A Method for Synchronous Control of a Dual-Motor Drive System Based on an Adaptive Disturbance Observer

Abstract

The present invention discloses a method for synchronous control of a dual-motor drive system based on an adaptive disturbance observer. The specific steps include: constructing the dynamic equation of a permanent magnet synchronous motor; according to the dynamic equation, redefining the state variables of the permanent magnet synchronous motor and rewriting them into a standard state equation; according to the standard state equation, introducing a sliding mode variable, and designing an adaptive disturbance observer in combination with an adaptive law to accurately estimate the disturbance; feeding back the observation result to the controller for disturbance compensation, designing a multi-sliding surface controller for a single-motor speed control system, and performing synchronous control of the dual motors. The adaptive disturbance observer adopted in the present invention combines the sliding mode control technology, effectively solves the problems of nonlinearity, model uncertainty, and external disturbance existing in the dual-motor drive system, thereby significantly improving the stability and robustness of the system, maintaining the stable operation of the system under a wider range of operating conditions, and reducing the risk of performance degradation of the system caused by disturbances.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor drive, and particularly relates to a method for synchronous control of a dual-motor drive system based on an adaptive disturbance observer. Background Art

[0002] At present, the research on multi-motor speed synchronization systems mainly focuses on two aspects: control strategies and control structures. In terms of control strategies, the traditional PID (Proportional Integral Derivative) control system has a simple structure, is easy to adjust, and is widely used. However, due to the inherent nonlinear and strong coupling characteristics of the permanent magnet synchronous motor servo system, and the fact that there are often strong external disturbances and parameter uncertainties during operation, for application scenarios with high performance and accuracy requirements, relying solely on PID control is difficult to meet the high-performance control. Therefore, many modern control methods have been applied to the field of motor control, such as sliding mode control, adaptive control, optimal control, etc., which have improved the control performance of permanent magnet synchronous motors from different aspects. Among them, sliding mode control has good robustness to disturbances and uncertainties and is widely used in motor control.

[0003] The basic idea of sliding mode control is to design a sliding surface and a control law so that the system state can quickly reach and stay on the sliding surface, thereby achieving precise control of the system state. However, the existing sliding mode control has the following disadvantages:

[0004] (1) Dependence on model accuracy: Existing control methods often rely on accurate mathematical models, but the actual dual-motor drive system may have complex nonlinear characteristics and uncertainties, which makes it difficult for traditional control strategies to achieve the expected performance in practical applications.

[0005] (2) Insufficient robustness to external disturbances: Although the sliding mode control method can improve the robustness of the system to disturbances, when there are unknown matching disturbances, the control effect of the existing technology may be affected, resulting in a decline in system performance.

[0006] (3) Trade-off between control accuracy and response speed: When improving control accuracy, the response speed of the system often needs to be sacrificed, and vice versa. It is difficult for the existing technology to achieve fast dynamic response while ensuring high precision.

[0007] (4) Difficulty in adjusting control parameters: Many existing control strategies require careful adjustment of control parameters to adapt to specific working conditions. This process is both time-consuming and requires professional knowledge, and once the working conditions change, the parameters may need to be readjusted. Summary of the Invention

[0008] To make up for the deficiencies of the existing technology, the present invention aims to provide a method for synchronous control of a dual-motor drive system based on an adaptive disturbance observer. Based on the cross-coupling structure and the sliding mode control method, the synchronous control ability of the system is improved by using speed synchronization.

[0009] The technical problems solved by the present invention can be realized through the following technical solutions:

[0010] The method for synchronous control of a dual-motor drive system based on an adaptive disturbance observer specifically includes the following steps:

[0011] Step 1: Construct the dynamic equation of the permanent magnet synchronous motor;

[0012] Step 2: According to the dynamic equation in Step 1, redefine the state variables of the permanent magnet synchronous motor and rewrite them into the standard state equation;

[0013] Step 3: According to the standard state equation in Step 2, introduce the sliding mode variable, design an adaptive disturbance observer in combination with the adaptive law, and accurately estimate the disturbance;

[0014] Step 4: Feed back the observation result in Step 3 to the controller for disturbance compensation, design a multiple sliding surface controller for the single-motor speed control system, and perform synchronous control of the dual motors.

[0015] Further, the dynamic equation in Step 1 is:

[0016] (1)

[0017] where i = 1, 2 represents two driving motors; are the angular positions of the two driving motors, are the angular accelerations of the two driving motors, are the angular velocities of the two driving motors, is the angular position of the load, is the angular velocity of the load, is the angular acceleration of the load; and are the moments of inertia of the driving motor and the load; is the control input of the two motors, is the motor viscous friction coefficient, is the frictional torque; represents the transmission torque between the two torques and the load, expressed as:

[0018] (2)

[0019] where, , and They are the torsion coefficient and the damping coefficient respectively; is the angular difference between the motor angular position and the load angular position, is the change in the angular difference between the motor position and the load angular position, is a friction function, represents the change rate of the friction function.

[0020] Furthermore, in the said step 2, a single-motor model is selected. Let , , the standard state equation of an nth-order nonlinear uncertain controlled object is:

[0021] (3)

[0022] In the formula, , is the load angular velocity, is the acceleration of the load; J is a positive constant and belongs to an intermediate variable; d is the uncertainty brought by model reduction and external disturbance. A tracking controller is developed for the motor using formula (3).

[0023] Furthermore, in the said step 3, the observer measures the output of the system and the known system input, and uses an adaptive algorithm to estimate the unknown matching disturbance in the system in real time. The design of the observer is based on the sliding mode principle as follows:

[0024] (4)

[0025] In the formula, is the estimation result. By designing an auxiliary function, the sliding mode variable tends to 0; and are the auxiliary variable and the auxiliary function respectively. The gain parameters and are designed as:

[0026] (5)

[0027] In the formula, , are both positive constants.

[0028] Furthermore, in the said step 4, the sliding mode variable is introduced into the observer. By designing the controller and adjusting the observer gains , , it can be made that the sliding mode variable tends to 0. By observing it is known that at this time , and thus from formula (4) it is calculated that to achieve the actual disturbance Approximation

[0029] Furthermore, in step 4, the synchronous control strategy of the dual-motor is as follows:

[0030] Design a sliding mode surface:

[0031] (6)

[0032] The reaching law is designed as:

[0033] (7)

[0034] The second sliding mode surface is expressed as:

[0035] (8)

[0036] From the dual-motor system, we get:

[0037] (9)

[0038] Wherein, 、 are all sliding mode surface parameters to be adjusted; is the first sliding mode surface, θ 1 and θ 2 are all state variables; is the derivative of the first sliding mode surface, is the second sliding mode surface, u i is the control input of the two motors, represents the transmission torque between the two torques and the load, J m is the moment of inertia of the drive motor.

[0039] Furthermore, the synchronous controller is designed as follows:

[0040] (10)

[0041] Wherein, is the tuning parameter, u i is the control input of the two motors, represents the transmission torque between the two torques and the load, are the angular velocities of the two drive motors, J m is the moment of inertia of the drive motor, b m is the motor viscous friction coefficient.

[0042] Compared with the prior art, the present invention has the following advantages:

[0043] (1) The adaptive disturbance observer combined with sliding mode control technology adopted in the present invention effectively solves the problems of nonlinearity, model uncertainty, and external disturbances in the dual-motor drive system, thereby significantly improving the stability and robustness of the system, enabling the system to maintain stable operation under a wider range of operating conditions, and reducing the risk of performance degradation of the system caused by disturbances.

[0044] (2) The finite-time stable adaptive disturbance observer designed by the present invention can accurately estimate and compensate the unknown matching disturbances in the system, thereby achieving higher trajectory tracking accuracy and synchronization. The tracking error can approach zero after the observer converges, greatly improving the tracking accuracy of the system and meeting the high-precision control requirements.

[0045] (3) The sliding mode controller designed by the present invention by adopting the multi-sliding surface technology not only effectively solves the problems of tracking and synchronization control, but also improves the control efficiency, can respond to system changes faster, reduces the delay in the control process, and thus improves the response speed and operation efficiency of the entire system.

[0046] (4) The design scheme of the present invention simplifies the control structure of the system, reduces the additional hardware requirements, thereby reducing the overall cost and complexity of the system; while maintaining high performance, it reduces the maintenance and operation costs of the system, making the technology more economically feasible. Brief Description of the Drawings

[0047] Figure 1 is the method flow chart of the present invention;

[0048] Figure 2 is the working diagram of the system of the present invention;

[0049] Figure 3 is the working flow chart of the sliding mode controller of the present invention;

[0050] Figure 4 is the block diagram of the dual-motor drive system of the present invention. Detailed Embodiment

[0051] In order to make the objectives, technical solutions and advantages of the present invention clearer, the following further details the present invention in conjunction with the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0052] As Figure 1 shown, a method for synchronous control of a dual-motor drive system based on an adaptive disturbance observer, the specific steps include:

[0053] Step 1: Construct the dynamic equation of the permanent magnet synchronous motor.

[0054] The dynamic equation of a specific permanent magnet synchronous motor is as follows:

[0055] (1)

[0056] where i = 1, 2 represents two driving motors; are the angular positions of the two driving motors, are the angular accelerations of the two driving motors, are the angular velocities of the two driving motors, is the angular position of the load, is the angular velocity of the load, is the angular acceleration of the load; and are the moments of inertia of the driving motor and the load; is the control input of the two motors, is the motor viscous friction coefficient, is the frictional torque; represents the transmission torque between the two torques and the load, expressed as:

[0057] (2)

[0058] where, , and are the torsional coefficient and the damping coefficient respectively; is the angular difference between the motor angular position and the load angular position, is the change in the angular difference between the motor position and the load angular position, is a friction function, represents the change rate of the friction function.

[0059] Step 2: According to the dynamic equation in Step 1, redefine the state variables of the permanent magnet synchronous motor and rewrite it into a standard state equation.

[0060] For the convenience of calculation, the present invention selects a single-motor model, and sets , , and the standard state equation of the nth-order nonlinear uncertain controlled object is:

[0061] (3)

[0062] In the formula, , is the load angular velocity, is the acceleration of the load; J is a positive constant and belongs to an intermediate variable; d is the uncertainty brought by model reduction and external interference, and a tracking controller is developed for the motor using formula (3).

[0063] Step 3: According to the standard state equation in Step 2, introduce the sliding mode variable, and design an adaptive disturbance observer in combination with the adaptive law to accurately estimate the disturbance.

[0064] The main idea of the adaptive disturbance observer (ADO) is to design a sliding variable to connect the estimated disturbance with the system state, and the adaptive law is designed in the form of a super-twisting structure. Different from other sliding mode observers, the proposed observer does not use the information of the disturbance upper bound, but only assumes that the disturbance is bounded by an unknown boundary.

[0065] As Figure 2 and Figure 3 shown, the observer estimates the unknown matching disturbance in the system in real time by measuring the output of the system and the known system input, and the design of the observer is based on the sliding mode principle, ensuring the accurate estimation of the disturbance within a finite time, as follows:

[0066] (4)

[0067] where, is the estimation result. By designing an auxiliary function, the sliding mode variable tends to 0; is the sliding variable, and are the auxiliary variables and the auxiliary function respectively, and the gain parameters and are designed as:

[0068] (5)

[0069] where, , are both positive constants.

[0070] Step 4: Feed back the observation result in Step 3 to the controller for disturbance compensation, design a multi-sliding surface controller for the single-motor speed control system, and perform the synchronous control of the dual motors.

[0071] As Figure 4 shown, the controller uses multiple sliding surfaces to process different dynamic characteristics of the system respectively. By designing an appropriate control law, it ensures that the system state can reach and stabilize on the sliding surface within a finite time.

[0072] For the dual-motor drive system, the synchronization of the drive motors is essential. Even if the same type of drive motors are selected, due to gear backlash, measurement errors, and external disturbances, there are still position errors. To avoid potential problems, a synchronization control strategy is embedded in the tracking controller of the dual-motor drive system. The synchronization control strategy of the dual motors is as follows:

[0073] Design a sliding mode surface:

[0074] (6)

[0075] The reaching law is designed as:

[0076] (7)

[0077] Wherein, 、 ;

[0078] The second sliding mode surface is expressed as:

[0079] (8)

[0080] From the dual-motor system, we get:

[0081] (9)

[0082] The synchronous controller is designed as follows:

[0083] (10)

[0084] Wherein, 、 are all sliding mode surface parameters to be adjusted; is the tuning parameter, is the first sliding mode surface, θ 1 and θ 2 are all state variables; is the derivative of the first sliding mode surface, is the second sliding mode surface, u i is the control input of the two motors, represents the transmission torque between the two torques and the load, is the angular velocity of the two drive motors, J m is the moment of inertia of the drive motor, b m is the motor viscous friction coefficient.

[0085] Through its unique technical solution, the present invention has significant advantages in improving system stability, tracking accuracy and control efficiency, while reducing costs and complexity, providing an effective solution for the precise control of the dual-motor drive system. The specific proof process is as follows:

[0086] Define a vector, , given , , ,

[0087] Derivative of:

[0088] ,

[0089] (a)

[0090] It can be seen that

[0091] (b)

[0092] The selected Lyapunov function is

[0093] (c)

[0094] and are all positive constants, is a positive definite matrix.

[0095] The derivative of Lyapunov is:

[0096] (d)

[0097] where is expressed as:

[0098] (e)

[0099] Also, because

[0100] (f)

[0101] So

[0102] (g)

[0103] Assume that the wave excitation force is bounded, then the positive constant always satisfies , therefore,

[0104] (h)

[0105] where is expressed as:

[0106] (i)

[0107] Substituting formula (5) gives:

[0108] (j)

[0109] Therefore, when , the following equation holds:

[0110] (k)

[0111] Wherein, and represent the minimum eigenvalue and the maximum eigenvalue of the matrix, because holds. If , it can be obtained that , ; once holds, then , that is, as the Lyapunov function decreases, the error of the model estimation also decreases. Using the finite-time theorem, the convergence time of this algorithm is:

[0112] (l)

[0113] By adjusting two auxiliary functions, the sliding mode surface tends to 0, and the real-time estimation of the system is completed within a time less than T.

[0114] The above formula (a) is derived in the process of constructing the adaptive disturbance observer (ADO) in order to analyze the finite-time stability of the observer. Through such an expression, the relationship between the system state and the estimated disturbance can be further analyzed, preparing for the subsequent stability analysis using the Lyapunov function; the derivative expression in formula (b) is arranged in matrix form for subsequent analysis using the Lyapunov stability theory. The matrix form can clearly represent the dynamic relationship between the system state and the disturbance d, which is a key step in analyzing the stability of the adaptive disturbance observer; the Lyapunov function in formula (c) plays an important role in analyzing the system stability. By selecting an appropriate Lyapunov function and analyzing the properties of its time derivative, it can be judged whether the system is stable; the Lyapunov function constructed by selecting the P matrix is for subsequent analysis of the stability of the adaptive disturbance observer. The derivation of formula (d) is based on the Lyapunov stability theory. By calculating the time derivative of Lyapunov, the stability of the system is judged. The Q matrix is an intermediate matrix that appears in the derivation process, reflecting the influence of the disturbance d on the Lyapunov time derivative; formula (e) is obtained in the process of calculating the time derivative of Lyapunov, and its elements are related to the previously defined parameters L 1 and L 2 as well as and related. The properties of the Q matrix play an important role in judging the positivity and negativity of the Lyapunov time derivative, and thus affect the judgment of the system stability; formula (f) is an intermediate result in the process of simplifying the Lyapunov time derivative, and Linking with a new vector G helps to further simplify the expression of the time derivative of Lyapunov, so as to better analyze the system stability. Equation (g) more concisely represents the relationship between the time derivative of Lyapunov, the system state, the disturbance d, and the related matrices Q and vector G. Through this expression, it is more convenient to analyze the system stability in the presence of disturbances. Equation (h) takes into account the boundedness of the disturbance. By introducing the J matrix, the expression of the time derivative of Lyapunov is further adjusted to judge the system stability according to the properties of the Q+J matrix. The matrix in equation (i) is introduced considering the boundedness of the disturbance, and its elements are related to the disturbance d and the previously defined λ. The properties of the Q+J matrix obtained by adding the J matrix and the Q matrix play a key role in judging the positive or negative of the time derivative of Lyapunov, thus affecting the judgment of the system stability; the matrix in equation (j) is obtained by adding the Q matrix and the J matrix considering the boundedness of the disturbance.

[0115] It is very important for judging the positive or negative of the time derivative of Lyapunov, and then the stability of the adaptive disturbance observer can be judged; all the parameters in this proof process are randomly listed and have no practical significance. The main purpose is to prove the conclusion of convergence within the finite time T.

[0116] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for synchronous control of a dual-motor drive system based on an adaptive disturbance observer, characterized in that: The specific steps include: Step 1: Construct the dynamic equation of permanent magnet synchronous motor; Step 2: Based on the dynamic equation of step 1, redefine the state variables of the permanent magnet synchronous motor and rewrite it into the standard state equation; Step 3: According to the standard state equation in step 2, the sliding mode variable is introduced, and the adaptive disturbance observer is designed in combination with the adaptive law to accurately estimate the disturbance; the observer uses an adaptive algorithm to estimate the unknown matching disturbance in the system in real time by measuring the output of the system and the known system input. The design of the observer is based on the sliding mode principle, as follows: In the formula, To estimate the result, an auxiliary function is designed to make the sliding mode variable σ approach 0; J = 1 / (nJ m +J L ), x2 is the load angular velocity, is the acceleration of the load; J is a positive constant and an intermediate variable; let x1 = θ L , θ L is the angular position of the load, is the angular velocity of the load, is the friction torque; h and y are auxiliary variables and auxiliary functions respectively, and the gain parameters L1 and L2 are designed as: In the formula, ε and λ are both positive constants; Step 4: Feedback the observation results of step 3 to the controller for disturbance compensation, design a multiple sliding surface controller for the single motor speed control system, and perform synchronous control of the dual motors; the synchronous control strategy of the dual motors is as follows: Design a sliding surface: s s1 =θ1-θ2 (6) The arrival law is designed as: The second sliding surface is expressed as: From the dual motor system, we get: Among them, α s ≥1, k s1 >0 are sliding surface parameters to be adjusted; σ s1 is the first sliding surface, θ1 and θ2 are both state variables; is the derivative of the first sliding surface, is the derivative of the second sliding surface, i=1,2 represents two drive motors, u i is the control input of the two motors, τ i Represents the transmission torque between the two motors and the load, J m is the moment of inertia of the driving motor; b m is the motor viscous friction coefficient; The synchronous controller is designed as follows: Among them, k s2 To tune the parameters, are the angular velocities of the two drive motors.

2. The method for synchronous control of a dual-motor drive system based on an adaptive disturbance observer according to claim 1, characterized in that: The kinetic equation in step 1 is: Where i=1,2 represents two drive motors; θ i are the angular positions of the two drive motors, is the angular acceleration of the two drive motors, is the angular velocity of the two drive motors, θ L is the angular position of the load, is the angular velocity of the load, is the angular acceleration of the load; J m and J L is the rotational inertia of the drive motor and load; u i are the control inputs of the two motors, b m is the motor viscous friction coefficient, is the friction torque; τ i It represents the transmission torque between the two motors and the load, expressed as: Among them, δ i =θ i -θ L , k and c are the torsion coefficient and damping coefficient respectively; δ i is the angle difference between the motor angle position and the load angle position, is the change in the angle difference between the motor position and the load angle position, f(δ i ) is a friction function, Represents the rate of change of the friction function.

3. The method for synchronous control of a dual-motor drive system based on an adaptive disturbance observer according to claim 2, characterized in that: In step 2, a single motor model is selected, and x1=θ L , The standard state equation of a nonlinear uncertain controlled object is: Where, J = 1 / (nJ m +J L ), x2 is the load angular velocity, is the acceleration of the load; J is a normal number and an intermediate variable; d is the uncertainty caused by model reduction and external disturbance. Formula (3) is used to develop a tracking controller for the motor.

4. The method for synchronous control of a dual-motor drive system based on an adaptive disturbance observer according to claim 3 is characterized in that: In step 4, the sliding mode variable σ is introduced into the observer. By designing the controller and adjusting the observer gains L1 and L2, the sliding mode variable σ can be made to approach 0. By observing σ, it is known that x2 = -h at this time, which can be calculated from formula (4) In order to achieve the approximation of the actual disturbance d.

Images