Predictive performance control method and system for dual-motor servo system considering external disturbance

Abstract

The application discloses a kind of double-motor servo system's pre-determined performance control method considering external disturbance, the method comprises: the dynamics model of double-motor servo system considering external disturbance is established;Define the total disturbance and state variable of double-motor servo system;According to the total disturbance and state variable of double-motor servo system, the dynamics model of double-motor servo system considering external disturbance is transformed, and the state equation of double-motor servo system is obtained;Radial basis neural network is constructed to estimate load end total disturbance and motor end total disturbance respectively, and the approximation value of load end total disturbance and motor end total disturbance is obtained;According to the prescribed performance function, the prediction tracking error constraint condition is established, and the transformation error is solved according to the smooth strictly increasing function of introduced transformation error;Combined with tracking controller and synchronization controller, the pre-determined performance controller based on state predictor is designed.The application realizes group on the tracking of motor under the premise of guaranteeing double-motor synchronization, and the stability of system is proved by Lyapunov criterion.

Description

Technical Field

[0001] This invention relates to a predetermined performance control method and system for a dual-motor servo system that takes into account external disturbances, and belongs to the field of load tracking technology for dual-motor servo systems. Background Technology

[0002] In recent years, as industrial production demands increasingly higher system drive capabilities, multi-motor servo systems have received growing attention in industrial production. Two main challenges exist in multi-motor servo systems: first, the gear transmission and non-smooth surfaces cause backlash and frictional nonlinearity issues, which need to be addressed in controller design; second, while considering load tracking accuracy, the impact of synchronization performance must also be taken into account, and the coupling between synchronization and tracking is also a crucial issue that needs to be addressed in controller design.

[0003] Nonlinearity in servo systems is a major factor affecting the system's dynamic performance, therefore it must be properly addressed during controller design. With ongoing research, scholars have developed numerous control methods to handle nonlinear problems, such as fuzzy control, neural network control, and adaptive control. The core of these methods is selecting a suitable adaptive law to approximate the nonlinear function using a linear function. However, if the nonlinearity in the system is high, it can lead to high-frequency oscillations, significantly reducing the adaptive speed and thus affecting the control performance.

[0004] To improve tracking performance and ensure system safety, synchronous control between motors is equally important. Dynamic surface control, as a complex high-order system, is widely used in multi-motor servo systems, utilizing filters to address the complexity explosion problem. While dynamic surface control can reduce the order of high-order systems to decrease complexity, higher gain is required to improve control accuracy, which leads to increased overshoot and reduced system stability.

[0005] In recent years, various synchronization decoupling control strategies have been proposed to address the coupling problem in multi-motor systems, such as cross-coupling control, loop coupling control, and relative coupling control. The coupling problem between the synchronization performance and tracking performance of dual motors can affect the transient performance of the control system. Summary of the Invention

[0006] This invention provides a predetermined performance control method for a dual-motor servo system that takes into account external disturbances. For dual-motor servo systems, a tracking controller that incorporates a neural network dynamic surface into the predictor and a specified performance function is proposed, as well as a synchronization controller that combines an average deviation coupling control strategy with optimal sliding mode control. This achieves the tracking of the motors by the system while ensuring the synchronization of the two motors. Finally, the stability of the system is proved by the Lyapunov criterion.

[0007] The technical solution of this invention is:

[0008] According to a first aspect of the present invention, a method for predetermined performance control of a dual-motor servo system taking into account external disturbances is provided, comprising the following steps:

[0009] S1. Establish a dynamic model of the dual-motor servo system that takes into account external disturbances;

[0010] S2. Define the total disturbance and state variables of the dual-motor servo system; based on the total disturbance and state variables of the dual-motor servo system, transform the dynamic model of the dual-motor servo system considering external disturbances to obtain the state equation of the dual-motor servo system; construct a radial basis function neural network to estimate the total disturbance at the load end and the total disturbance at the motor end respectively, and obtain approximate values ​​of the total disturbance at the load end and the total disturbance at the motor end; wherein, the total disturbance of the dual-motor servo system includes the total disturbance at the load end and the total disturbance at the motor end;

[0011] S3. Based on the specified performance function, establish the prediction tracking error constraint conditions; introduce a smooth and strictly increasing function of the transformation error to transform the prediction tracking error constraint conditions into equivalent unconstrained conditions; and solve for the transformation error based on the introduced smooth and strictly increasing function of the transformation error; wherein, the transformation error includes the first transformation error, the second transformation error, the third transformation error, and the fourth transformation error;

[0012] S4. Combine the tracking controller and the synchronization controller to design a predetermined performance controller based on the state predictor as the input torque of the two motors in the dual-motor servo system, so as to realize the synchronization and tracking control of the dual-motor servo system.

[0013] Furthermore, S4 specifically includes:

[0014] S4.1 Design a tracking controller based on state predictor, transformation error, and dynamic surface control method;

[0015] S4.2 Based on the approximation value of the total disturbance at the motor end, design an integral sliding mode optimal synchronous controller based on the average deviation coupling strategy;

[0016] S4.3. Combine the tracking controller and the synchronization controller to design a predetermined performance controller based on the state predictor as the input torque of the two motors in the dual-motor servo system, so as to realize the synchronization and tracking control of the dual-motor servo system.

[0017] Furthermore, the design process of the tracking controller is as follows:

[0018] Define the following variable: e1 = x1 - x d e g+1 =x g+1 -η g , χ g =η g -α g Among them, e1, e g+1 To track errors, To predict tracking error; For the predicted state, x1, x g+1 Let x be a state variable. d For the desired signal, η g Represents the virtual control law, α g For the output of a first-order filter, χ g For the first-order filter output error, j = 1, 2, 3, 4; g = 1, 2, 3;

[0019] The first-state predictor is designed as follows:

[0020]

[0021] Among them, the prediction error of the first state variable This represents the predicted values ​​of state variables x1 and x2. express The first derivative of , where c1 is a positive constant;

[0022] The first virtual control law η1 is designed as follows:

[0023]

[0024] Where δ1>0, k1>0; For positive constants; z1 is the first transformation error, ρ1 and ρ2 are specified performance functions; 0 <p1≤p m1 p m1 It is a positive integer; To predict tracking error; It is the first derivative of ρ1; For x d The first derivative;

[0025] The second state predictor is designed as follows:

[0026]

[0027] Among them, the prediction error of the second state variable ψ1 is the estimated value of the weight matrix W1 and the Gaussian function used in approximating the total perturbation at the load end using a radial basis function neural network. c2 represents the predicted value of the state variable x3, and c2 is a positive constant. express The first derivative;

[0028] The second virtual control law η2 is designed as follows:

[0029]

[0030] Where δ2>0, k2>0; z1 is a positive constant; z2 is the second transformation error; ρ3 is the specified performance function; 0 <p2≤p m2 p m2 It is a positive integer; It is the first derivative of ρ2; The first derivative of the first-order filter output α1;

[0031] The third-state predictor is designed as follows:

[0032]

[0033] Among them, the prediction error of the third state variable c3 is a positive constant. This represents the predicted value of the state variable x4; express The first derivative;

[0034] The third virtual control law η3 is designed as follows:

[0035]

[0036] Where δ3>0, k3>0; z is a positive constant; z3 is the third transformation error; ρ4 is the specified performance function; 0 <p3≤p m3 p m3 It is a positive integer; It is the first derivative of ρ3; The first derivative of the output α2 of the first-order filter;

[0037] The fourth state predictor is designed as follows:

[0038]

[0039] Among them, the prediction error of the fourth state variable ψ2 is the estimated value of the weight matrix W2 in the approximation of the total disturbance at the motor terminals using a radial basis function neural network, the Gaussian function, c4 is a positive constant, and u tr Indicates the tracking controller; J m This refers to the motor's inertia. express The first derivative;

[0040] Tracking controller u tr Designed as follows:

[0041]

[0042] Where k4>0, z4 is the fourth transformation error; It is the first derivative of ρ⁴; The first derivative of the first-order filter output α3 is given.

[0043] Furthermore, the design of the synchronization controller is as follows:

[0044] For the two motors in a dual-motor servo system, the system model of the dual-motor subsystem is established as follows:

[0045]

[0046] In the formula, u i f represents the input torque of the i-th motor; 2i This represents the total disturbance at the i-th motor terminal; J mi θ mi Let be the motor inertia and motor angular position of the i-th motor, respectively.

[0047] Based on the average deviation coupling strategy, the synchronization error is defined as:

[0048]

[0049] in, e s1i Let e ​​be the average position error of the i-th motor. s2i The average speed error of the i-th motor;

[0050]

[0051] Define the integral sliding surface as:

[0052]

[0053] Among them, s i Let β be the integral sliding surface of the i-th motor; s For s, it is a positive real number; i Differentiation yields:

[0054]

[0055] in, u syi For the synchronous controller of the i-th motor, u tr For tracking controller;

[0056] The ideal equivalent virtual control law is designed as u. eqi :

[0057]

[0058] The integral sliding surface derivative is rewritten as:

[0059]

[0060] in, k c It is a constant;

[0061] Define the error vector as follows:

[0062]

[0063] Taking the derivative of the error vector, we get:

[0064]

[0065] in,

[0066] Based on the optimal control method, the optimal synchronization performance index J is selected. s for:

[0067]

[0068] Among them, Q s and R s Given a positive definite symmetric matrix; design optimal control. for:

[0069]

[0070] In the formula, P s Solve from the Ricardi equation;

[0071] Based on the approximation value of the total disturbance at the motor end, the integral sliding mode optimal synchronous controller based on the average deviation coupling strategy is designed as follows:

[0072]

[0073] in, ψ 2iIt is the estimate of the weight matrix W2 and the Gaussian function in the approximation of the total disturbance at the motor end using a radial basis function neural network.

[0074] According to a second aspect of the present invention, a predetermined performance control system for a dual-motor servo system that takes into account external disturbances is provided, comprising:

[0075] The first module is used to establish a dynamic model of a dual-motor servo system that takes into account external disturbances;

[0076] The second module defines the total disturbance and state variables of the dual-motor servo system. Based on the total disturbance and state variables of the dual-motor servo system, the dynamic model of the dual-motor servo system considering external disturbances is transformed to obtain the state equation of the dual-motor servo system. A radial basis function neural network is constructed to estimate the total disturbance at the load end and the total disturbance at the motor end, respectively, and to obtain approximate values ​​of the total disturbance at the load end and the total disturbance at the motor end. The total disturbance of the dual-motor servo system includes the total disturbance at the load end and the total disturbance at the motor end.

[0077] The third module is used to establish the prediction tracking error constraints based on the specified performance function; introduce a smooth and strictly increasing function of the transformation error to transform the prediction tracking error constraints into equivalent unconstrained conditions; and solve for the transformation error based on the introduced smooth and strictly increasing function of the transformation error; wherein the transformation error includes the first transformation error, the second transformation error, the third transformation error, and the fourth transformation error;

[0078] The fourth module is used to design a predetermined performance controller based on a state predictor, which combines a tracking controller and a synchronization controller, as the input torque of the two motors in a dual-motor servo system, so as to realize the synchronization and tracking control of the dual-motor servo system.

[0079] According to a third aspect of the invention, a processor is provided for running a program, wherein the program, when running, executes a predetermined performance control method for a dual-motor servo system taking into account external disturbances as described in any of the preceding embodiments.

[0080] The beneficial effects of this invention are:

[0081] First, this invention introduces a state predictor, which enables fast and smooth approximation without high-frequency oscillations and eliminates prediction errors. By using the prediction error in the predictor to update the adaptive law, smooth and fast estimation can be achieved without generating high-frequency vibrations.

[0082] Second, by combining it with the specified performance function, both the prediction tracking error and the tracking error are constrained within the specified range; furthermore, it can prevent the tracking error from overshooting beyond the performance limit and reduce the convergence time.

[0083] Third, this invention designs an average deviation coupling synchronization structure, which solves the coupling problem between load tracking and motor synchronization in a dual-motor servo system, greatly reducing the difficulty of tracking controller design; it achieves tracking of the motors while ensuring dual-motor synchronization; finally, the stability of the system is proven by the Lyapunov criterion. Attached Figure Description

[0084] Figure 1 This is a schematic diagram of the control flow of the control method of the present invention;

[0085] Figure 2 This is a schematic diagram illustrating the load position tracking effect and tracking error of the present invention;

[0086] Figure 3 This is a schematic diagram illustrating the motor disturbance estimation and estimation error of the dual-motor servo system involved in the present invention.

[0087] Figure 4 The radial basis function neural network provided in this embodiment of the invention provides the estimation curve and estimation error curve for the motor-side disturbance;

[0088] Figure 5 The radial basis function neural network provided in this embodiment of the invention provides an estimation curve and an estimation error curve for load-side perturbations;

[0089] Figure 6 The motor synchronization position curve of the dual-motor servo system provided in the embodiments of the present invention;

[0090] Figure 7 This is a schematic diagram of motor synchronization error in a dual-motor servo system provided in an embodiment of the present invention. Detailed Implementation

[0091] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other.

[0092] Example 1: As Figures 1-7 As shown, according to a first aspect of the present invention, a predetermined performance control method for a dual-motor servo system taking into account external disturbances is provided, comprising the following steps:

[0093] S1. Establish the dynamic model of the dual-motor servo system considering external disturbances, and initialize the state and parameters of the dual-motor servo system considering external disturbances. The process is as follows:

[0094] The dynamic model of the dual-motor servo system taking into account external disturbances is expressed as follows:

[0095]

[0096] Where: i = 1, 2 represent the two motors in the dual-motor servo system (i = 1 represents the first motor, i = 2 represents the second motor); J mi θ mi b mi 、Td mi These represent the motor inertia, angular position, viscous friction coefficient, and external disturbance at the motor end of the i-th motor, respectively; J l For load inertia; θ l b is the load angle position. l Td is the coefficient of viscous friction under load. l For external disturbances at the load end, u i τ is the system input torque for the i-th motor. i Let be the torque transmitted when the i-th motor comes into contact with the load.

[0097] Because the transmitted torque is nonlinear, a nonlinear dead-zone function is used to describe the transmitted torque τ. i The expression is:

[0098]

[0099] Where: z i =θ mi -vθ l α is the angular position difference between the i-th motor and the load, α is the gap width, k is the slope of the nonlinear dead function, i.e. the stiffness coefficient of the gear connecting the load, and v is the transmission ratio. In this embodiment of the invention, α = 0.1 and v = 1 are set.

[0100] S2. Define the total disturbance and state variables of the dual-motor servo system; based on the total disturbance and state variables of the dual-motor servo system, transform the dynamic model of the dual-motor servo system considering external disturbances to obtain the state equation of the dual-motor servo system; construct a radial basis function neural network to estimate the total disturbance at the load end and the total disturbance at the motor end respectively, and obtain the approximate values ​​of the total disturbance at the load end and the total disturbance at the motor end; wherein, the total disturbance of the dual-motor servo system includes the total disturbance at the load end and the total disturbance at the motor end;

[0101] Further, S2 includes:

[0102] S2.1 Define the total disturbance and state variables of the dual-motor servo system; based on the total disturbance and state variables of the dual-motor servo system, transform the dynamic model of the dual-motor servo system that takes into account external disturbances to obtain the state equation of the dual-motor servo system; wherein, the total disturbance of the dual-motor servo system includes the total disturbance at the load end and the total disturbance at the motor end;

[0103] The total disturbance of the dual-motor servo system is defined as follows:

[0104]

[0105] Where: f1 is the total disturbance at the load end; f 2i Let be the total disturbance at the i-th motor end.

[0106] Select system state variables as Define state variables definition The state equation of the dual-motor servo system is:

[0107]

[0108] Where y is the output of the dual-motor servo system; Let x1, x2, x3, and x4 represent the first derivatives of the first state variable, x4, x5, x6, x7, x8, x9, x1, x2, x3, x4, x4, x1, x2, x3, x4, x4, x4, x6, x7, x8, x9 ...

[0109] Assumption 1: In a dual-motor servo system, both motors are of the same model, therefore the system parameters are: J m =J m1 =J m2 b m =b m1 =b m2 ;

[0110] Assumption 2: f1 and f2 are both unknown, bounded, and continuous, and their derivatives satisfy... Where f 1m and f 2m It is a number greater than zero.

[0111] S2.2 Construct a radial basis function neural network to approximate the total disturbance at the load end and the total disturbance at the motor end, respectively, and obtain the approximation values ​​of the total disturbance at the load end and the total disturbance at the motor end;

[0112] Radial basis function neural networks (RBNs) are a type of fully connected network with a simple structure and fast convergence speed, which can be used to approximate any nonlinear function.

[0113] The hidden layer of the network is a Gaussian function, represented as:

[0114]

[0115] Among them, C I ∈R m This represents the vector value of the center point of the function. Let n be the width of the function and I be the number of hidden layer nodes. A higher number of hidden layer nodes results in a better approximation of the unknown function by the neural network, but also a slower approximation speed. In this embodiment of the invention, n = 9 is set; this value is applied to approximate the total disturbance at the load end and the total disturbance at the motor end, showing good approximation results.

[0116] Using radial basis function neural networks to analyze the total perturbation f1 and f 2i To approximate, that is:

[0117]

[0118] Where W1 and W2 are the actual first and second weight matrices, ε1 and ε 2i To approximate the error, ‖W1‖≤W 1N ||W2||≤W 2N , |ε1|≤ε 1N ,|ε 2i |≤ε 2iN W 1N W 2N ε 1N ε 2iN ε is a constant. 21N =ε 22N .

[0119] S3. Based on the specified performance function, establish the prediction tracking error constraint conditions; introduce a smooth, strictly increasing function of the transformation error to transform the prediction tracking error constraint conditions into equivalent unconstrained conditions; and solve for the transformation error based on the introduced smooth, strictly increasing function of the transformation error; wherein, the transformation error includes the first transformation error, the second transformation error, the third transformation error, and the fourth transformation error.

[0120] This invention uses a positive monotonically decreasing function as the specified performance function ρ. j (t) is used to meet the controller design requirements, and its expression is as follows:

[0121]

[0122] Where j = 1, ..., 4, ρ 0j >ρ ∞j >0, β j >0 represents a positive constant in the design.

[0123] The prediction tracking error constraint is achieved through the following equation:

[0124]

[0125] in, To predict tracking error, m j and It is a positive number.

[0126] To transform this constraint (8) into an equivalent unconstrained condition, a transformation error z is introduced. j S of a smooth, strictly increasing function ∈ R j (z j )for:

[0127]

[0128] The transformation error z can be solved from the above equation. j for:

[0129]

[0130] Among them, intermediate variables

[0131] S4. Based on state predictors, transformation errors, and dynamic surface control methods, design a tracking controller and a synchronization controller based on average deviation coupling strategy, integral sliding surface, and optimal control. Combine these two to design a state predictor-based predetermined performance controller as the input torque for a dual-motor servo system, achieving synchronous operation between motors while simultaneously realizing the system output x1 against the desired signal x. d The tracking. Further, this includes the following:

[0132] S4.1 Design a tracking controller based on state predictor, transformation error, and dynamic surface control method;

[0133] To avoid the "differential explosion" problem during computation, this invention employs a dynamic surface control method that combines a first-order filter with the backstepping method.

[0134] Because the proposed controller is implemented in multiple steps, the following variable is defined: e1 = x1 - x d e g+1 =x g+1 -η g , χ g =η g -α g ; where e j To track errors, To predict tracking error, i.e. To predict the state, x j For state variables, η g Represents the virtual control law, α g For the output of a first-order filter, χ gLet j = 1, ..., 4; g = 1, 2, 3 be the filter output error.

[0135] The expression for the first-order filter is as follows:

[0136]

[0137] Among them, T g It is a time constant. Represents α g The first derivative, α g (0), η g (0) represents α g η g The initial value of η g α g It is a function of time, i.e., η g (t), α g (t).

[0138] The first-state predictor is designed as follows:

[0139]

[0140] Among them, the prediction error of the first state variable This represents the predicted values ​​of x1 and x2. express The first derivative of , where c1 is a positive constant.

[0141] Choose the Lyapunov function as:

[0142]

[0143] Differentiating equation (13) yields:

[0144]

[0145] In the above, the first derivative of the first transformation error z1 for:

[0146]

[0147] in, when At that time, we can get 0. <p1≤p m1 p m1 It is a positive constant; ξ1 is ξ1(t). Right now ρ1 is ρ1(t);

[0148] Combining equations (14) and (15), the first virtual control law η1 is designed as follows:

[0149]

[0150] Where δ1>0, k1>0.

[0151] Design the first adaptive law for the first unknown weight matrix in the approximation of the total disturbance at the load end. The expression is:

[0152]

[0153] In this context, Γ1 and σ1 are both positive constants.

[0154] The second state predictor is designed as follows:

[0155]

[0156] Among them, the prediction error of the second state variable This is an estimate of W1. c represents the predicted value of x3, and c2 is a positive constant.

[0157] Choose the Lyapunov function as:

[0158]

[0159] Differentiating equation (19) yields:

[0160]

[0161] In the above, the first derivative of the second transformation error for:

[0162]

[0163] in, when At that time, we can get 0. <p2≤p m2 p m2 It is a positive integer.

[0164] Combining equations (20) and (21), the second virtual control law η2 is designed as follows:

[0165]

[0166] Among them, δ2>0, k2>0.

[0167] The third-state predictor is designed as follows:

[0168]

[0169] Among them, the prediction error of the third state variable c3 is a positive constant. This represents the predicted value of x4.

[0170] Choose the Lyapunov function as:

[0171]

[0172] Differentiating equation (24) yields:

[0173]

[0174] In the above, the third transformation error The first derivative is:

[0175]

[0176] in, when At that time, we can get 0. <p3≤p m3 p m3 It is a positive integer.

[0177] Combining equations (25) and (26), the third virtual control law η3 is designed as follows:

[0178]

[0179] Among them, δ3>0, k3>0.

[0180] The second adaptive law for the second unknown weight matrix in the approximation of the total disturbance at the load end. The expression is:

[0181]

[0182] In this context, Γ2 and σ2 are both positive constants.

[0183] The fourth state predictor is designed as follows:

[0184]

[0185] Among them, the prediction error of the fourth state variable This is an estimate of W2, c4 is a positive constant, and u tr This indicates a tracking controller.

[0186] Choose the Lyapunov function as:

[0187]

[0188] Differentiating equation (30) yields:

[0189]

[0190] In the above, the first derivative of the fourth transformation error for:

[0191]

[0192] in, when At that time, we can get 0. <p4≤p m4 p m4 It is a positive integer.

[0193] Combining equations (31) and (32), the tracking controller u tr Designed as follows:

[0194]

[0195] Where k4>0.

[0196] The stability of the tracking controller of the present invention is demonstrated below:

[0197] Tracking controller u tr Substituting into equation (31), we get:

[0198]

[0199] in, m1 is a constant.

[0200] Using Young's inequality, we can obtain:

[0201]

[0202] Among them, ι j γ and γ are positive constants.

[0203] make Substituting equation (35) into equation (34), we get:

[0204]

[0205] in,

[0206] Integrating both sides of equation (36) yields:

[0207]

[0208] because Since both ∈ are bounded, the systematic error will converge to the minimum neighborhood of the origin.

[0209] S4.2 Establish a system model of the dual-motor subsystem, design an integral sliding mode optimal synchronous controller based on the average deviation coupling strategy based on the approximation value of the total disturbance at the motor end, and prove its stability.

[0210] In dual-motor servo systems, synchronous control of the motors is also very important. This invention combines the average deviation coupling strategy, sliding mode, and optimal control to design an integral sliding mode optimal synchronous controller based on the average deviation coupling strategy.

[0211] For the two motors in a dual-motor servo system, the system model of the dual-motor subsystem is established as follows:

[0212]

[0213] In the formula, u i f represents the input torque of the i-th motor; 2i This represents the total disturbance at the i-th motor terminal;

[0214] Based on the average deviation coupling strategy, the synchronization error is defined as:

[0215]

[0216] in, e s1i Let e ​​be the average position error of the i-th motor. s2i Let be the average speed error of the i-th motor.

[0217] Define the integral sliding surface as:

[0218]

[0219] Among them, s i Let β be the integral sliding surface of the i-th motor; s For s, it is a positive real number; i Differentiation yields:

[0220]

[0221] in, u syi Let i be the synchronous controller for the i-th motor.

[0222] To keep the system state on the sliding surface, i.e. e si =u syi -u eqi The ideal equivalent virtual control law is designed as follows:

[0223]

[0224] Combining equations (40) and (42), equation (41) can be rewritten as:

[0225]

[0226] in, k c It is a constant.

[0227] Define the error vector as:

[0228]

[0229] Differentiating equation (44) yields:

[0230]

[0231] in, B s =[0 0 1] T .

[0232] Based on the optimal control method, the optimal synchronization performance index J is selected. s for:

[0233]

[0234] Among them, Q s and R s It is a positive definite symmetric matrix. To minimize equation (46) and thus achieve the optimal control objective, an optimal control algorithm is designed. for:

[0235]

[0236] In the formula, P s The solution can be found from the following Riccati equation:

[0237]

[0238] Based on the approximation value of the total disturbance at the motor end, the integral sliding mode optimal synchronous controller based on the average deviation coupling strategy is designed as follows:

[0239]

[0240] in,

[0241] Proof: Choosing the Lyapunov function:

[0242]

[0243] Differentiating it, we get:

[0244]

[0245] in,

[0246] Combining equation (48), we can obtain:

[0247]

[0248] Using Young's inequality, we can obtain:

[0249]

[0250] From equations (52) and (53) above, we can obtain:

[0251]

[0252] Where, k s And δ are respectively:

[0253]

[0254] As can be seen from equation (55), all signals in the closed-loop system are bounded, and the system error can converge to the neighborhood of the origin.

[0255] S4.3. Design a pre-defined performance controller based on a state predictor, combining a tracking controller and a synchronization controller, to provide the input torque for the two motors in a dual-motor servo system:

[0256]

[0257] In the formula, u1 and u2 are the input torques of the first and second motors, respectively; u sy1 u sy2 These are the synchronous controllers for the first and second motors, respectively; u tr For tracking controllers.

[0258] Based on the aforementioned predetermined performance controller using a state predictor, on the one hand, the system output x1 is made to match the desired signal x. d On the one hand, it tracks the motor; on the other hand, it enables synchronous operation between the first motor and the second motor.

[0259] According to a second aspect of the present invention, a predetermined performance control system for a dual-motor servo system considering external disturbances is provided, comprising: a first module for establishing a dynamic model of the dual-motor servo system considering external disturbances; a second module for defining the total disturbance and state variables of the dual-motor servo system; transforming the dynamic model of the dual-motor servo system considering external disturbances based on the total disturbance and state variables of the dual-motor servo system to obtain the state equation of the dual-motor servo system; constructing a radial basis function neural network to estimate the total disturbance at the load end and the total disturbance at the motor end, respectively, to obtain approximate values ​​of the total disturbance at the load end and the total disturbance at the motor end; wherein, the total disturbance of the dual-motor servo system... The system includes total disturbance at the load end and total disturbance at the motor end; the third module is used to establish predictive tracking error constraints based on a specified performance function; it introduces a smooth, strictly increasing function of the transformation error to transform the predictive tracking error constraints into equivalent unconstrained conditions; and it solves for the transformation error based on the introduced smooth, strictly increasing function of the transformation error; wherein the transformation error includes a first transformation error, a second transformation error, a third transformation error, and a fourth transformation error; the fourth module is used to design a predetermined performance controller based on a state predictor, combining the tracking controller and the synchronization controller, as the input torque of the two motors in the dual-motor servo system, so as to realize the synchronization and tracking control of the dual-motor servo system. For parts of the above modules not described in detail, please refer to the relevant descriptions in this embodiment.

[0260] According to a third aspect of the present invention, a processor is provided for running a program, wherein the program, when running, executes a predetermined performance control method for a dual-motor servo system taking into account external disturbances as described in any of the preceding embodiments.

[0261] Example 2: To verify the feasibility of the method described in Example 1, this example provides a control simulation experiment of the above control method in a dual-motor servo system. The specific parameter settings are as follows:

[0262] Establish the dynamic model of the dual-motor servo system as follows

[0263]

[0264] A dual-motor servo system is used as the research object. The system parameters are selected as follows: J m =J m1 =J m2 =0.185 kg·m 2 b m =b m1 =b m2 = 1.2 N·m·s / rad, J l =0.028 kg·m 2 b l=1.3N·m·s / rad, k=56N·m / rad, Td m1 =Td m2 =2,Td l =1. The initial state of the dual-motor servo system is defined as: x1 = 0.2, x2 = 0, x3 = 0.3, x4 = 0.1; the desired signal is defined as: x d =sin(t).

[0265] The specific parameters of the control method designed in this invention are as follows: Controller parameters: ρ 01 =0.04,ρ 02 =ρ 03 =ρ 04 =0.02,ρ ∞1 =ρ ∞2 =ρ ∞3 =ρ ∞4 =0.005, β1=2, β j =1 (j=2,3,4), C I =[-4 -3 -2 -1 0 1 2 3 4], I=1,2,...,9, Γ1=17000, Γ2=1000, σ1=700, σ2=600, k1=28, k2=69, k3=35, k4=58, T1=T2=T3=0.01, β s =0.1, R s =0.01; c1=22, c2=54, c3=18, c4=26; δ1=10, δ2=10, δ3=10; k c =10.

[0266] Meanwhile, the proposed control method was compared with three other control methods: 1) Reference 1 Du Renhui, Wu Yifei, Chen Wei, et al. Backstepping Adaptive Fuzzy Control (DSC) Considering Backlash Servo System; 2) PI Control (PI); 3) Reference 2 Ding Jiacheng, Wang Shubo. Dual Motor Tracking and Synchronization Control Based on Finite Time Extended State Observer (FUNNELDSC_SMC); 4) The control method designed in this invention (PPNDSC_OPSMC). Among these, the parameters in References 1) and 3) are based on those in the references used, and the parameters in Reference 2) are designed as follows: k p =45,k i =0.1.

[0267] The proposed control method was compared with three other control methods through simulation, and the simulation results are as follows: Figures 2-7 As shown, the tracking curve of the output signal to the desired signal and the tracking error curve in the dual-motor servo system are respectively as follows: Figure 2 and Figure 3 As shown; the estimation curves and estimation error curves of the radial basis function neural network for the disturbances on the motor side and the load side are as follows. Figure 4 and Figure 5 As shown; the synchronous position curve and synchronous error curve of the motor are as follows. Figure 6 and Figure 7 As shown.

[0268] pass Figure 2 and Figure 3 It can be seen that the predetermined performance control method of the dual-motor servo system that takes into account external disturbances proposed in this invention has a faster response speed and smaller tracking error compared with the other three control methods, and its control performance is relatively superior.

[0269] from Figure 4 and Figure 5 It can be seen that the radial basis neural network introduced in this invention can effectively estimate system disturbances and has good estimation results.

[0270] from Figure 6 and Figure 7 It can be seen that the predetermined performance control method for a dual-motor servo system that takes into account external disturbances proposed in this invention achieves motor synchronization in a shorter time and with a smaller synchronization error compared to the other three control methods.

[0271] In summary, the predetermined performance control method for a dual-motor servo system that takes into account external disturbances can effectively improve the convergence speed of the system and achieve better control results.

[0272] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for controlling the predetermined performance of a dual-motor servo system considering external disturbances, characterized in that, Includes the following steps: S1. Establish a dynamic model of the dual-motor servo system that takes into account external disturbances; S2. Define the total disturbance and state variables of the dual-motor servo system; based on the total disturbance and state variables of the dual-motor servo system, transform the dynamic model of the dual-motor servo system considering external disturbances to obtain the state equation of the dual-motor servo system; construct a radial basis function neural network to estimate the total disturbance at the load end and the total disturbance at the motor end respectively, and obtain approximate values ​​of the total disturbance at the load end and the total disturbance at the motor end; wherein, the total disturbance of the dual-motor servo system includes the total disturbance at the load end and the total disturbance at the motor end; S3. Based on the specified performance function, establish the prediction tracking error constraint conditions; introduce a smooth and strictly increasing function of the transformation error to transform the prediction tracking error constraint conditions into equivalent unconstrained conditions; and solve for the transformation error based on the introduced smooth and strictly increasing function of the transformation error; wherein, the transformation error includes the first transformation error, the second transformation error, the third transformation error, and the fourth transformation error; S4. Design a predetermined performance controller based on a state predictor, combining a tracking controller and a synchronization controller, as the input torque of the two motors in the dual-motor servo system, so as to realize the synchronization and tracking control of the dual-motor servo system. Based on the approximation value of the total disturbance at the motor end, the integral sliding mode optimal synchronous controller based on the average deviation coupling strategy is designed as follows: in, For the first Synchronization controller for each motor For an ideal equivalent virtual control law, For optimal control, For the first The inertia of a single motor. , , ; , It is the weight matrix used in approximating the total disturbance at the motor terminals using a radial basis function neural network. The estimated value, Gaussian function, It is a positive real number. For the first Average speed error of each motor For the first Average position error of each motor For the first The integral sliding surface of each motor, It is a constant.

2. The predetermined performance control method for a dual-motor servo system taking into account external disturbances according to claim 1, characterized in that, Specifically, S4 is: S4.1 Design a tracking controller based on state predictor, transformation error, and dynamic surface control method; S4.2 Based on the approximation value of the total disturbance at the motor end, design an integral sliding mode optimal synchronous controller based on the average deviation coupling strategy; S4.

3. Combine the tracking controller and the synchronization controller to design a predetermined performance controller based on the state predictor as the input torque of the two motors in the dual-motor servo system, so as to realize the synchronization and tracking control of the dual-motor servo system.

3. The predetermined performance control method for a dual-motor servo system taking into account external disturbances according to claim 2, characterized in that, The design process of the tracking controller is as follows: Define the following variables: , , , ;in, , To track errors, To predict tracking error; To predict the state, , For state variables, For the desired signal, Represents a virtual control law. This is the output of a first-order filter. This refers to the output error of the first-order filter. ; The first-state predictor is designed as follows: Among them, the prediction error of the first state variable , , Represents state variables , The predicted value, express The first derivative, It is a positive number; First Virtual Control Law Designed as follows: in, , ; It is a positive number; This is the first transformation error. , To define the performance function; , It is a positive integer; To predict tracking error; for The first derivative; for The first derivative; The second state predictor is designed as follows: Among them, the prediction error of the second state variable , , It is the weight matrix used in approximating the total perturbation at the load end using a radial basis function neural network. The estimated value, Gaussian function, Represents state variables The predicted value, It is a positive number; express The first derivative; Second Virtual Control Law Designed as follows: in, , ; It is a positive number; This is the second transformation error. To define the performance function; , It is a positive integer; for The first derivative; For the output of a first-order filter The first derivative; The third state predictor is designed as follows: Among them, the prediction error of the third state variable , For positive integers, Represents state variables The predicted value; express The first derivative; The third virtual control law Designed as follows: in, , ; It is a positive number; This is the third transformation error. To define the performance function; , It is a positive integer; for The first derivative; For the output of a first-order filter The first derivative; The fourth state predictor is designed as follows: Among them, the prediction error of the fourth state variable , , It is the weight matrix used in approximating the total disturbance at the motor terminals using a radial basis function neural network. The estimated value, Gaussian function, For positive integers, Indicates the tracking controller; This refers to the motor's inertia. express The first derivative; Tracking Controller Designed as follows: in, , This is the fourth transformation error; for The first derivative; For the output of a first-order filter The first derivative.

4. The predetermined performance control method for a dual-motor servo system taking into account external disturbances according to claim 3, characterized in that, The design of the synchronization controller is as follows: For the two motors in a dual-motor servo system, the system model of the dual-motor subsystem is established as follows: In the formula, This represents the input torque of the i-th motor; This represents the total disturbance at the i-th motor terminal; ; For the first The motor angular position of each motor; Based on the average deviation coupling strategy, the synchronization error is defined as: in, , , ; Define the integral sliding surface as: right Differentiation yields: in, , For tracking controller; ; ; Design an ideal equivalent virtual control law as follows: : The integral sliding surface derivative is rewritten as: in, ; Define the error vector as follows: Taking the derivative of the error vector, we get: in, , ; Based on the optimal control method, select the optimal synchronization performance index. for: in, and Given a positive definite symmetric matrix; design optimal control. for: In the formula, Solve from the Ricardi equation.

5. A predetermined performance control system for a dual-motor servo system that takes into account external disturbances, characterized in that, include: The first module is used to establish a dynamic model of a dual-motor servo system that takes into account external disturbances; The second module defines the total disturbance and state variables of the dual-motor servo system. Based on the total disturbance and state variables of the dual-motor servo system, the dynamic model of the dual-motor servo system considering external disturbances is transformed to obtain the state equation of the dual-motor servo system. A radial basis function neural network is constructed to estimate the total disturbance at the load end and the total disturbance at the motor end, respectively, and to obtain approximate values ​​of the total disturbance at the load end and the total disturbance at the motor end. The total disturbance of the dual-motor servo system includes the total disturbance at the load end and the total disturbance at the motor end. The third module is used to establish the prediction tracking error constraints based on the specified performance function; introduce a smooth and strictly increasing function of the transformation error to transform the prediction tracking error constraints into equivalent unconstrained conditions; and solve for the transformation error based on the introduced smooth and strictly increasing function of the transformation error; wherein the transformation error includes the first transformation error, the second transformation error, the third transformation error, and the fourth transformation error; The fourth module is used to design a predetermined performance controller based on a state predictor, which combines a tracking controller and a synchronization controller, as the input torque of the two motors in a dual-motor servo system, so as to realize the synchronization and tracking control of the dual-motor servo system. Based on the approximation value of the total disturbance at the motor end, the integral sliding mode optimal synchronous controller based on the average deviation coupling strategy is designed as follows: in, For the first Synchronization controller for each motor For an ideal equivalent virtual control law, For optimal control, For the first The inertia of a single motor. , , ; , It is the weight matrix used in approximating the total disturbance at the motor terminals using a radial basis function neural network. The estimated value, Gaussian function, It is a positive real number. For the first Average speed error of each motor For the first Average position error of each motor For the first The integral sliding surface of each motor, It is a constant.

6. A processor, characterized in that: The processor is used to run a program, wherein the program executes a predetermined performance control method for a dual-motor servo system taking into account external disturbances as described in any one of claims 1-4.

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