A nonlinear predictive position control method for dual-axis permanent magnet servo system

Abstract

The present invention discloses a nonlinear predictive position control method suitable for a dual-axis permanent magnet servo system. Considering the existence of uncertain disturbances in the dual-axis permanent magnet synchronous motor drive system, a value function and its constraints for the dual-axis permanent magnet synchronous motor drive system are constructed, the value function is solved to obtain the voltage control amount of the permanent magnet synchronous motor, and the voltage control amount of the permanent magnet synchronous motor is input to the stator voltage input terminal of the permanent magnet synchronous motor, thereby realizing the nonlinear predictive position regulation control of the dual-axis permanent magnet synchronous motor drive system. The present invention can effectively suppress the influence of parameter uncertainty disturbances on the motor position tracking of the dual-axis system by estimating the uncertain disturbances of the system by constructing a nonlinear disturbance observer, simplifying the traditional cascade controller structure, effectively reducing the amount of system calculation, and improving the dynamic response performance of the system.

Description

Technical Field

[0001] The invention relates to a control method of a permanent magnet synchronous motor, and in particular to a nonlinear predictive position control method suitable for a dual-axis permanent magnet synchronous motor. Background Art

[0002] Permanent magnet synchronous motors have the advantages of simple structure, high power density, and wide speed regulation range, and are widely used in CNC machine tool precision machining, semiconductor micromachining, robots and other applications. However, in the actual working process, due to factors such as the turning of the reference contour trajectory and the unbalanced load of the dual-axis drive motor, the performance of the dual-axis permanent magnet synchronous motor drive system deteriorates and the contour tracking accuracy decreases. Therefore, it is of great significance to study the position tracking control strategy of the permanent magnet synchronous motor to achieve efficient and stable operation of the dual-axis permanent magnet synchronous motor drive system.

[0003] In recent years, domestic and foreign scholars have conducted in-depth research on dual-axis contour control methods. Among them, model predictive control methods have been widely used in multi-motor control systems due to their advantages such as fast dynamic response speed. Reference [1], based on generalized model predictive control, adds the permanent magnet synchronous motor tracking error as the control target to the value function, solves the single-axis drive motor cascade generalized predictive controller to drive each axis motor, and combines cross-coupling control decoupling to realize the contour tracking control of the dual-axis permanent magnet synchronous motor drive system. Reference [2] combines the model predictive control method, introduces the tracking error and contour error as control targets into the value function at the same time, and solves the control law based on the optimal control theory, determines the controller structure of the system, and realizes the drive control of the dual-axis motor. However, most traditional model predictive control methods use a cascade controller structure to realize the control of the dual-axis drive motor. Its controller structure is relatively redundant and has limited dynamic response performance. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a nonlinear predictive position control method that can improve the dynamic response capability of a dual-axis drive motor and improve the contour tracking accuracy of a dual-axis permanent magnet synchronous motor drive system. The present invention has a simple structure, fast dynamic response, and high position tracking accuracy, and is of great significance for improving the dual-axis contour tracking accuracy.

[0005] The technical solution adopted by the present invention is:

[0006] Taking into account the uncertainty disturbance of the dual-axis permanent magnet synchronous motor drive system, the value function and its constraints for the dual-axis permanent magnet synchronous motor drive system are constructed, and the value function is solved to obtain the voltage control quantity of the permanent magnet synchronous motor. The voltage control quantity of the permanent magnet synchronous motor is input to the stator voltage input terminal of the permanent magnet synchronous motor, thereby realizing the nonlinear predictive position regulation control of the dual-axis permanent magnet synchronous motor drive system.

[0007] The following value function is constructed for the dual-axis permanent magnet synchronous motor drive system:

[0008]

[0009] H 1 =[1 τ],

[0010]

[0011]

[0012] Where J is the value function used by the predictive controller, T 1 、T 2 are the prediction steps of the permanent magnet synchronous motor current loop and position loop respectively; Y 1 ref , Respectively represent the reference output vector of the value function, H 1 , H 2 Respectively represent the value function weight coefficient matrix, Y 1 , Y 2 They represent the output evaluation vector of the value function, t represents the time, and τ represents the future control time domain; y 1 (t), y 2 (t) represent the first component and the second component of the actual output vector of the control system at time t respectively; They represent the first-order derivatives of the first component and the second component of the actual output vector of the control system at time t respectively; They represent the second-order derivative of the second component of the actual output vector of the control system at time t respectively; represent the first component and the second component of the reference output vector of the control system at time t respectively; represent the first-order derivatives of the first component and the second component of the reference output vector of the control system at time t respectively; They represent the second-order derivative and third-order derivative of the second component of the reference output vector of the control system at time t respectively; i di (t) They represent the actual value and reference value of the d-axis current of the two permanent magnet synchronous motors at time t, respectively. i (t) They represent the actual value and reference value of the position angle of the two permanent magnet synchronous motors at time t, respectively, and i=1, 2 represent the numbers of the two permanent magnet synchronous motors;

[0013] The above value function enables the permanent magnet synchronous motor system to track the given value as quickly as possible.

[0014] The following nonlinear constraints of the permanent magnet synchronous motor for the dual-axis system permanent magnet synchronous motor are also established under the value function:

[0015]

[0016]

[0017]

[0018] x(t)=[i di i qi ω i θ i ] T

[0019] u(t)=[u di u qi ] T

[0020] y(t)=[y 1 y 2 ] T

[0021] b(t)=[b di b qi b ωi b θi ] T

[0022] In the formula, x(t) represents the state variable at time t, represents the first-order derivative of the state variable at time t, i qi represents the actual value of the q-axis current of the two permanent magnet synchronous motors, ω i is the mechanical angular velocity of the two permanent magnet synchronous motors, u(t) represents the input vector of the motor control system at time t, and u di 、u qi Respectively represent the voltage control quantity of the d-axis and q-axis of the permanent magnet synchronous motor; b di 、b qi 、b ωi 、b θi They represent the disturbances introduced by d-axis parameter changes, q-axis parameter changes, external load changes and mechanical interference in the permanent magnet synchronous motor system; f() represents the nonlinear function of the motor control system, h() represents the output function of the motor control system, b(t) represents the uncertain disturbance vector at time t, and g 1 (), g 2 () represent the coefficient matrix functions of the input vector and the disturbance vector respectively; R s , L s , f , p, J m, B are the stator resistance, inductance, rotor permanent magnet flux, pole pair number, moment of inertia and friction coefficient of the permanent magnet synchronous motor respectively;

[0023] Then, the voltage control quantity u(t) of the permanent magnet synchronous motor is obtained by solving the value function with the goal of minimization, that is, Solve for the goal.

[0024] The voltage control amount u(t) of the permanent magnet synchronous motor is the voltage control amount u of the d-axis and q-axis. di u qi The input is input to the stator voltage input terminal of the permanent magnet synchronous motor, thereby realizing the nonlinear predictive position regulation control of the dual-axis permanent magnet synchronous motor drive system.

[0025] The uncertain disturbance b(t) is obtained by establishing a nonlinear disturbance observer.

[0026] The nonlinear disturbance observer of the present invention can realize high-precision control of trajectory tracking of a dual-axis permanent magnet synchronous motor drive system and perform real-time estimation of uncertain disturbances b(t) of the permanent magnet synchronous motor system.

[0027] The nonlinear disturbance observer is as follows:

[0028]

[0029]

[0030] q(x(t))=[l 1 i di l 2 i qi l 3 ω i l 4 θ i ] T

[0031]

[0032] In the formula, represents the perturbed observation; z and They represent the state variables and their first-order derivatives inside the nonlinear observer respectively; q() is the nonlinear function to be designed for the nonlinear observer; L is the gain matrix of the nonlinear observer; l 1 , l 2 , l 3 , l 4 They represent the first, second, third, and fourth gain coefficients of the nonlinear observer, respectively, and the gain coefficient l 1 , l 2 , l 3 , l 4>0; Respectively represent b di 、b qi 、b ωi 、b θi Observed value of

[0033] The disturbance observation value is obtained by the above nonlinear disturbance observer processing Perturb the observed value Substitute the uncertain disturbance b(t) into the value function.

[0034] The voltage control quantity u(t) of the permanent magnet synchronous motor obtained by the method is specifically calculated as:

[0035]

[0036]

[0037] K 1 =[1 0 0 0],

[0038] In the formula, G() represents the coefficient matrix related to the motor parameters in the voltage control quantity; and Represents the coefficient related to the predicted step length in the voltage control quantity; K 1 , K 2 Respectively represent the constant matrices in the voltage control quantity; represents the symbol of Lie derivative.

[0039] The characteristics and beneficial effects of the present invention are:

[0040] The method of the invention applies a nonlinear predictive control algorithm to the position control of a permanent magnet synchronous motor of a dual-axis system, and establishes an optimal control value function of the nonlinear predictive position control.

[0041] The present invention adopts a nonlinear predictive control algorithm to construct a non-cascade controller for a single-axis motor, thereby simplifying the structure of a traditional cascade controller. At the same time, the present invention adopts an optimization principle to solve a nonlinear predictive value function, which can effectively reduce the amount of system calculations, improve the system's dynamic response performance, and thereby improve the contour tracking accuracy of a dual-axis permanent magnet synchronous motor drive system.

[0042] The present invention can effectively suppress the influence of parameter uncertainty disturbance on the motor position tracking of the dual-axis system by constructing a nonlinear disturbance observer to estimate the system uncertainty disturbance. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a schematic diagram of an embodiment of a control system under the method of the present invention;

[0044] Figure 2 This is the schematic diagram of the nonlinear predictive control algorithm for a single-axis motor. DETAILED DESCRIPTION

[0045] The present invention is described in detail below in conjunction with embodiments and drawings. The specific embodiments described are only used to explain the present invention and are not intended to limit the present invention.

[0046] In view of the problems of slow dynamic response and large contour error in the traditional dual-axis contour control structure, the present invention constructs a cascaded single-loop nonlinear predictive position controller based on the nonlinear predictive control algorithm, thereby improving the dynamic response performance of the system. At the same time, a nonlinear disturbance observer is constructed to observe uncertainty disturbances such as system parameter mismatch and load mutation, so as to suppress the impact of system uncertainty disturbances. In addition, in order to coordinate the control of the two axes, the position correction link is combined to realize the compensation of the given position of the dual-axis drive motor.

[0047] The specific implementation of the present invention is as follows:

[0048] Figure 1 This is a system block diagram of the nonlinear predictive position control method for a dual-axis permanent magnet synchronous motor drive system according to the present invention. are the given values ​​of the x-axis and y-axis motor rotor positions, θ x ,θ y are the actual values ​​of the x-axis and y-axis motor rotor positions, ω x ,ω y are the mechanical angular velocities of the x-axis and y-axis motors, are the given currents of the x-axis and y-axis motors, i dx 、i dy are the actual values ​​of the d-axis current of the x-axis and y-axis motors, respectively. qx 、i qy They are the actual values ​​of the x-axis and y-axis motor q-axis currents, are the disturbance observation values ​​of the x-axis and y-axis motors, θ cx ,θ cy is the given position correction value output by the cross-coupling control structure; p* and p are the given position and actual position matrices of the dual-axis system respectively; C x , C y is the contour error compensation coefficient of each axis; C c is the cross-coupling controller gain coefficient; ε is the dual-axis contour error.

[0049] The following value function is constructed for the dual-axis permanent magnet synchronous motor drive system:

[0050]

[0051] H 1 =[1 τ],

[0052]

[0053]

[0054] The following nonlinear constraints of the permanent magnet synchronous motor for the dual-axis system permanent magnet synchronous motor are also established under the value function:

[0055]

[0056]

[0057]

[0058] x(t)=[i di i qi ω i θ i ] T

[0059] u(t)=[u di u qi ] T

[0060] y(t)=[y 1 y 2 ] T

[0061] b(t)=[b di b qi b ωi b θi ] T

[0062] The uncertain disturbance b(t) is obtained by establishing a nonlinear disturbance observer. The nonlinear disturbance observer is as follows:

[0063]

[0064]

[0065] q(x(t))=[l 1 i di l 2 i qi l 3 ω i l 4 θ i ] T

[0066]

[0067] The disturbance observation value is obtained by the above nonlinear disturbance observer processing Perturb the observed value Substitute the uncertain disturbance b(t) into the value function.

[0068] Then, the voltage control quantity u(t) of the permanent magnet synchronous motor is obtained by solving the value function with the goal of minimization, that is, Solve for the goal.

[0069] The voltage control quantity u(t) of the permanent magnet synchronous motor finally obtained is calculated as follows:

[0070]

[0071]

[0072] K 1 =[1 0 0 0],

[0073] The voltage control amount u(t) of the permanent magnet synchronous motor is the voltage control amount u of the d-axis and q-axis. di u qi The input is input to the stator voltage input terminal of the permanent magnet synchronous motor, thereby realizing the nonlinear predictive position regulation control of the dual-axis permanent magnet synchronous motor drive system.

[0074] Figure 2 The schematic diagram of the nonlinear predictive position algorithm for a single-axis motor is shown in Figure 2. The specific implementation of the nonlinear predictive position control process uses the permanent magnet synchronous motor d-axis current given value. The control mode is used to set the mechanical rotor position angle of each axis motor corresponding to the given contour trajectory of the dual-axis permanent magnet synchronous motor drive system. As the given input of the nonlinear predictive position controller, the permanent magnet synchronous motors of each axis are controlled in combination with the nonlinear disturbance observer.

[0075] The present invention is described above in conjunction with the drawings, but the present invention is not limited to the above-mentioned specific embodiments. The above-mentioned specific embodiments are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many modifications without departing from the purpose of the present invention, which are all protected by the present invention.

Claims

1. A nonlinear predictive position control method suitable for a dual-axis permanent magnet servo system, characterized in that: Methods include: The dual-axis permanent magnet servo system is a dual-axis permanent magnet synchronous motor drive system. Considering the existence of uncertainty disturbance in the dual-axis permanent magnet synchronous motor drive system, a value function and its constraints for the dual-axis permanent magnet synchronous motor drive system are constructed, the value function is solved to obtain the voltage control amount of the permanent magnet synchronous motor, and the voltage control amount of the permanent magnet synchronous motor is input to the stator voltage input terminal of the permanent magnet synchronous motor, thereby realizing the nonlinear prediction position adjustment control of the dual-axis permanent magnet synchronous motor drive system; The following value function is constructed for the dual-axis permanent magnet synchronous motor drive system: H1=[1 t], Among them, J is the value of the value function, T1 and T2 are the prediction steps of the permanent magnet synchronous motor current loop and position loop respectively; Y1 ref 、Y2 ref They represent the reference output vector of the value function, H1 and H2 represent the weight coefficient matrix of the value function, Y1 and Y2 represent the output evaluation vector of the value function, t represents the time, and t represents the future control time domain; y1(t) and y2(t) represent the first component and the second component of the actual output vector of the control system at time t, respectively; They represent the first-order derivatives of the first component and the second component of the actual output vector of the control system at time t respectively; They represent the second-order derivative of the second component of the actual output vector of the control system at time t respectively; represent the first component and the second component of the reference output vector of the control system at time t respectively; represent the first-order derivatives of the first component and the second component of the reference output vector of the control system at time t respectively; They represent the second-order derivative and third-order derivative of the second component of the reference output vector of the control system at time t respectively; i di (t) They represent the actual value and reference value of the d-axis current of the two permanent magnet synchronous motors at time t, respectively. i (t) They represent the actual value and reference value of the position angle of the two permanent magnet synchronous motors at time t, respectively, and i=1, 2 represent the numbers of the two permanent magnet synchronous motors; The following nonlinear constraints of the permanent magnet synchronous motor are also established under the value function: x(t)=[i di i qi ω i θ i ] T u(t)=[u di u qi ] T y(t)=[y1 y2] T b(t)=[b di b qi b ωi b θi ] T In the formula, x(t) represents the state variable at time t, represents the first-order derivative of the state variable at time t, i qi represents the actual value of the q-axis current of the two permanent magnet synchronous motors, ω i is the mechanical angular velocity of the two permanent magnet synchronous motors, u(t) represents the input vector of the motor control system at time t, and u di 、u qi Respectively represent the voltage control quantity of the d-axis and q-axis of the permanent magnet synchronous motor; b di , b qi , b ωi , b θi They represent the disturbances introduced by d-axis parameter changes, q-axis parameter changes, external load changes and mechanical interference in the permanent magnet synchronous motor system respectively; f() represents the nonlinear function of the motor control system, h() represents the output function of the motor control system, b(t) represents the uncertain disturbance vector at time t, g1() and g2() represent the coefficient matrix functions of the input vector and the disturbance vector respectively; R s , L s ,y f , p, J m , B are the stator resistance, inductance, rotor permanent magnet flux, pole pair number, moment of inertia and friction coefficient of the permanent magnet synchronous motor respectively; Then, the voltage control value u(t) of the permanent magnet synchronous motor is obtained by solving the value function with the goal of minimization.

2. The nonlinear predictive position control method for a dual-axis permanent magnet servo system according to claim 1, characterized in that: The voltage control amount u(t) of the permanent magnet synchronous motor is the voltage control amount u of the d-axis and q-axis. di u qi The input is input to the stator voltage input terminal of the permanent magnet synchronous motor, thereby realizing the nonlinear predictive position regulation control of the dual-axis permanent magnet synchronous motor drive system.

3. The nonlinear predictive position control method for a dual-axis permanent magnet servo system according to claim 1, characterized in that: The uncertain disturbance b(t) is obtained by establishing a nonlinear disturbance observer.

4. The nonlinear predictive position control method for a dual-axis permanent magnet servo system according to claim 3, characterized in that: The nonlinear disturbance observer is as follows: q(x(t))=[l1i di l2i qi l3ω i l4θ i ]] T In the formula, represents the perturbed observation; z and They represent the state variables and their first-order derivatives inside the nonlinear observer respectively; q() is the nonlinear function to be designed for the nonlinear observer; L is the gain matrix of the nonlinear observer; l1, l2, l3, l4 represent the first, second, third, and fourth gain coefficients of the nonlinear observer respectively, and the gain coefficients l1, l2, l3, l4>0; Respectively represent b di , b qi , b ωi , b θi Observed value of The disturbance observation value is obtained by the above nonlinear disturbance observer processing Perturb the observed value Substitute the uncertain disturbance b(t) into the value function.

5. The nonlinear predictive position control method for a dual-axis permanent magnet servo system according to claim 4, characterized in that: The voltage control quantity u(t) of the permanent magnet synchronous motor obtained by the method is specifically calculated as: K1＝[1 0 0 0]， In the formula, G() represents the coefficient matrix related to the motor parameters in the voltage control quantity; and Represents the coefficient related to the prediction step length in the voltage control quantity; K1 and K2 respectively represent the constant matrix in the voltage control quantity.

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