Predetermined performance control method and system of dual-motor servo system considering external disturbance

Abstract

The invention discloses a predetermined performance control method of a dual-motor servo system considering external disturbance. The method comprises the following steps: establishing a kinetic model of the dual-motor servo system considering the external disturbance; defining total disturbance and state variables of the dual-motor servo system; according to the total disturbance and the state variable of the dual-motor servo system, the kinetic model of the dual-motor servo system considering the external disturbance is transformed, and a state equation of the dual-motor servo system is obtained; constructing a radial basis function neural network to respectively estimate load end total disturbance and motor end total disturbance, and obtaining approximation values of the load end total disturbance and the motor end total disturbance; according to a specified performance function, a prediction tracking error constraint condition is established, and a transformation error is solved according to an introduced smooth strict increasing function of the transformation error; and designing a predetermined performance controller based on a state predictor in combination with the tracking controller and the synchronous controller. According to the method, the motors are tracked on the premise of ensuring the synchronization of the two motors, and the stability of the system is proved through the Lyapunov criterion.

Description

Technical Field

[0001] The invention relates to a predetermined performance control method and system for a dual-motor servo system taking external disturbance into account, and belongs to the technical field of load tracking of dual-motor servo systems. Background Art

[0002] In recent years, as industrial production has placed higher and higher demands on system driving capabilities, multi-motor servo systems have received more and more widespread attention in industrial production. There are two main difficulties in multi-motor servo systems: first, the gear transmission and surface non-smoothness cause the servo system to have backlash and friction nonlinearity problems, which are also problems that need to be solved in controller design; second, while considering the load tracking accuracy, we must also consider the impact of synchronization performance on it. The coupling of synchronization and tracking is also an important problem that needs to be solved in the controller design process.

[0003] The nonlinear problem in the servo system is the main reason that affects the dynamic performance of the system, so it must be properly handled in the design process of the controller. With the continuous in-depth research of scholars, more and more control methods are designed to deal with nonlinear problems, such as fuzzy control, neural network control, adaptive control, etc. The core of these control methods is to select appropriate adaptive laws and approximate nonlinear functions through linear functions. However, if the nonlinearity in the system is large, it will cause high-frequency oscillation in the system, which will greatly reduce the speed of adaptation and thus affect the control effect.

[0004] In order to improve tracking performance and ensure system safety, synchronous control between motors is equally important. As a complex high-order system, dynamic surface control is widely used in multi-motor servo systems, using filters to solve the complexity explosion problem in the system. Dynamic surface control can reduce the order of high-order systems to reduce system complexity, but in order to improve control accuracy, a larger gain is required, which will increase the system overshoot and reduce system stability.

[0005] In recent years, a variety of synchronous decoupling control strategies have been proposed to address the coupling problem of 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 may affect the transient performance of the control system. Summary of the invention

[0006] The present invention provides a method for predicting the performance of a dual-motor servo system taking into account external disturbances. For the dual-motor servo system, a tracking controller that introduces a neural network dynamic surface into a predictor and a prescribed performance function and a synchronization controller that combines an average deviation coupling control strategy with an optimal sliding mode control are proposed. The tracking of the motors is achieved while ensuring the synchronization of the dual motors. Finally, the stability of the system is proved by the Lyapunov criterion.

[0007] The technical solution of the present invention is:

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

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

[0010] S2. Define the total disturbance and state variables of the dual-motor servo system; transform the dynamic model of the dual-motor servo system taking into account the external disturbance according to the total disturbance and state variables of the dual-motor servo system to obtain the state equation of the dual-motor servo system; construct a radial basis 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;

[0011] S3. Establish a prediction tracking error constraint condition according to the specified performance function; introduce a smooth and strictly increasing function of the transformation error to convert the prediction tracking error constraint condition into an equivalent unrestricted condition; and solve the transformation error according to the introduced smooth and 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;

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

[0013] Furthermore, the S4 is specifically:

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

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

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

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

[0018] Define the following variables: e1 = x1-x d , e g+1 =x g+1 -η g , χ g =η g -α g ; Among them, e1, e g+1 is the tracking error, To predict tracking error; is the predicted state, x1, x g+1 is the state variable, x d is the expected signal, η g represents the virtual control law, α g is the first-order filter output, χ g is the first-order filter output error, j = 1, 2, 3, 4; g = 1, 2, 3;

[0019] The first state predictor is designed as:

[0020]

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

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

[0023]

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

[0025] The second state predictor is designed as:

[0026]

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

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

[0029]

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

[0031] The third state predictor is designed as:

[0032]

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

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

[0035]

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

[0037] The fourth state predictor is designed as:

[0038]

[0039] Among them, the prediction error of the fourth state variable is ψ2 is the estimated value of the weight matrix W2 in the radial basis neural network to approximate the total disturbance at the motor end, the Gaussian basis function, c4 is a positive constant, u tr represents the tracking controller; J m is the motor inertia; express The first derivative of

[0040] Tracking Controller tr Designed for:

[0041]

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

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

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

[0045]

[0046] In the formula, u i represents the input torque of the i-th motor; f 2i is the total disturbance at the i-th motor end; J mi ,θ mi are the motor inertia and motor angular position of the i-th motor respectively;

[0047] According to the average deviation coupling strategy, the synchronization error is defined as:

[0048]

[0049] in, e s1i is the average position error of the ith motor, e s2i is the average speed error of the i-th motor;

[0050]

[0051] The integral sliding surface is defined as:

[0052]

[0053] Among them, s i is the integral sliding surface of the i-th motor; β s is a positive real number; for s i The derivative is:

[0054]

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

[0056] Design the ideal equivalent virtual control law as u eqi :

[0057]

[0058] Rewrite the integrated sliding surface derivative as:

[0059]

[0060] in, k c is a constant;

[0061] Define the error vector as:

[0062]

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

[0064]

[0065] in,

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

[0067]

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

[0069]

[0070] Where P s Solve from the Riccati equation;

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

[0072]

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

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

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

[0076] The second module is used to define the total disturbance and state variables of the dual-motor servo system; according to the total disturbance and state variables of the dual-motor servo system, the dynamic model of the dual-motor servo system taking into account the external disturbance is transformed to obtain the state equation of the dual-motor servo system; a radial basis neural network is constructed to estimate the total disturbance at the load end and the total disturbance at the motor end respectively, and the approximate values ​​of the total disturbance at the load end and the total disturbance at the motor end are obtained; 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;

[0077] The third module is used to establish a prediction tracking error constraint condition according to a specified performance function; introduce a smooth and strictly increasing function of the transformation error to convert the prediction tracking error constraint condition into an equivalent unrestricted condition; and solve the transformation error according to the introduced smooth and 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;

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

[0079] According to a third aspect of the present invention, a processor is provided, wherein the processor is used to run a program, wherein when the program is run, the predetermined performance control method of the dual-motor servo system taking into account external disturbances as described in any one of the above is executed.

[0080] The beneficial effects of the present invention are:

[0081] First, the present invention introduces a state predictor to achieve fast and smooth approximation without high-frequency oscillation and eliminate 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, combined with the specified performance function, the predicted tracking error and the tracking error are constrained within the specified range; and, excessive overshoot of the tracking error beyond the performance limit can be prevented, thereby reducing the convergence time.

[0083] Thirdly, the present invention designs an average deviation coupling synchronization structure, which solves the coupling problem of load tracking and motor synchronization in the dual-motor servo system, greatly reducing the difficulty of tracking controller design; it realizes the tracking of the motors while ensuring the synchronization of the dual motors; finally, the stability of the system is proved by the Lyapunov criterion. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0085] Figure 2 A schematic diagram of the load position tracking effect and tracking error involved in the present invention;

[0086] Figure 3 A schematic diagram of motor disturbance estimation and estimation error of a dual-motor servo system according to the present invention;

[0087] Figure 4 An estimation curve and an estimation error curve of the motor side disturbance by the radial basis function neural network provided in an embodiment of the present invention;

[0088] Figure 5 An estimation curve and an estimation error curve of a load-side disturbance by a radial basis function neural network provided in an embodiment of the present invention;

[0089] Figure 6 A motor synchronous position curve of a dual-motor servo system provided by an embodiment of the present invention;

[0090] Figure 7 A schematic diagram of motor synchronization error of a dual-motor servo system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0091] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. It should be noted that the embodiments in this application and the features in the embodiments can be combined with each other arbitrarily without conflict.

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

[0093] S1. Establish a dynamic model of the dual-motor servo system taking into account external disturbances, and initialize the state and parameters of the dual-motor servo system taking into account 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 are the motor inertia, motor angular position, motor viscous friction coefficient and external disturbance at the motor end of the i-th motor; J l is the load inertia; θ l is the load angular position; b l is the load viscous friction coefficient; Td l is the external disturbance at the load end, u i is the system input torque of the ith motor, τ i is the transmitted torque when the i-th motor contacts 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 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, that is, the stiffness coefficient of the gear connected to the load; v is the transmission ratio, and in the embodiment of the present invention, α=0.1 and v=1 are set.

[0100] S2. Define the total disturbance and state variables of the dual-motor servo system; transform the dynamic model of the dual-motor servo system taking into account the external disturbance according to the total disturbance and state variables of the dual-motor servo system to obtain the state equation of the dual-motor servo system; construct a radial basis 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] Furthermore, the S2 includes:

[0102] S2.1. Define the total disturbance and state variables of the dual-motor servo system; transform the dynamic model of the dual-motor servo system taking into account the external disturbance according to the total disturbance and state variables of the dual-motor servo system 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 is the total disturbance at the i-th motor terminal.

[0106] Select the system state variable as Defining state variables definition Then the state equation of the dual-motor servo system is:

[0107]

[0108] Where y is the output of the dual-motor servo system; Respectively represent the first derivatives of the first state variable x1, the second state variable x2, the third state variable x3, and the fourth state variable x4;

[0109] Assumption 1: The two motors in the dual-motor servo system are of the same model, so 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 A number greater than zero.

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

[0112] RBF neural network is a fully connected network with 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 basis function, expressed as:

[0114]

[0115] Among them, C I ∈R m represents the center point vector value of the function, is the width of the function, and I is the number of hidden layer nodes. The more hidden layer nodes there are, the better the neural network approximates the unknown function, but the approximation speed will be slower. In the embodiment of the present invention, n=9 is set; based on this value, it is applied in the approximation of the total disturbance at the load end and the total disturbance at the motor end, and a better approximation effect is achieved.

[0116] The total disturbance f1 and f are analyzed by using radial basis function neural network. 2i Approximation, that is:

[0117]

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

[0119] S3. Establish prediction tracking error constraints based on the specified performance function; introduce a smooth and strictly increasing function of the transformation error to convert the prediction tracking error constraints into equivalent unrestricted conditions; and solve the transformation error based on the introduced smooth and 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.

[0120] The present invention adopts a positive monotonically decreasing function as the specified performance function ρ j (t) 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 is a designed normal number.

[0123] The forecast tracking error constraint is implemented by the following equation:

[0124]

[0125] in, To predict the tracking error, m j and Is a normal number.

[0126] In order to transform the constraint condition (8) into an equivalent unconstrained condition, the transformation error z is introduced j Smooth strictly increasing function S∈R j (z j )for:

[0127]

[0128] The above formula can be used to solve the transformation error z j for:

[0129]

[0130] Among them, the intermediate variable

[0131] S4, based on the state predictor, transformation error, dynamic surface control method to design tracking controller and based on the average deviation coupling strategy, integral sliding surface and optimal control of the synchronous controller, the two are combined to design the state predictor based on the predetermined performance controller as the dual motor servo system input torque, to achieve synchronous operation between the motors while achieving the system output x1 to the desired signal x d Further, including the following:

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

[0133] In order to avoid the problem of "differential explosion" during calculation, the present invention adopts a dynamic surface control method combining a first-order filter with a backstepping method.

[0134] Because the proposed controller is completed in multiple steps, the following variables are defined: e1 = x1-x d , e g+1 =x g+1 -η g , χ g =η g -α g ; Among them, e j is the tracking error, is the forecast tracking error, that is is the predicted state, x j is the state variable, η g represents the virtual control law, α g is the first-order filter output, χ gis the filter output error, j=1,…,4; g=1,2,3.

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

[0136]

[0137] Among them, T g is the time constant, Represents α g The first derivative of g (0), η g (0) indicates α g , η g The initial value of η g , α g is a function of time, namely η g (t), α g (t).

[0138] The first state predictor is designed as:

[0139]

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

[0141] Choose the Lyapunov function as:

[0142]

[0143] By taking the derivative of formula (13), we can get:

[0144]

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

[0146]

[0147] in, when When , we can get 0 <p1≤p m1 , p m1 is a normal number; 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:

[0149]

[0150] Among them, 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] Among them, Γ1 and σ1 are both positive constants.

[0154] The second state predictor is designed as:

[0155]

[0156] Among them, the prediction error of the second state variable is is the estimated value of W1, represents the predicted value of x3, and c2 is a normal number.

[0157] Choose the Lyapunov function as:

[0158]

[0159] By taking the derivative of formula (19), we can get:

[0160]

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

[0162]

[0163] in, when When , we can get 0 <p2≤p m2 , p m2 is a normal number.

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

[0165]

[0166] Among them, δ2>0, k2>0.

[0167] The third state predictor is designed as:

[0168]

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

[0170] Choose the Lyapunov function as:

[0171]

[0172] By taking the derivative of formula (24), we can get:

[0173]

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

[0175]

[0176] in, when When , we can get 0 <p3≤p m3 , p m3 is a normal number.

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

[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] Among them, Γ2 and σ2 are both positive constants.

[0183] The fourth state predictor is designed as:

[0184]

[0185] Among them, the prediction error of the fourth state variable is is the estimated value of W2, c4 is a positive constant, u tr Represents a tracking controller.

[0186] Choose the Lyapunov function as:

[0187]

[0188] By taking the derivative of formula (30), we can get:

[0189]

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

[0191]

[0192] in, when When , we can get 0 <p4≤p m4 , p m4 is a normal number.

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

[0194]

[0195] Among them, k4>0.

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

[0197] Will track the controller u tr Substituting into formula (31) we get:

[0198]

[0199] in, m1 is a constant.

[0200] Using Young's inequality we can get:

[0201]

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

[0203] make Substituting formula (35) into formula (34), we can obtain:

[0204]

[0205] in,

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

[0207]

[0208] because Both and ∈ are bounded, so the system error will converge to a very small neighborhood of the origin.

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

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

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

[0212]

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

[0214] According to the average deviation coupling strategy, the synchronization error is defined as:

[0215]

[0216] in, e s1i is the average position error of the ith motor, e s2i is the average speed error of the i-th motor.

[0217] The integral sliding surface is defined as:

[0218]

[0219] Among them, s i is the integral sliding surface of the i-th motor; β s is a positive real number; for s i The derivative is:

[0220]

[0221] in, u syi is the synchronous controller of the i-th motor,

[0222] In order to keep the system state on the sliding surface, that is, e si =u syi -u eqi , the ideal equivalent virtual control law is designed as:

[0223]

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

[0225]

[0226] in, k c is a constant.

[0227] Define the error vector as:

[0228]

[0229] By taking the derivative of formula (44), we can get:

[0230]

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

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

[0233]

[0234] Among them, Q s and R s is a positive symmetric matrix. In order to minimize equation (46) and achieve the optimal control objective, the optimal control is designed. for:

[0235]

[0236] Where P s It can be solved from the Riccati equation as follows:

[0237]

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

[0239]

[0240] in,

[0241] Proof: Select the Lyapunov function:

[0242]

[0243] Taking its derivative we get:

[0244]

[0245] in,

[0246] Combining formula (48), we can get:

[0247]

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

[0249]

[0250] From the above formula (52) and formula (53), we can get:

[0251]

[0252] Among them, k s and δ are:

[0253]

[0254] It can be seen from formula (55) that 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 predetermined performance controller based on a state predictor by combining a tracking controller and a synchronous controller as the input torque of the two motors in the dual-motor servo system:

[0256]

[0257] Where, u1 and u2 are the input torques of the first motor and the second motor respectively; u sy1 、u sy2 They are the synchronous controllers for the first motor and the second motor respectively; u tr For tracking controller.

[0258] According to the above-mentioned predetermined performance controller based on the state predictor, on the one hand, the system output x1 is realized to the expected signal x d On the other hand, it realizes the synchronous operation between the first motor and the second motor.

[0259] According to a second aspect of an embodiment of the present invention, a predetermined performance control system for a dual-motor servo system taking into account external disturbances is provided, comprising: a first module for establishing a dynamic model of the dual-motor servo system taking into account external disturbances; a second module for defining a total disturbance and state variables of the dual-motor servo system; transforming the dynamic model of the dual-motor servo system taking into account external disturbances according to the total disturbance and state variables of the dual-motor servo system to obtain a 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 is The first module is used to establish the predicted tracking error constraint condition according to the specified performance function; introduce the smooth and strict increasing function of the transformation error to convert the predicted tracking error constraint condition into an equivalent unrestricted condition; and solve the transformation error according to the smooth and strict increasing function of the introduced 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 the state predictor in combination with 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 the parts not described in detail in the above modules, please refer to the relevant description of this embodiment.

[0260] According to a third aspect of an embodiment of the present invention, a processor is provided, wherein the processor is used to run a program, wherein when the program is run, the predetermined performance control method of a dual-motor servo system taking into account external disturbances as described in any one of the above is executed.

[0261] Example 2: In order 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, and the specific parameters are set as follows:

[0262] The dynamic model of the dual-motor servo system is established as

[0263]

[0264] The dual motor servo system is used as the research object. The system parameters are selected as follows: m =J m1 =J m2 =0.185kg·m 2 , b m =b m1 =b m2 =1.2N·m·s / rad, J l =0.028kg·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 expected signal is defined as: x d =sin(t).

[0265] The specific parameters of the control method of the present invention are designed as follows: The designed controller parameters: 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] At the same time, the proposed control method is compared with three other control methods: 1) Reference 1 Du Renhui, Wu Yifei, Chen Wei, etc. Backstep 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 by the present invention (PPNDSC_OPSMC). Among them, the parameters in references 1 and 3) are all based on the parameters in the references, and the parameters in reference 2) are designed as follows: k p =45, k i =0.1.

[0267] The proposed control method is simulated and compared with the other three control methods, and the simulation results are as follows: Figure 2-Figure 7 As shown, the tracking curve of the output signal to the expected signal and the tracking error curve in the dual-motor servo system are shown as follows: Figure 2 and Figure 3 As shown in the figure; the estimation curve of the radial basis neural network for the disturbance on the motor side and the load side and the estimation error curve are shown in the figure 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 shown.

[0268] pass Figure 2 and Figure 3 It can be seen that the predetermined performance control method of the dual-motor servo system taking into account external disturbances proposed in the present invention has a faster response speed and a smaller tracking error than the other three control methods, and relatively speaking, has better control performance.

[0269] from Figure 4 and Figure 5 It can be seen that the radial basis function neural network introduced in the present invention can estimate the system disturbance well and has a good estimation effect.

[0270] from Figure 6 and Figure 7 It can be seen that the predetermined performance control method for the dual-motor servo system taking into account external disturbances proposed in the present invention takes less time to achieve motor synchronization and has a smaller synchronization error than the other three control methods.

[0271] In summary, the predetermined performance control method of the dual-motor servo system taking into account external disturbances can effectively improve the convergence speed of the system and has a better control effect.

[0272] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A method for controlling the predetermined performance of a dual-motor servo system taking into account external disturbances, characterized in that: The following steps are involved: S1. Establish a dynamic model of the dual-motor servo system taking into account external disturbances; S2. Define the total disturbance and state variables of the dual-motor servo system; transform the dynamic model of the dual-motor servo system taking into account the external disturbance according to the total disturbance and state variables of the dual-motor servo system to obtain the state equation of the dual-motor servo system; construct a radial basis 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; S3. Establish a prediction tracking error constraint condition according to the specified performance function; introduce a smooth and strictly increasing function of the transformation error to convert the prediction tracking error constraint condition into an equivalent unrestricted condition; and solve the transformation error according to the introduced smooth and 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; S4. Combining the tracking controller and the synchronization controller, a predetermined performance controller based on a state predictor is designed as the input torque of the two motors in the dual-motor servo system to achieve synchronization and tracking control of the dual-motor servo system.

2. The method for controlling the predetermined performance of a dual-motor servo system taking into account external disturbances according to claim 1, characterized in that: The S4 is specifically: S4.

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

2. Based on the approximate value of the total disturbance at the motor end, an integral sliding mode optimal synchronization controller based on the average deviation coupling strategy is designed; S4.

3. Combining the tracking controller and the synchronization controller, a predetermined performance controller based on the state predictor is designed as the input torque of the two motors in the dual-motor servo system to achieve synchronization and tracking control of the dual-motor servo system.

3. The method for controlling the predetermined performance of 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 specifically as follows: Define the following variables: e1 = x1-x d , e g+1 =x g+1 -η g , χ g =η g -α g ; Among them, e1, e g+1 is the tracking error, To predict tracking error; is the predicted state, x1, x g+1 is the state variable, x d is the expected signal, η g represents the virtual control law, α g is the first-order filter output, χ g is the first-order filter output error, j = 1, 2, 3, 4; g = 1, 2, 3; The first state predictor is designed as: Among them, the prediction error of the first state variable is represents the predicted values ​​of state variables x1 and x2, express The first derivative of , c1 is a positive constant; The first virtual control law η1 is designed as: Among them, δ1>0, k1>0; is a positive constant; z1 is the first transformation error, ρ1 and ρ2 are the specified performance functions; 0 <p1≤p m1 , p m1 is a positive constant; To predict tracking error; is the first-order derivative of ρ1; For x d The first derivative of The second state predictor is designed as: Among them, the prediction error of the second state variable is ψ1 is the estimated value of the weight matrix W1 and the Gaussian basis function in approximating the total disturbance at the load end using the radial basis neural network. represents the predicted value of the state variable x3, c2 is a normal number; express The first derivative of The second virtual control law η2 is designed as: Among them, δ2>0, k2>0; is a positive constant; z2 is the second transformation error, ρ3 is the specified performance function; 0 <p2≤p m2 , p m2 is a positive constant; is the first derivative of ρ2; The first-order derivative of the first-order filter output α1; The third state predictor is designed as: Among them, the prediction error of the third state variable is c3 is a positive constant, represents the predicted value of the state variable x4; express The first derivative of The third virtual control law η3 is designed as: Among them, δ3>0, k3>0; is a positive constant; z3 is the third transformation error, ρ4 is the specified performance function; 0 <p3≤p m3 , p m3 is a positive constant; is the first derivative of ρ3; The first-order derivative of the first-order filter output α2; The fourth state predictor is designed as: Among them, the prediction error of the fourth state variable is ψ2 is the estimated value of the weight matrix W2 in the radial basis neural network to approximate the total disturbance at the motor end, the Gaussian basis function, c4 is a positive constant, u tr represents the tracking controller; J m is the motor inertia; express The first derivative of Tracking Controller tr Designed for: Wherein, k4>0, z4 is the fourth transformation error; is the first derivative of ρ4; is the first-order derivative of the first-order filter output α3;.

4. The method for controlling the predetermined performance of a dual-motor servo system taking into account external disturbances according to claim 3, characterized in that: The design of the synchronous controller is specifically as follows: For the two motors in the dual-motor servo system, the system model of the dual-motor subsystem is established as follows: In the formula, u i represents the input torque of the i-th motor; f 2i is the total disturbance at the i-th motor end; J mi ,θ mi are the motor inertia and motor angular position of the i-th motor respectively; According to the average deviation coupling strategy, the synchronization error is defined as: in, e s1i is the average position error of the ith motor, e s2i is the average speed error of the i-th motor; The integral sliding surface is defined as: Among them, s i is the integral sliding surface of the i-th motor; β s is a positive real number; for s i The derivative is: in, u syi is the synchronous controller of the i-th motor, u tr For tracking controller; Design the ideal equivalent virtual control law as u eqi : Rewrite the integrated sliding surface derivative as: in, k c is a constant; Define the error vector as: Taking the derivative of the error vector we get: in, B s =[0 0 1] T ; Based on the optimal control method, select the optimal synchronization performance index J s for: Among them, Q s and R s is a positive definite symmetric matrix; design optimal control for: Where P s Solve from the Riccati equation; Based on the approximate value of the total disturbance at the motor end, the integral sliding mode optimal synchronization controller based on the average deviation coupling strategy is designed as follows: in, ψ 2i It is the estimated value and Gaussian basis function of the weight matrix W2 in approximating the total disturbance at the motor end using the radial basis neural network.

5. A predetermined performance control system for a dual-motor servo system taking into account external disturbances, characterized in that: include: The first module is used to establish a dynamic model of a dual-motor servo system taking into account external disturbances; The second module is used to define the total disturbance and state variables of the dual-motor servo system; according to the total disturbance and state variables of the dual-motor servo system, the dynamic model of the dual-motor servo system taking into account the external disturbance is transformed to obtain the state equation of the dual-motor servo system; a radial basis neural network is constructed to estimate the total disturbance at the load end and the total disturbance at the motor end respectively, and the approximate values ​​of the total disturbance at the load end and the total disturbance at the motor end are obtained; 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; The third module is used to establish a prediction tracking error constraint condition according to a specified performance function; introduce a smooth and strictly increasing function of the transformation error to convert the prediction tracking error constraint condition into an equivalent unrestricted condition; and solve the transformation error according to the introduced smooth and 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 in combination with a tracking controller and a synchronization controller as the input torque of two motors in a dual-motor servo system to achieve synchronization and tracking control of the dual-motor servo system.

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

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