A time optimal control method and system for a multi-motor servo system

Abstract

This invention discloses a time-optimal control method and system for a multi-motor servo system. The time-optimal control method for a multi-motor servo system features high control efficiency and precision, enabling the system to quickly reach a stable state. First, the state parameters of the multi-motor servo system are acquired. Then, the position and speed of the motors, as well as the position and speed of the load, are input into a first-order disturbance observer. Auxiliary variables are used to update and determine the estimated system disturbance. Based on the estimated disturbance, a time-optimal controller for the multi-motor servo system is constructed. The time-optimal controller is then used to control the multi-motor servo system.

Description

Technical Field

[0001] This invention relates to the field of electromechanical control technology, specifically to a time-optimal control method and system for a multi-motor servo system. Background Technology

[0002] A multi-motor linkage system consists of several motors that share load torque. This configuration is less expensive than a set of single-motor drives because some resources are shared among the units. Furthermore, it is easily expandable by adding new units compared to a single drive, and the inherent redundancy can be used to mitigate the effects of certain types of converter and motor failures.

[0003] Multi-motor drives are the optimal solution for high-inertia and high-power drives, such as belt conveyors and long, continuous production lines. In recent years, the application of multi-motor drives in electric vehicles and robotic manipulators has increased significantly. Control objectives are defined according to the drive application. Clearly, control objectives vary greatly depending on the drive application. For example, the primary objective of drive control for continuous production lines is decoupled tracking of speed and tension. On the other hand, in electric vehicles, the primary objective of drive control is speed control and torque distribution to ensure the stability of such vehicles. The drive accuracy and efficiency of multi-motor systems are also important requirements in industrial and transportation applications.

[0004] The development of multi-motor system control begins with selecting the relationships between motor drive units and determining the number and type of feedback and controllers—that is, establishing a multi-motor control strategy. The next step is to develop and implement control algorithms, which will ensure the system's stability and expected behavior. Various control algorithms have been developed for multi-motor system control, such as classic proportional-integral-derived (PID) control, optimal control, and artificial intelligence-based control methods.

[0005] While the tracking performance of a single motor can be improved by applying the aforementioned control strategies, good tracking performance for each motor does not guarantee a reduction in synchronization errors across multiple motors. Therefore, high synchronization accuracy between motors is crucial for system reliability and product quality, leading to the development of numerous synchronization control methods for multi-motor systems in recent years. Among these methods, concurrent control and master-slave or subordinate control methods struggle to guarantee ideal synchronization accuracy under conditions of disturbance and drive dynamic mismatch. In contrast, coupling-based frameworks are popular in academia and engineering. Techniques such as deviation coupling, cross coupling, adjacent cross coupling, and ring coupling have been proposed and applied, demonstrating better synchronization accuracy than other strategies. However, existing control algorithms do not consider the time required to achieve control, focusing only on drive accuracy while neglecting drive efficiency.

[0006] Therefore, designing a controller that enables a multi-motor servo system to quickly reach a stable state is a technical challenge that urgently needs to be solved in the current technology. Summary of the Invention

[0007] In view of this, the present invention provides a time-optimal control method and system for a multi-motor servo system, which has the characteristics of high control efficiency and precise control, and enables the multi-motor servo system to quickly reach a stable state.

[0008] To achieve the above objectives, the technical solution of the present invention is: a time-optimal control method for a multi-motor servo system, wherein the multi-motor servo system includes two or more motors and one load, and the time-optimal control method includes the following steps:

[0009] Obtain the status parameters of the multi-motor servo system.

[0010] The position and speed of the motor, as well as the position and speed of the load, are input into a first-order disturbance observer. The system disturbance estimate is then updated and determined using auxiliary variables.

[0011] Based on the estimated system disturbance, a time-optimal controller for the multi-motor servo system is constructed.

[0012] A time-optimized controller is used to control the multi-motor servo system.

[0013] Furthermore, the state parameters include the position and speed of the motor and the position and speed of the load.

[0014] Furthermore, after obtaining the state parameters of the multi-motor servo system, the following steps are also included:

[0015] A multi-motor servo system includes a load subsystem and a motor subsystem.

[0016] The state-space equations of the multi-motor servo system are constructed based on the state parameters; the state-space equations are:

[0017]

[0018]

[0019] in, For load vector, Where x1 and x2 represent the position and velocity of the load, respectively; z i Let z be the vector corresponding to motor i. i =[x 3i ,x 4i ] T , where x 3i ,x 4iLet A1, A2, B1, B2, C1, and C2 represent the position and velocity of motor i, respectively. The six coefficient matrices in the state equation are A1, A2, B1, B2, C1, and C2, where... C1 = C2 = [1 0] T ; y1 represents the output of the load subsystem; y 2i Indicates the output of the motor subsystem; d1 represents the virtual control input of the load subsystem; d2 represents the nonlinear disturbance of the load subsystem. d 2i For the nonlinear disturbance of the motor subsystem, d 2i =f mi (x 4i )+γ1(x 3i -x1)+γ2(x 4i -x2)+(-1) i ω i -ψ i γ1 is the torque coefficient, γ2 is the damping coefficient, and f l For the unknown friction at the load end, f mi For the unknown friction of the i-th motor, ω i ψ is the bias torque at the motor end. i For the nonlinear part that transmits torque, u i J is the time-optimal control input. m J is the moment of inertia of the motor. l Let l be the moment of inertia of the load, m be the motor, i be the motor number, and n be the total number of motors in the multi-motor servo system.

[0020] Furthermore, the system disturbance estimates include: disturbance estimates for the motor subsystem. and load subsystem disturbance estimates

[0021] Furthermore, the position and speed of the motor, as well as the position and speed of the load, are input into the first-order disturbance observer. The system disturbance estimate is then updated and determined using auxiliary variables, specifically:

[0022] The first-order perturbation observer used is:

[0023]

[0024] in This is an estimate of the nonlinear disturbance d1 of the load subsystem; For the nonlinear disturbance d of the motor subsystem 2i The estimated value; the two weight matrices of the perturbation observer are L1 and L2, where L1 = [0, l1]. T And L2 = [0, l2] Tl1 and l2 are adjustable positive numbers, α1 and α 2i These are the introduced auxiliary variables, α1 and α 2i The update law is:

[0025]

[0026] in It is the updated α1. It is the updated α 2i ;

[0027] Based on the constructed first-order disturbance observer, the system disturbance estimate is updated and determined using auxiliary variables.

[0028] Furthermore, based on the estimated system disturbance values, a time-optimal controller for the multi-motor servo system is constructed, including:

[0029] Based on the estimated disturbance values ​​of the load subsystem Constructing an integral sliding mode tracking controller for a multi-motor servo system, the virtual control input η of the load subsystem is obtained as follows:

[0030]

[0031] Among them, y d It is the tracking reference signal, s is the integral sliding surface, and k p The control gain is set, and k1 and k2 are two constant parameters.

[0032] Based on the disturbance estimate of the motor subsystem Based on the virtual control input η of the load subsystem, a time-optimal synchronous controller for the multi-motor servo system is constructed, the structure of which is as follows:

[0033]

[0034] Among them, u i e is the time-optimal control input for the i-th motor. i Let h(e) be the synchronization error of the i-th motor. t ) is a piecewise function. e i For synchronization error, ε is the width of the linear control region, m1 and m2 are both set control coefficients, and k s The coefficients set are m1, m2, and k. s Adjust according to the final control effect; u m To control the maximum amplitude of the input.

[0035] Beneficial effects:

[0036] 1. The time-optimal control method for a multi-motor linkage system provided by the present invention obtains the structural parameters of the multi-motor servo system, inputs them into a first-order disturbance observer, updates and determines the estimated value of the system disturbance based on the auxiliary variables, and then constructs a time-optimal controller for the multi-motor servo system based on the disturbance estimate. The time-optimal controller is then used to precisely control the multi-motor servo system so that the multi-motor servo system can quickly reach a stable state.

[0037] 2. The unknown nonlinearities such as backlash and friction in multi-motor drive servo systems can adversely affect the control performance of the system. In order to solve this problem, this invention treats the system nonlinearity as a disturbance and designs a first-order disturbance observer to estimate the total disturbance of the load subsystem and the motor subsystem, effectively compensating for the system nonlinearity.

[0038] 3. This invention addresses the motor synchronization problem in multi-motor driven servo systems by designing an approximately time-optimal synchronization controller. This controller enables rapid synchronization between motors, ensuring optimal system response time. Furthermore, a linear element is introduced into the synchronization controller. When the synchronization error is less than a threshold, linear control is implemented to reduce chattering and improve system robustness.

[0039] 4. This invention introduces virtual control quantities and designs an integral sliding mode tracking controller for multi-motor servo systems. At the same time, it designs a synchronization error to ensure that the motor position is synchronized to the virtual tracking signal. Through the synchronization controller, load tracking and motor synchronization are realized simultaneously, eliminating the coupling effect between synchronization and tracking. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the multi-motor servo system on which the present invention is based;

[0041] Figure 2 This is a flowchart of the time-optimal control method for a multi-motor servo system provided in an embodiment of the present invention;

[0042] Figure 3 This is a schematic diagram of the structure of the time-optimal control system of the multi-motor linkage system provided in an embodiment of the present invention. Detailed Implementation

[0043] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0044] The purpose of this invention is to provide a time-optimal control method for a multi-motor linkage system, which features high control efficiency and precise control, enabling the multi-motor servo system to quickly reach a stable state.

[0045] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] The specific structure of existing multi-motor servo systems is as follows: Figure 1 As shown. The control method disclosed in this invention is a time-optimal control method for a multi-motor linkage system built upon the above-described multi-motor servo system structure. Figure 2 As shown, the time-optimal control method for this multi-motor linkage system includes:

[0047] S100. Obtain the status parameters of the multi-motor servo system; the status parameters include: the position and speed of the motors and the position and speed of the load.

[0048] This invention also constructs the state equations of a multi-motor servo system based on state parameters.

[0049] The state equations for a multi-motor servo system are constructed based on the state parameters, specifically including:

[0050] Based on the structure and physical characteristics of the multi-motor servo system, a mathematical model of the multi-motor servo system is constructed. The mathematical model is as follows:

[0051]

[0052] Where, θ mi θ represents the angular position of the i-th motor. l Indicates the angular position of the load. This represents the angular velocity of the i-th motor. Indicates the angular velocity of the load. This represents the angular acceleration of the i-th motor. J represents the angular acceleration of the load. m J represents the moment of inertia of the i-th motor. l The moment of inertia of the load, f mi f represents the unknown friction at the motor end. l ω represents the unknown friction at the load end. i δ represents the bias torque applied to the motor terminals. i u represents the torque transmitted between the i-th motor and the load. i The input torque is limited in magnitude, and the limiting function is expressed as follows:

[0053]

[0054] Among them, u m To control the maximum amplitude of the input.

[0055] Due to the influence of backlash during motor transmission, the expression for the transmitted torque is as follows:

[0056]

[0057] Among them, h i =θ mi -θ l γ1 represents the torque coefficient, and γ2 represents the damping coefficient. β represents the tooth gap width, and β is a positive constant.

[0058] Define the state variables of the motor servo system as follows: Combining formulas (1) and (3), the state equation of the multi-motor servo system can be obtained as follows:

[0059]

[0060] in,

[0061] Based on (4), the state-space equation of the system can be obtained.

[0062]

[0063]

[0064] in, z i =[x 3i ,x 4i ] T , C1 = C2 = [1 0] T y1 and y 2i These represent the outputs of the load subsystem and the motor subsystem, respectively. d1 represents the virtual control input of the load subsystem, and d1 represents the nonlinearity of the load subsystem. d 2i For the nonlinearity of the motor subsystem, d 2i =f mi (x 4i )+γ1(x 3i -x1)+γ2(x 4i -x2)+(-1) i ω i -ψ i γ1 is the torque coefficient, γ2 is the damping coefficient, and f l For the unknown friction at the load end, f mi For the unknown friction of the i-th motor, u i J is the time-optimal control input. m J is the moment of inertia of the motor. l Let l be the moment of inertia of the load, l be the load, and m be the motor.

[0065] The complex frictional nonlinearity and dead-zone nonlinearity in multi-motor servo systems can severely impact system performance and even cause instability, especially at low speeds. Therefore, the unknown nonlinearity of the multi-motor servo system is treated as a bounded disturbance, and a first-order disturbance observer is designed to estimate the unknown disturbance in order to eliminate the adverse effects of the unknown nonlinearity on system performance.

[0066] S101. Input the position and velocity of the motor and load into the first-order disturbance observer, and use auxiliary variables to update and determine the estimated values ​​of the disturbance of the multi-motor system. The estimated values ​​include: motor disturbance estimate and load disturbance estimate.

[0067] Unknown nonlinearities such as backlash and friction in multi-motor drive servo systems can adversely affect the system's control performance. To address this issue, this invention treats system nonlinearity as a disturbance and designs a first-order disturbance observer to estimate the total disturbance of the load subsystem and motor subsystem, effectively compensating for system nonlinearity.

[0068] The first-order perturbation observer used in S101 has the following structural design:

[0069]

[0070] in and d1 and d 2i The estimated values ​​are given by L1 and L2, which are the weight matrices of the perturbation observer, where L1 = [0, l1]. T And L2 = [0, l2] T l1 and l2 are adjustable positive numbers, α1 and α 2i These are the introduced auxiliary variables, and their update law is designed as follows:

[0071]

[0072] S102. Based on the estimated system disturbance, construct the time-optimal controller for the multi-motor servo system; specifically including:

[0073] Based on the different motors and loads, multi-motor servo systems are divided into load subsystems and motor subsystems.

[0074] Based on the estimated disturbance values ​​of the load subsystem, an integral sliding mode tracking controller for a multi-motor servo system is constructed. This invention introduces virtual control quantities to design an integral sliding mode tracking controller, and simultaneously designs a synchronization error mechanism to ensure that the motor position is synchronized to the virtual tracking signal. Through the synchronization controller, load tracking and motor synchronization are simultaneously achieved, eliminating the coupling effect between synchronization and tracking.

[0075] Based on the disturbance estimate of the motor subsystem and the virtual tracking control input, a time-optimal synchronous controller for the multi-motor servo system is constructed.

[0076] The specific process is as follows:

[0077] Define the system's tracking error and integral sliding surface as follows:

[0078] e p =y1-y d (9)

[0079]

[0080] Where y d It is a tracking reference signal, k1 and k2 are positive constants, e p (0) and These are the position tracking errors e p and speed tracking error The initial value.

[0081] Combining the perturbation observer and Lyapunov stability theory, a virtual tracking controller is designed as follows:

[0082]

[0083] Where, k p It is a normal number.

[0084] Then, according to the definition of virtual control input The synchronization error is defined as follows:

[0085]

[0086] Where a ij Both ι and ι are positive numbers.

[0087] Based on the minimum value theory, the approximate time-optimal synchronization control can be obtained as follows:

[0088]

[0089]

[0090] Where m1, m2 and k s All are positive constants and 0 < k s ≤1, where ε represents the width of the linear control region.

[0091] This invention addresses the motor synchronization problem in multi-motor driven servo systems by designing an approximately time-optimal synchronization controller. This controller enables rapid synchronization between motors, ensuring optimal system response time. Furthermore, a linear element is introduced into the synchronization controller. When the synchronization error is less than a threshold, linear control is implemented to reduce chattering and improve system robustness.

[0092] S103. A time-optimized controller is used to control the multi-motor servo system.

[0093] During the control of a four-motor servo system using the time-optimal control method for multi-motor servo systems provided by this invention, y d =2sin(2πt / 10) is the tracking reference signal. The parameters of the motor, load, and backlash are shown in Table 1.

[0094] Table 1

[0095]

[0096] The time-optimal control method for multi-motor servo systems disclosed in this invention can track targets quickly and accurately. Furthermore, the synchronous controller designed based on an approximate time-optimal strategy ensures rapid synchronization of the multiple motors, thereby significantly improving the tracking accuracy and response speed of the entire multi-motor servo system.

[0097] Figure 3 This is a schematic diagram of the structure of the time-optimal control system of the multi-motor linkage system provided in an embodiment of the present invention.

[0098] To address the time-optimal control method for the aforementioned multi-motor servo system, the following system is constructed:

[0099] It includes a state parameter acquisition module, a disturbance estimation module, a time-optimal controller construction module, and a multi-motor servo system control module.

[0100] The status parameter acquisition module is used to acquire the status parameters of the multi-motor servo system.

[0101] The disturbance estimation determination module is used to input the position and speed of the motor and the position and speed of the load into the first-order disturbance observer, and update and determine the system disturbance estimate using auxiliary variables.

[0102] The time-optimal controller construction module is used to construct a time-optimal controller for a multi-motor servo system based on the estimated system disturbance values.

[0103] The multi-motor servo system control module is used to control the multi-motor servo system using a time-optimized controller.

[0104] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., 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 time optimal control method of a multi-motor servo system, wherein the multi-motor servo system includes two or more motors and a load, characterized by, The time optimal control method comprises the following steps: acquiring state parameters of a multi-motor servo system; inputting the position and speed of the motor and the position and speed of the load into a first-order disturbance observer, updating and determining a system disturbance estimation value by using an auxiliary variable; constructing a time optimal controller of the multi-motor servo system according to the system disturbance estimation value; controlling the multi-motor servo system by using the time optimal controller; the state parameters comprise the position and speed of the motor and the position and speed of the load; after the step of acquiring the state parameters of the multi-motor servo system, the following step is further included: the multi-motor servo system comprises a load subsystem and a motor subsystem; constructing a state space equation of the multi-motor servo system according to the state parameters; the state space equation is: wherein, is the load vector, wherein x1, x2 represent the position and velocity of the load respectively; z i is the motor i corresponding vector, z i = [x 3i , x 4i ] T wherein x 3i , x 4i represent the position and velocity of the motor i respectively, the six coefficient matrices in the state equation are A1, A2, B1, B2, C1 and C2 respectively, wherein C1 = C2 = [1 0] T ; y1 represents the output of the load subsystem; y 2i represents the output of the motor subsystem; is the virtual control input of the load subsystem; d1 is the nonlinear disturbance of the load subsystem, d 2i is the nonlinear disturbance of the motor subsystem, d 2i = f mi (x 4i ) + γ1(x 3i -x1) + γ2(x 4i -x2) + (-1) i ω i -ψ i , γ1 is the torque coefficient, γ2 is the damping coefficient, f l is the unknown friction at the load end, f mi is the unknown friction of the i-th motor, ω i is the bias torque at the motor end, ψ i is the nonlinear part of the transmission torque, u i is the time optimal control input, J m is the moment of inertia of the motor, J l is the moment of inertia of the load, l is the load, m is the motor, i is the motor serial number, and n is the total number of motors in the multi-motor servo system.

2. The time optimal control method of a multi-motor servo system according to claim 1, wherein The system disturbance estimate includes: motor subsystem disturbance estimate and load subsystem disturbance estimate 3. The time optimal control method of a multi-motor servo system according to claim 2, wherein the step of inputting the position and speed of the motor and the position and speed of the load into a first-order disturbance observer, updating and determining a system disturbance estimation value by using an auxiliary variable is specifically as follows: the first-order disturbance observer used is: in This is an estimate of the nonlinear disturbance d1 of the load subsystem; For the nonlinear disturbance d of the motor subsystem 2i The estimated value; the two weight matrices of the perturbation observer are L1 and L2, where L1 = [0, l1]. T And L2 = [0, l2] T l1 and l2 are adjustable positive numbers, α1 and α 2i These are the introduced auxiliary variables, α1 and α 2i The update law is: wherein is the updated a1, is the updated a 2i ; updating and determining a system disturbance estimation value by using an auxiliary variable according to the constructed first-order disturbance observer.

4. The time optimal control method of a multi-motor servo system according to claim 2, wherein the step of constructing a time optimal controller of the multi-motor servo system according to the system disturbance estimation value comprises: According to the load subsystem disturbance estimation value The integral sliding mode tracking controller of the multi-motor servo system is constructed, and the virtual control input η of the load subsystem is obtained: wherein y d is a tracking reference signal, s is an integral sliding surface, k p is a set control gain, and k1 and k2 are two set constant parameters. According to the motor subsystem disturbance estimate and the virtual control input η of the load subsystem, a time-optimal synchronous controller of the multi-motor servo system is constructed, which structure is wherein u i is the time-optimal control input of the i-th motor, e i is the synchronization error of the i-th motor, h(e t ) is a piecewise function, e i is the synchronization error, ε is the width of the linear control region, m1 and m2 are both control coefficients set, k s is a set coefficient, the coefficients m1, m2 and k s are adjusted according to the final control effect; u m is the maximum amplitude of the control input.

5. A time optimal control system for a multi-motor servo system, characterized by, for the time optimal control method of the multi-motor servo system as claimed in any one of claims 1 to 4, the following system is constructed: comprising a state parameter acquisition module, a disturbance estimation value determination module, a time optimal controller construction module and a multi-motor servo system control module; the state parameter acquisition module is used for acquiring state parameters of a multi-motor servo system; the disturbance estimation value determination module is used for inputting the position and speed of the motor and the position and speed of the load into a first-order disturbance observer, updating and determining a system disturbance estimation value by using an auxiliary variable; the time optimal controller construction module is used for constructing a time optimal controller of the multi-motor servo system according to the system disturbance estimation value; the multi-motor servo system control module is used for controlling the multi-motor servo system by using the time optimal controller.

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