference to form a discrete data layer [L0, L1, L2, L3...L n ] and [R0, R1, R2, R3...R n ], where the subscript corresponds to a temperature interval of ΔT;

[0051] b. Data interpolation: interpolate the discrete data layer and fit it into continuous functions L(T) and R(T);

[0052] c. Series expansion: Perform Taylor series expansion on the continuous functions L(T) and R(T) to obtain the linear data layers [a1T 1 +a2T 2 +a3T 3 +......a n T n ]、[b1T 1 +b2T 2 +b3T 3 +......b n T n ];

[0053] d. Data model: Extract the first k items from the linear data layer as the temperature-inductance-resistance data model.

[0054] The temperature compensation module calculates the resistance and inductance at the current temperature through the real-time measured temperature, and updates the state equation input of the model in real time.

[0055] The beneficial effects of adopting the above technical solution are:

[0056] The present invention divides the control system of the voice coil motor into three loops, and uses the ADRC strategy to control the position loop. First, disturbance estimation and compensation are performed on it to improve the anti-interference ability and robustness of the system. The ADRC control method has the structural characteristics of not relying on the control object model and not distinguishing between internal and external disturbances of the system.

[0057] The speed loop is optimized using sliding mode control to achieve rapid response and stable control to speed changes; sliding mode control has the advantages of rapid response, insensitivity to parameter changes and disturbances, no need for system online identification, and simple physical implementation.

[0058] PI control is applied to the current loop to ensure the stability and accuracy of current control; PI control can accumulate and correct the system errors, and eventually make the steady-state error of the system approach zero, thereby achieving precise control; combining the fast response of proportional control and the ability of integral control to eliminate steady-state errors can effectively offset the impact of interference on the system, so that the system can still maintain good control performance in the presence of interference.

[0059] The present invention designs a temperature compensation module to update the resistance and inductance parameters of the input state equation, further improving the accuracy and robustness of the system, reducing the impact of temperature on the system, and providing more accurate system parameters for subsequent position loop, speed loop, and current loop control. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0061] Figure 1 The present invention proposes a three-closed-loop voice coil motor control method based on sliding mode-auto-disturbance rejection technology.

[0062] Figure 2 The present invention proposes a general block diagram of a three-closed-loop voice coil motor control method based on sliding mode-auto-disturbance rejection technology;

[0063] Figure 3 is a schematic diagram of the sliding mode control motion of the sliding mode control strategy proposed in the present invention;

[0064] Figure 4 It is a schematic diagram of the sliding surface motion points of the sliding mode control strategy proposed by the present invention;

[0065] Figure 5 It is the overall block diagram of ADRC in the control method proposed by the present invention;

[0066] Figure 6 It is a comparison diagram of the PID method, the SMC method and the method proposed by the present invention with respect to a unit step signal;

[0067] Figure 7 yes Figure 6 A partial enlarged view of part a;

[0068] Figure 8 yes Figure 6 A partial enlarged view of part b;

[0069] Fig. 9 It is a comparison diagram of the PID method, the SMC method and the method proposed by the present invention for sinusoidal signals;

[0070] Fig.10 It is a comparison diagram of the PID method, the SMC method and the method proposed by the present invention for sinusoidal signals;

[0071] Fig.11 yes Fig. 9 A partial enlarged view of part a in FIG.

[0072] Fig.12 yes Fig. 9 Figure 2. Local method diagram of part b in . DETAILED DESCRIPTION

[0073] In order to make the technical solution and advantages of the present invention clearer, the present invention is further described below. The present invention is specifically implemented according to the following steps:

[0074] The embodiment of the present invention discloses a three-closed-loop voice coil motor control method based on sliding mode-auto-disturbance rejection technology, comprising the following steps:

[0075] like Figure 1-2 First, the voice coil motor is subjected to electrical and mechanical analysis, and the electrical balance equations of the voice coil motor are obtained.

[0076]

[0077] Among them, U is the circuit voltage, R is the circuit resistance, I is the circuit current, e is the circuit back electromotive force, and L is the coil inductance.

[0078] Dynamic equilibrium equations in mechanics

[0079] FF f =ma (2)

[0080] Among them, electromagnetic force F = NBLI, B is the magnetic field strength, friction force F f =K f v, K f is the friction coefficient, and m is the mover mass.

[0081] The state space equation of the voice coil motor is obtained as follows:

[0082]

[0083] Then, ADRC control is used to optimize the position loop, SMC control is designed for the speed loop, PI control is used for the current loop, and the temperature compensation mechanism is used to optimize the parameters in the input state in real time.

[0084] The voice coil motor position loop is designed with ADRC control strategy, such as Figure 5 These include linear differential tracker design, extended state tracker design, and linear error feedback control rate design.

[0085] The specific steps include:

[0086] 1) Design a linear differential tracker. The function of the tracking differentiator is to arrange the transition process in advance for the input signal of the controlled object and extract the input signal containing random noise and its differential signal.

[0087] In order to make the target input smoother, the present invention adopts a linear tracking differentiator, the principle of which is derived from a transfer function of a second-order system, namely:

[0088]

[0089] Among them, taking ξ=1, the system can achieve the target value in one time without overshoot, and the transfer function is:

[0090]

[0091] Among them, r represents the convergence speed of the system. The larger r is, the faster the convergence speed of the system is. r can be adjusted manually. The input target value x_ref is transitioned to obtain the transition value and differential value.

[0092] 2) Design an extended state observer and apply it to the position loop. As the core component of the active disturbance rejection control, the extended state observer can track important state variables in the system to facilitate real-time understanding of the system status. On the other hand, it can also compensate for the overall amount of internal and external disturbances in the system model in a timely manner in the form of feedback, which helps to improve the robustness of the system.

[0093] Assume a second-order system:

[0094]

[0095] The state space equation is:

[0096]

[0097] The state space equation of the current system position loop is obtained as follows:

[0098]

[0099] Among them, x1 and x2 are the transition value and differential value of the target value, u is the control amount, and D is the total disturbance. At this time, equation (7) becomes:

[0100]

[0101] 3) Design a linear error feedback control law. The present invention adopts a linear error feedback control law. The difference between x1 and x2 and the estimated values ​​z1 and z2 of the ESO output is used to obtain error values ​​e1=x1-z1 and e2=x2-z2. e1 and e2 are input into the linear error feedback control law to obtain the control output u0. The control output u1 of ADRC is calculated based on u0. The expression is:

[0102]

[0103] Among them, b0, b1, b are gain coefficients, z1, z2, z3 are the ESO's estimated values ​​of x1, x2, x3, and u1 is the input value of the speed loop, set to v * .

[0104] The sliding mode control design is optimized for the speed loop. The core idea of ​​sliding mode control is to establish a sliding surface such as Figure 3 s(x)=s(x1,x2,…,x n )=0, the controller makes the system state quickly approach and keep moving on the sliding surface. The sliding surface divides the state space into two parts, upper and lower. When the system state is on both sides of the sliding surface, it corresponds to the respective control laws:

[0105]

[0106] The controlled system first moves from the initial position to the vicinity of the sliding surface according to the preset setting. When it reaches the vicinity of the sliding surface, due to the different control rates, the control system will shuttle the sliding surface in the neighborhood of the sliding surface. At this time, the system state will switch back and forth on both sides of the sliding surface. When the control system reaches the sliding surface, Figure 4 The movement modes are divided into three categories: the normal point, which is the point that the moving point needs to cross when it moves near the sliding surface; the starting point, which is the point that the moving point moves to both sides of the sliding surface when it moves near the sliding surface; and the ending point, which is the point that the moving point moves to both sides of the sliding surface when it moves near the sliding surface. In sliding mode control, the normal point and the starting point are not very meaningful, but the ending point is of great significance. Because the ending point represents the stable trend of the system state near the sliding surface, it is the key feature point to achieve stable operation of the control system. When the sliding mode controller satisfies:

[0107] ① The sliding mode exists;

[0108] ② Satisfy the reachability condition, that is, all moving points other than the sliding surface s(x) = 0 reach the sliding surface within a limited time;

[0109] ③ Under the premise of ensuring the stability of sliding mode motion, the dynamic requirements of the control system are met.

[0110] Finally, the sliding mode control law u can be obtained, thus establishing a sliding mode control system.

[0111] 1) Design a sliding surface for the speed loop. Subtract the reference signal input into the speed loop from the actual speed of the voice coil motor to obtain the speed error e = v*-v. Based on e, design a sliding surface s(x) for the sliding mode controller. The expression is:

[0112]

[0113] Among them, v* is the input value of the speed loop, v is the actual speed, and c1 is the control parameter.

[0114] 2) The control law u2 is calculated by the simultaneous exponential reaching law. The specific process is as follows:

[0115] The acceleration a can be obtained from the state space equation

[0116]

[0117] , the exponential approach rate is selected for sliding mode control, where the sign function sgn(s) is optimized using the saturation function sat(s), and the formula is as follows:

[0118]

[0119] Derivative the sliding surface s and substitute the derivative of a into the calculation to obtain:

[0120]

[0121] Taking the derivative of I as the control rate u, the exponential approach rate is combined with formula (10) to obtain:

[0122]

[0123] Integrating u2 gives the output of the sliding mode controller, which is also the input i of the current loop. * ,

[0124]

[0125] Among them, ε and η are control parameters, and sat(s) is the saturation function.

[0126] Optimize the current loop PI control design.

[0127] The input value of the current loop i *The error value with the actual current value i is input into the PI controller to obtain the control law:

[0128]

[0129] Where Kp is the gain coefficient and Ti is the integration time constant.

[0130] In view of the influence of external temperature changes on the parameters of the motor, especially the resistance and inductance, a temperature compensation mechanism is added to the system to reduce the errors caused by the changes in the resistance and capacitance parameters due to temperature in the subsequent three closed-loop control; first, a temperature-electrical parameter model is established

[0131] First, data collection is performed: the resistance and inductance data points are obtained by the temperature sensor at a fixed temperature difference to form discrete data layers [L0, L1, L2, L3...Ln] and [R0, R1, R2, R3...Rn], where the subscript corresponds to the sampling interval ΔT;

[0132] Data interpolation for discrete data layers: Interpolate discrete data layers and fit them to continuous functions L(T) and R(T), where T is a variable.

[0133] Series expansion: The continuous functions L(T) and R(T) obtained by data interpolation are expanded by Taylor series. For the inductance function L(T), its Taylor series expansion is L(T) = L(0) + a1T 1 +a2T 2 +a3T 3 +…+a n T n , where (a1, a2, a3, …, a n ) are the coefficients of the Taylor series expansion, which are related to the derivatives of the function L(T) at each order; for the resistance function R(T), the expansion is R(T) = R(0) + b1T 1 +b2T 2 +b3T 3 +…+b n T n ,(b1,b2,b3,…,b n ) are the corresponding coefficients. Through Taylor series expansion, the originally complex nonlinear function relationship is approximately expressed as a polynomial form. This polynomial form is not only convenient for mathematical analysis and processing, but also can use the characteristics of polynomials to extract and characterize the key features of data.

[0134] Data model: Using the properties of Taylor series, the first k terms of the expansion are selected as the temperature-inductance-resistance data model. Specifically, for the inductance model, it can be expressed as L(T)≈L(0)+a1T 1 +a2T 2+…+a k T k ; For the resistor model, it is expressed as R(T)≈R(0)+b1T 1 +b2T 2 +…+b k T k The k value here needs to be determined according to the accuracy requirements of the actual system and the characteristics of the data. Usually, the appropriate k value is selected by weighing the relationship between model complexity and accuracy. In general, the larger the k value, the higher the model's fitting accuracy for the original data, but at the same time the model will become more complex and the amount of calculation will increase accordingly. In practical applications, the optimal k value can be determined by comparing the prediction effects of the model under different k values ​​(such as the size of the error with the actual measured data).

[0135] The designed temperature compensation module can measure the temperature of the current environment of the motor in real time. Once the real-time temperature value is obtained, it is immediately substituted into the temperature-inductance-resistance data model constructed above to calculate the accurate resistance and inductance values ​​at the current temperature. Then, the calculated real-time resistance and inductance values ​​are used to update the input of the system state equation in real time. In the three-closed-loop control system, the state equation is a key mathematical model that describes the dynamic characteristics of the motor, and the accuracy of its input parameters directly affects the effectiveness and control accuracy of the control strategy. The real-time update of the state equation input by the temperature compensation module can effectively offset the adverse effects of changes in resistance and inductance parameters caused by temperature changes on system control, thereby ensuring that the three-closed-loop control system always maintains high control accuracy and stability under different temperature environments, so that the performance of the voice coil motor is not significantly affected by external temperature fluctuations, thereby improving the reliability and adaptability of the entire system in complex environments.

[0136] In view of the influence of inaccurate system modeling and external interference on voice coil motor control, this paper proposes an innovative three-closed-loop control method based on sliding mode-auto-disturbance rejection technology. This method uses auto-disturbance rejection control (ADRC) in the position loop to improve the robustness and anti-interference ability of the system, and sliding mode control (SMC) in the speed loop to enhance the rapid response and stability of the system. The current loop uses traditional PI control to ensure accurate current tracking, and adds a temperature compensation mechanism to reduce the interference of temperature on the system. Finally, the comparative test results with the traditional control method show that Figure 6-12 The control technology of the present invention shows significant advantages in improving position accuracy, accelerating dynamic response speed and enhancing system stability, providing strong support for high-performance control of voice coil motors.

Claims

1. A three-closed-loop voice coil motor control method based on sliding mode-auto-disturbance rejection technology, characterized in that: The following steps are involved: Conducting electrical and mechanical analysis on the voice coil motor, obtaining the electrical balance equation and mechanical dynamic balance equation of the voice coil motor respectively, thereby obtaining the state space equation of the voice coil motor; Use ADRC control optimization for the position loop, sliding mode control design for the speed loop, PI control for the current loop, and use temperature compensation mechanism to optimize the parameters in the input state equation; The voice coil motor is controlled by the output current of the current loop.

2. The three-closed-loop voice coil motor control method based on sliding mode-ADRS technology according to claim 1, characterized in that: The ADRC control strategy includes a linear differential tracker design, an extended state tracker design and a linear error feedback control rate design.

3. The three-closed-loop voice coil motor control method based on sliding mode-ADRS technology according to claim 2, characterized in that: The specific design steps of the ADRC control strategy include: 1) Design a linear differential tracker and choose a transfer function based on a second-order system: Where ξ is the damping coefficient, ξ=1, r is the convergence speed of the system, which can be adjusted manually; 2) Design an extended state observer and apply it to the position loop. The state space equation of the position loop is: Among them, x1 and x2 are the transition value and differential value of the target value, u is the control quantity, D is the total disturbance, K is the Ampere force constant, m is the mover mass, and K f is the friction coefficient; introduce the state variable x3 except the control quantity part: At this time, the state space equation is: 3) Design a linear error feedback control law, which is expressed as: Among them, b0, b1, b are gain coefficients, z1, z2, z3 are the estimated values ​​of x1, x2, x3 by the extended state observer, and u1 is the input value v* of the velocity loop.

4. The three-closed-loop voice coil motor control method based on sliding mode-ADRS technology according to claim 1, characterized in that: The sliding mode control design of the speed loop is optimized. The specific steps are as follows: 1) Set the sliding surface, the formula is as follows: Among them, v* is the input value of the speed loop, v is the actual speed of the motor, and c1 is the control parameter; 2) The control law is obtained by calculating the simultaneous exponential reaching laws.

5. The three-closed-loop voice coil motor control method based on sliding mode-ADR technology according to claim 4, characterized in that: The specific steps of calculating the control law by the simultaneous exponential reaching law include: The acceleration a can be obtained from the state space equation The exponential approach rate is selected for sliding mode control, in which the sign function sgn(s) is optimized by the saturation function sat(s), and the formula is as follows: Derivative the sliding surface s and substitute the derivative of a into the calculation to obtain: Taking the derivative of I as the control rate u, the exponential approach rate is combined with formula (10) to obtain: Integrating u2 gives the output of the sliding mode controller, which is also the input i of the current loop. * , Among them, ε and η are control parameters.

6. The three-closed-loop voice coil motor control method based on sliding mode-ADRS technology according to claim 1, characterized in that: The current loop PI control design is optimized, and the error value between the current loop input value i* and the actual current value i is input into the PI controller to obtain the control law u3: Where Kp is the gain coefficient and Ti is the integration time constant.

7. The three-closed-loop voice coil motor control method based on sliding mode-ADR technology according to claim 1, characterized in that: To set up the temperature compensation for the model: 1), establish a temperature-parameter relationship model; 2) Update the electrical parameters in the input state.

8. The three-closed-loop voice coil motor control method based on sliding mode-ADRS technology according to claim 6, characterized in that: Build the temperature parameter model: a. Data acquisition: The temperature sensor is used to obtain electrical parameter data points at a fixed temperature difference to form a discrete data layer [L0, L1, L2, L3...L n ] and [R0, R1, R2, R3...R n ], where the subscript corresponds to a temperature interval of ΔT; b. Data interpolation: interpolate the discrete data layer and fit it into continuous functions L(T) and R(T); c. Series expansion: Perform Taylor series expansion on the continuous functions L(T) and R(T) to obtain the linear data layers [a1T 1 +a2T 2 +a3T 3 +......a n T n ]、[b1T 1 +b2T 2 +b3T 3 +......b n T n ]; d. Data model: Extract the first k items from the linear data layer as the temperature-inductance-resistance data model.

9. The three-closed-loop voice coil motor control method based on sliding mode-ADRS technology according to claim 6, characterized in that: The temperature compensation module calculates the resistance and inductance at the current temperature through the real-time measured temperature, and updates the state equation input of the model in real time.

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