Precise double-drive motion platform synchronous control method based on composite adaptive online estimation

Abstract

The invention discloses a precise double-drive motion platform synchronous control method based on composite adaptive online estimation, and relates to the field of precise motion platform cooperative control. According to the invention, the problems of poor task tracking performance and low synchronization performance of the double-drive motion platform are solved. A B-spline wavelet neural network online identification model generates a neural network weight matrix # imgabs0 # for updating through a specially-designed neural network weight composite updating model, and unknown parameters of a system are updated through a constructed system parameter composite updating model. Real-time model compensation is carried out on the double-drive motion platform through a constructed expected compensation model, model compensation is carried out on unmodeled dynamics and external interference of a double-drive motion platform system through a constructed B-spline wavelet neural network online identification model, and then robust stabilization is carried out through constructing a robust feedback controller. Therefore, the task tracking performance and synchronism of the double-drive motion platform are improved. The method is mainly used for synchronously controlling the double-drive gantry motion platform.

Description

Technical Field

[0001] The invention relates to the field of coordinated control of precision motion platforms. Background Art

[0002] As a key component of modern industry, high-end equipment is playing an important role in more and more fields. Precision motion platforms have become an important part of the motion system of high-end equipment due to their high stiffness and excellent dynamic performance. Dual-drive motion platforms are the most common type of precision motion platforms and are widely used in industries such as electronic packaging and semiconductor manufacturing. Dual-drive motion platforms usually use two parallel symmetrical linear motors to drive the motion axis, and use additional linear motors to control the movement of the platform along a linear path. The synchronization accuracy between the two motors driving the motion axis is a key limiting factor affecting the overall performance of the system. Large synchronization errors between the two motors may seriously impair the task tracking capability of the platform and may even cause damage to the platform.

[0003] In recent years, researchers have proposed many control methods for this problem, such as PID, sliding mode, adaptive robust control methods, etc., which have alleviated the problem of excessive synchronization error during the movement of the dual-drive motion platform to a certain extent. However, these methods still have some limitations: First, the robust control method represented by sliding mode control is highly conservative, which is not conducive to the high-precision target tracking pursued by the control process; second, although the adaptive robust control method is widely used because it has the advantages of both adaptive and robust control methods, many researchers have pointed out that the adaptive performance of the method for model parameters in a time-varying environment is greatly reduced, which is very unfavorable in actual industrial applications.

[0004] In addition, nonlinear factors such as the cogging force and end effect of the linear motor, the load changes and external interference encountered by the platform during movement are also a great challenge for precision motion control. Traditional control methods often use increasing control gain to suppress interference, but this method is not completely applicable to precision motion control. Too high control gain will cause the platform to vibrate. In order to solve this problem, the control method of "controller + neural network compensation" has become the research focus of more and more researchers, but most neural networks have too much calculation due to their complex structure, which is not conducive to ensuring the high real-time performance of precision motion control. To this end, relevant researchers proposed a B-spline wavelet neural network, which improves the calculation efficiency by designing a special activation function and can adjust parameters according to the platform characteristics, providing a basis for network structure design. Although the above progress has been made in compensating for nonlinear factors such as uncertainty encountered by the platform, most of these methods still rely on the use of Lyapunov theory to update the weights of the neural network, ignoring the accuracy of the neural network's approximation of nonlinear factors, which will lead to an increase in approximation errors, affect the compensation performance of the neural network, and ultimately reduce the synchronous control performance.

[0005] The introduction of the composite adaptive control method provides a new solution to the synchronous control problem of the dual-drive motion platform. Unlike the traditional adaptive method that only relies on the tracking error of the system to update the parameters, the composite adaptive control uses the tracking error and parameter prediction error to simultaneously drive the update of the unknown parameters of the system, thereby improving the tracking ability of the model parameters in a time-varying environment. However, the existing composite adaptive control is a fragile adaptive control with poor robustness. Under strong external interference, it will lead to a decrease in the synchronous control performance. Therefore, the above problems need to be solved urgently. Summary of the invention

[0006] The purpose of the present invention is to solve the problems of poor task tracking performance and low synchronization performance of a dual-drive motion platform; the present invention provides a precision dual-drive motion platform synchronization control method based on composite adaptive online estimation.

[0007] A precision dual-drive motion platform synchronization control method based on composite adaptive online estimation is implemented based on a composite adaptive robust controller, a neural network weight composite update model and a system parameter composite update model, and the composite adaptive robust controller includes an expected compensation model, a B-spline wavelet neural network online identification model and a robust feedback controller; the method includes:

[0008] Step 1: Establish a rigid-flexible coupling dynamics model of the dual-drive motion platform, and set the initial values ​​of each parameter in the system unknown parameter vector of the rigid-flexible coupling dynamics model at the initial moment, as well as the virtual control vector at the initial moment;

[0009] Step 2: Neural network weight compound update model, according to the beam position vector p of the dual-drive motion platform at time t-1 s (t-1), velocity vector Reference position vector p d (t-1), reference velocity vector And the beam position vector p at time t-2 s (t-2), velocity vector Reference position vector p d (t-2), reference velocity vector Get the neural network weight matrix at time t at the same time,

[0010] The system parameter compound update model is based on the beam position vector p of the dual-drive motion platform at time t-1. s (t-1), velocity vector Reference position vector p d (t-1), reference velocity vector Virtual control vector τ(t-1) and system unknown parameter vector Estimate the unknown parameter vector of the system at time t , and Send to the expected compensation model;

[0011] Step 3: Expected compensation model, based on the received reference position vector p at the current time t d (t), reference velocity vector Reference acceleration vector and the unknown system parameter vector Generate model compensation signal τ a (t);

[0012] The B-spline wavelet neural network online identification model is based on the real-time acquisition of the beam position vector p of the dual-drive motion platform at the current time t. s (t), velocity vector and the neural network weight matrix Generate feedforward compensation signal τ nn (t);

[0013] The robust feedback controller is based on the real-time acquired beam position vector p of the dual-drive motion platform at the current time t s (t), velocity vector and the reference position vector p d (t) and the reference velocity vector Generate a robust feedback compensation signal τ s (t);

[0014] Step 4: Compensate the model signal τa (t), feedforward compensation signal τ nn (t) and robust feedback compensation signal τ s After superposition of (t), the actual control vector τ is calculated based on the obtained virtual control vector τ(t) u (t), to control the two linear motors of the dual-drive motion platform.

[0015] Preferably, in step 2, the neural network weight matrix at time t is obtained The implementation methods include

[0016] Step 2: According to the beam position vector p s (t-1), velocity vector Reference position vector p d (t-1) and the reference velocity vector Calculate the sliding surface vector ρ(t-1) at time t-1;

[0017] According to the beam position vector p at time t-2 s (t-2), velocity vector Reference position vector p d (t-2), reference velocity vector Calculate the sliding surface vector ρ(t-2) at time t-2;

[0018] According to the beam position vector p at time t-2 s (t-2) and the reference position vector p d (t-2), calculate the system tracking error z(t-2) at time t-2;

[0019] Step 2: According to ρ(t-1), ρ(t-2) and z(t-2), the neural network prediction error vector δ(t-1) at time t-1 is obtained. Specifically,

[0020]

[0021] M s is the mass of the system, K ρ is the sliding mode control gain matrix, K z is the proportional control gain matrix, is the first-order derivative of ρ(t-1);

[0022] Step 2-3: According to δ(t-1) and ρ(t-1), obtain the rate of change of the neural network weights in the direction of motion at time t-1 and the rate of change of the neural network weights in the beam rotation direction

[0023] Step 214: and Perform integral processing to obtain and

[0024] according to and get

[0025] according to and get

[0026] in, and are the neural network weight estimation vectors of the beam movement direction and beam rotation direction at time t-1, and are the neural network weight estimation vectors of the beam motion direction and beam rotation direction at time t respectively;

[0027] Step 215: According to and get

[0028] Preferably, in step 2-3, and The implementation is:

[0029] First, rewrite δ(t-1) and ρ(t-1) to obtain:

[0030] δ(t-1)=[δ y (t-1), δ α (t-1)] T ;

[0031] ρ(t-1)=[ρ y (t-1), ρ α (t-1)] T ;

[0032] Secondly, according to δ y (t-1) and ρ y (t-1), get the rate of change of the neural network weights in the direction of beam movement at time t-1 According to δ α (t-1) and ρ α (t-1), get the rate of change of the neural network weights in the beam rotation direction at time t-1 in,

[0033]

[0034] χ y and χ αare the composite learning gains of the neural network weights in the beam motion direction and the beam rotation direction, respectively. and They are the hidden layer activation functions of the neural network of the neural network weight compound update model in the beam movement direction and the beam rotation direction respectively;

[0035] κ ry and κ rα are the neural network prediction error weight matrices in the beam motion direction and beam rotation direction, respectively. y (·) and Proj α (·) represent the projection mapping function in the beam motion direction and beam rotation direction, respectively, δ y (t-1) and δ α (t-1) are the beam motion direction prediction error and beam rotation error at time t-1, ρ y (t-1) and ρ α (t-1) are the components of the sliding surface vector in the direction of beam movement and the component of the sliding surface vector in the direction of beam rotation at time t-1 respectively.

[0036] Preferably,

[0037]

[0038] b wy and b wα They are the upper bounds of the neural network weights in the direction of beam movement and beam rotation, respectively.

[0039] Preferably, in step 214,

[0040] h is the system sampling time interval.

[0041] Preferably, in step 2, the unknown parameter vector of the system at time t is estimated The implementation methods of the value include:

[0042] Step 221: According to the beam position vector p s (t-1), velocity vector Reference position vector p d (t-1) and the reference velocity vector Calculate the sliding surface vector ρ(t-1) at time t-1; where,

[0043]

[0044] z(t-1)=p s (t-1)-p d (t-1);

[0045]

[0046] is the derivative of z(t-1), z(t-1) is the system tracking error at time t-1, Λ is a 2×2 positive definite diagonal gain matrix;

[0047] At the same time, according to the virtual control vector τ(t-1) and the system unknown parameter vector Calculate the system unknown parameter prediction error vector ξ(t-1); where,

[0048]

[0049] τ f (t-1) is the value after filtering the virtual control vector τ(t-1);

[0050] Step 222: According to ρ(t-1) and ξ(t-1), obtain the change rate of the unknown parameters of the system at time t-1

[0051] Step 223: Perform integration to obtain the unknown parameter vector of the system at time t-1

[0052] Step 224: According to and Get the unknown parameter vector of the system at time t

[0053] Preferably, in step 222, the change rate of the unknown parameter of the system at time t-1 is obtained The implementation methods include:

[0054]

[0055] in, is the projection mapping function of the unknown system parameters, Γ(t-1) is the composite update adaptive gain matrix of the unknown system parameters at time t-1, ψ d (t-1) is the generalized regression matrix using the reference trajectory signal at time t-1, Q is the system unknown parameter prediction error weight matrix, is the unknown parameter estimation vector of the system, I is the identity matrix, for The unit normal vector at θ represents the set of closures that restrict the unknown parameter vector, and Respectively represent Ω θ The boundaries and interior sets of represent The unit normal vector at time .

[0056] Preferably, in step 224,

[0057]

[0058] Preferably, the robust feedback controller generates a robust feedback compensation signal τ s (t) is implemented as follows:

[0059] τ s (t) = -K ρ ρ(t)-K z z(t);

[0060] z(t)=p s (t)-p d (t),

[0061] ρ(t) is the sliding surface vector at time t, z(t) is the system tracking error at time t, is the derivative of z(t), Λ is a 2×2 positive definite diagonal gain matrix;

[0062] The expected compensation model generates the model compensation signal τ a (t) is implemented as follows:

[0063]

[0064] ψ d (t) is the reference position vector p d (t), reference velocity vector Reference acceleration vector The generalized regression matrix formed;

[0065] B-spline wavelet neural network online identification model generates feedforward compensation signal τ nn (t) is implemented as follows:

[0066] τ nn (t) = [τ nny (t), τ nnα (t)] T ;

[0067] in,

[0068]

[0069] τ nny (t) is the feedforward compensation signal in the direction of beam motion, τ nnα (t) is the feedforward compensation signal in the direction of beam rotation, i y is the horizontal coordinate number of the node marked as the beam movement direction in the hidden layer of the B-spline wavelet neural network, is the ordinate number of the node marked as the beam motion direction in the hidden layer of the B-spline wavelet neural network, i α is the horizontal coordinate number of the node marked as the beam rotation direction in the hidden layer of the B-spline wavelet neural network, is the ordinate number of the node marked as the beam rotation direction in the hidden layer of the B-spline wavelet neural network, b y is the beam position vector p s (t) Center of mass position of the middle beam y G The translation factor, is the velocity vector Center of mass speed of middle beam The translation factor, b α is the beam position vector p s (t) is the translation factor for the beam rotation angle α, is the beam position vector p s (t) Angular velocity of the middle beam The translation factor,

[0070] is the activation function value of the node marked as the direction of beam movement in the hidden layer of the B-spline wavelet neural network;

[0071] is the activation function value of the node marked as the rotation direction of the beam in the hidden layer of the B-spline wavelet neural network.

[0072] Preferably,

[0073] τ u (t) = Π -1 τ(t);

[0074] Π=[1,K m , -L m1 , K m L m2 ];

[0075] Among them, Π is the thrust distribution matrix, K m is the ratio of the thrust coefficients of the two linear motors, L m1 and L m2 are the distances from the center of mass of the beam to the two linear motors M1 and M2 respectively.

[0076] The beneficial effects brought by the present invention are:

[0077] 1. The precision dual-drive motion platform synchronization control method based on composite adaptive online estimation designed by the present invention is based on a robust feedback controller, a B-spline wavelet neural network online identification model with a neural network weight composite update model, and an expected compensation model with a system parameter composite update model. The method of the present invention constructs a composite adaptive robust controller based on composite adaptive online estimation, and the composite adaptive robust controller includes a robust feedback controller, a B-spline wavelet neural network online identification model and an expected compensation model;

[0078] Among them, the B-spline wavelet neural network online identification model generates a neural network weight matrix through a specially designed neural network weight composite update model Make updates;

[0079] The unknown parameters of the system are updated through the constructed system parameter composite update model; the real-time model compensation of the dual-drive motion platform is performed through the constructed expected compensation model, and the unmodeled dynamics and external disturbances of the dual-drive motion platform system are model compensated through the constructed B-spline wavelet neural network online identification model. Then, robust stabilization is performed by constructing a robust feedback controller, thereby improving the task tracking and synchronous controllability of the dual-drive motion platform.

[0080] 2. In terms of controller design, the present invention adopts composite adaptive control to improve the existing adaptive robust control method, which is of great significance for dual-drive motion platforms in time-varying environments. At the same time, in terms of neural network design, the method is used to design a new B-spline wavelet neural network, which can also achieve high-precision compensation for nonlinear factors and interference while ensuring the real-time performance of the system.

[0081] 3. The precision dual-drive motion platform synchronization control method based on composite adaptive online estimation designed by the present invention can achieve a balance between task tracking performance and synchronization performance of the dual-drive motion platform system when faced with complex unmodeled dynamics and unknown interference in actual industrial production. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a schematic diagram of the principle of the precise dual-drive motion platform synchronization control method based on composite adaptive online estimation described in the present invention;

[0083] Figure 2 This is a schematic diagram of the internal principle of the neural network weight compound update model;

[0084] Figure 3 It is a schematic diagram of the internal principle of the system parameter composite update model;

[0085] Figure 4 It is a schematic diagram of the mechanism model of the dual-drive motion platform;

[0086] Figure 5 This is a physical picture of the experimental platform;

[0087] Figure 6 Comparison diagram of tracking errors using a traditional indirect adaptive robust control method, a composite adaptive robust control method based on expected compensation, a control method formed by combining a composite adaptive robust controller based on expected compensation and a B-spline wavelet neural network compensator, and the method of the present invention;

[0088] Figure 7 A comparison diagram of the beam rotation angles using the traditional indirect adaptive robust control method, the composite adaptive robust control method based on expected compensation, the control method formed by combining a composite adaptive robust controller based on expected compensation and a B-spline wavelet neural network compensator, and the method of the present invention;

[0089] Figure 8 Comparison diagrams of maximum tracking error and root mean square error using a traditional indirect adaptive robust control method, a composite adaptive robust control method based on expected compensation, a control method formed by combining a composite adaptive robust controller based on expected compensation and a B-spline wavelet neural network compensator, and the method of the present invention;

[0090] Fig. 9 The figures are a comparison of the traditional indirect adaptive robust control method, the composite adaptive robust control method based on expected compensation, the control method formed by combining a composite adaptive robust controller based on expected compensation and a B-spline wavelet neural network compensator, and the maximum crossbeam rotation angle and the root mean square of the crossbeam rotation angle under the method of the present invention. DETAILED DESCRIPTION

[0091] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0092] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0093] Specific implementation method 1. Figure 1The present embodiment is described. The precision dual-drive motion platform synchronization control method based on composite adaptive online estimation described in the present embodiment is implemented based on a composite adaptive robust controller, a neural network weight composite update model and a system parameter composite update model, and the composite adaptive robust controller includes an expected compensation model, a B-spline wavelet neural network online identification model and a robust feedback controller; the method includes:

[0094] Step 1: Establish a rigid-flexible coupling dynamics model of the dual-drive motion platform, and set the initial values ​​of each parameter in the system unknown parameter vector of the rigid-flexible coupling dynamics model at the initial moment, as well as the virtual control vector at the initial moment;

[0095] Step 2: Neural network weight compound update model, according to the beam position vector p of the dual-drive motion platform at time t-1 s (t-1), velocity vector Reference position vector p d (t-1), reference velocity vector And the beam position vector p at time t-2 s (t-2), velocity vector Reference position vector p d (t-2), reference velocity vector Get the neural network weight matrix at time t at the same time,

[0096] The system parameter compound update model is based on the beam position vector p of the dual-drive motion platform at time t-1. s (t-1), velocity vector Reference position vector p d (t-1), reference velocity vector Virtual control vector τ(t-1) and system unknown parameter vector Estimate the unknown parameter vector of the system at time t , and Send to the expected compensation model;

[0097] Step 3: Expected compensation model, based on the received reference position vector p at the current time t d (t), reference velocity vector Reference acceleration vector and the unknown system parameter vector Generate model compensation signal τ a (t);

[0098] The B-spline wavelet neural network online identification model is based on the real-time acquisition of the beam position vector p of the dual-drive motion platform at the current time t. s (t), velocity vector and the neural network weight matrix Generate feedforward compensation signal τ nn (t);

[0099] The robust feedback controller is based on the real-time acquired beam position vector p of the dual-drive motion platform at the current time t s (t), velocity vector and the reference position vector p d (t) and the reference velocity vector Generate a robust feedback compensation signal τ s (t);

[0100] Step 4: Compensate the model signal τ a (t), feedforward compensation signal τ nn (t) and robust feedback compensation signal τ s After superposition of (t), the actual control vector τ is calculated based on the obtained virtual control vector τ(t) u (t), to control the two linear motors of the dual-drive motion platform.

[0101] The invention discloses a precision dual-drive motion platform synchronous control method based on composite adaptive online estimation, which is based on a robust feedback controller, a B-spline wavelet neural network online identification model with a neural network weight composite update model, and an expected compensation model with a system parameter composite update model. The invention also constructs a composite adaptive robust controller based on composite adaptive online estimation, and the composite adaptive robust controller includes a robust feedback controller, a B-spline wavelet neural network online identification model and an expected compensation model.

[0102] Among them, the B-spline wavelet neural network online identification model generates a neural network weight matrix through a specially designed neural network weight composite update model Update the

[0103] The unknown parameters of the system are updated through a specially designed system parameter composite update model;

[0104] The dual-drive motion platform is compensated in real time by the expected compensation model. The unmodeled dynamics and external disturbances of the dual-drive motion platform system are compensated by the B-spline wavelet neural network online identification model. Then, robust stabilization is performed by the robust feedback controller, thereby improving the task tracking and synchronization controllability of the dual-drive motion platform.

[0105] The rigid-flexible coupling dynamics model of the dual-drive motion platform can be established through existing technologies, such as Figure 4As shown in the figure, considering the guide rail deformation and friction caused by the torsion of the beam of the dual-drive gantry motion platform, a rigid-flexible coupling dynamic model is established, and the intersection points of the beam and the two guide rails are set to p1 and p2 respectively. The input variable of the system model is the thrust τ of the linear motor M1 m1 and the thrust τ of the linear motor M2 m2 The output variables are the beam rotation angle α and the displacement y of the beam center of mass G .

[0106] The rigid-flexible coupling dynamic model of the dual-drive motion platform is given as:

[0107]

[0108] Among them, t is the time, p s (t) = [y G (t), α(t)] T , Represent the position vector, velocity vector and acceleration vector of the beam respectively, y G (t) is the center of mass of the beam, is the velocity of the beam's center of mass, α(t) is the beam's rotation angle, is the angular velocity of the beam.

[0109] represents the inertia matrix of the system, M is the mass of beam L, J is the moment of inertia of beam L,

[0110] The matrix representing the viscous friction coefficient of the system, B f is the first coupling coefficient matrix of the viscous friction force on motors M1 and M2, B g is the second coupling coefficient matrix of the viscous friction force on motors M1 and M2, B m is the third coupling coefficient matrix of the viscous friction force on motors M1 and M2;

[0111] The matrix representing the system stiffness, K α is the rotational stiffness of the beam.

[0112] The matrix representing the Coulomb friction coefficient of the system, A f is the first coupling coefficient matrix of the Coulomb friction force on motors M1 and M2, A g is the second coupling coefficient matrix of the Coulomb friction force on motors M1 and M2;

[0113] represents the nominal value matrix of the system external disturbance, τ dny is the nominal value of the external disturbance on the beam motion direction during platform motion, τ dnαIt is the nominal value of the external interference on the beam rotation direction during the platform movement;

[0114] Among the above variables, K1 is the thrust coefficient of motor M1;

[0115] τ(t)=[τ1(t),τ2(t)] T is the virtual control vector, τ1(t) represents the virtual control quantity of the beam motion direction in the rigid-flexible coupling model, τ2(t) represents the virtual control quantity of the beam rotation direction in the rigid-flexible coupling model, and there exists τ1(t) = τ u1 (t)+K m τ u2 (t), τ2(t)=K m τ u2 (t)L m2 -τ u1 (t)L m1 ; K m is the ratio of the thrust coefficients of the two linear motors, L m1 and L m2 are the distances from the center of mass of the beam to the two linear motors Y1 and Y2 respectively;

[0116] The actual control vector τ u (t)τ u (t) = Π -1 τ(t), thrust distribution matrix Π=[1,K m , -L m1 , K m L m2 ],∏ -1 is the inverse matrix of the thrust distribution matrix ∏, and the actual control vector τ u (t) = [τ u1 (t), τ u2 (t)] T ;

[0117] is the time-varying component matrix of the system’s external interference.

[0118] In specific applications, in order to facilitate the subsequent design of the composite adaptive robust controller, the unknown parameter vector of the system is defined as:

[0119]

[0120] In specific applications, the beam position vector p collected in real time s (t), velocity vector The implementation is:

[0121] See also Figure 4 and Figure 5The grating ruler is used to collect the motor M1 position y1(t), motor M2 position y2(t), motor M1 speed in real time Motor M2 speed The implementation is:

[0122] Calculate the beam center of mass position y G (t):

[0123]

[0124] Calculate the beam center of mass velocity

[0125]

[0126] Calculate the beam rotation angle α(t):

[0127]

[0128] Calculate the angular velocity of the beam

[0129]

[0130] Finally, the beam position vector p can be obtained in real time s (t) = [y G (t), α(t)] T , the velocity vector L e2 is the distance between the grating ruler E2 and the center of mass of the beam, L e1 is the distance between the grating ruler E1 and the center of mass of the beam, L e is the distance between the grating scales E1 and E2.

[0131] See also Figure 2 In step 2, the neural network weight matrix at time t is obtained The implementation methods include:

[0132] Step 2: According to the beam position vector p s (t-1), velocity vector Reference position vector p d (t-1) and the reference velocity vector Calculate the sliding surface vector ρ(t-1) at time t-1;

[0133] According to the beam position vector p at time t-2 s (t-2), velocity vector Reference position vector p d (t-2), reference velocity vector Calculate the sliding surface vector ρ(t-2) at time t-2;

[0134] According to the beam position vector p at time t-2 s (t-2) and the reference position vector p d (t-2), calculate the system tracking error z(t-2) at time t-2;

[0135] Step 2: According to ρ(t-1), ρ(t-2) and z(t-2), the neural network prediction error vector δ(t-1) at time t-1 is obtained. Specifically,

[0136]

[0137] M s For the quality of the system;

[0138] K ρ is the sliding mode control gain matrix, K z is the proportional control gain matrix, is the first-order derivative of ρ(t-1);

[0139] Step 213: According to δ(t-1) and ρ(t-1), obtain the rate of change of the neural network weights in the direction of beam movement at time t-1 and the rate of change of the neural network weights in the beam rotation direction

[0140] When applied specifically, and The implementation is:

[0141] First, rewrite δ(t-1) and ρ(t-1) to obtain:

[0142] δ(t-1)=[δ y (t-1), δ α (t-1)] T ;

[0143] ρ(t-1)=[ρ y (t-1), ρ α (t-1)] T ;

[0144] Secondly, according to δ y (t-1) and ρ y (t-1), get the rate of change of the neural network weights in the direction of beam movement at time t-1 According to δ α (t-1) and ρ α (t-1), get the rate of change of the neural network weights in the beam rotation direction at time t-1 in,

[0145]

[0146]

[0147] χ y and χ α are the composite learning gains of the neural network weights in the beam motion direction and the beam rotation direction, respectively;

[0148] and They are the hidden layer activation functions of the neural network of the neural network weight compound update model in the beam movement direction and the beam rotation direction respectively;

[0149] κ ry and κ rα are the neural network prediction error weight matrices in the beam motion direction and beam rotation direction respectively;

[0150] Project y (·) and Proj α (·) represent the projection mapping functions in the beam motion direction and beam rotation direction, respectively;

[0151] δ y (t-1) and δ α (t-1) are the beam motion direction prediction error and beam rotation error at time t-1 respectively;

[0152] ρ y (t-1) and ρ α (t-1) are the components of the sliding surface vector in the direction of beam movement and the component of the sliding surface vector in the direction of beam rotation at time t-1 respectively;

[0153] b wy and b wα They are the upper bounds of the neural network weights in the beam motion direction and the beam rotation direction, respectively;

[0154] The above given and Compared with the existing direct adaptive method that relies solely on the system tracking error to drive the update, this method is more accurate in approximating the optimal weights of the neural network. Step 2-4: and Perform integral processing to obtain and

[0155] according to and get

[0156] according to and get

[0157]

[0158] Where h is the system sampling time interval, and are the neural network weight estimation vectors of the beam movement direction and beam rotation direction at time t-1, and are the neural network weight estimation vectors of the beam motion direction and beam rotation direction at time t respectively;

[0159] Step 215: According to and get

[0160] In this preferred embodiment, the and The specific process has the advantage of being more accurate in approximating the optimal weights of the neural network under complex working conditions, and thus more accurately compensating for unmodeled dynamics and external disturbances.

[0161] See also Figure 3 In step 2, the unknown parameter vector of the system at time t is estimated The implementation methods of the value include:

[0162] Step 221: According to the beam position vector p s (t-1), velocity vector Reference position vector p d (t-1) and the reference velocity vector Calculate the sliding surface vector ρ(t-1) at time t-1; where,

[0163]

[0164] z(t-1)=p s (t-1)-p d (t-1);

[0165]

[0166] is the derivative of z(t-1), z(t-1) is the system tracking error at time t-1, Λ is a 2×2 positive definite diagonal gain matrix;

[0167] At the same time, according to the virtual control vector τ(t-1) and the system unknown parameter vector Calculate the system unknown parameter prediction error vector ξ(t-1); where,

[0168]

[0169] τ f (t-1) is the value after filtering the virtual control vector τ(t-1);

[0170] Step 222: According to ρ(t-1) and ξ(t-1), obtain the change rate of the unknown parameters of the system at time t-1 Specifically,

[0171]

[0172] in, is the projection mapping function of the unknown system parameters, Γ(t-1) is the composite update adaptive gain matrix of the unknown system parameters at time t-1, ψ d (t-1) is the generalized regression matrix using the reference trajectory signal at time t-1, Q is the system unknown parameter prediction error weight matrix, is the unknown parameter estimation vector of the system, I is the identity matrix, for The unit normal vector at θ represents the set of closures that restrict the unknown parameter vector, and Respectively represent Ω θ The boundaries and interior sets of represent The unit normal vector at time ;

[0173] Step 223: Perform integration to obtain the unknown parameter vector of the system at time t-1

[0174] Step 224: According to and Get the unknown parameter vector of the system at time t in,

[0175] In this preferred embodiment, the unknown parameter vector of the system is obtained by The implementation method of the value of can more accurately approximate the unknown parameters of the system, and thus more accurately compensate the expected model.

[0176] The present invention mainly improves the composite update model of neural network weights and system parameter composite update model, while the expected compensation model, B-spline wavelet neural network online identification model and robust feedback controller can all be realized by existing technologies. In specific applications,

[0177] The robust feedback controller generates a robust feedback compensation signal τ s (t) is implemented as follows:

[0178] τ s (t) = -K ρ ρ(t)-K z z(t);

[0179]

[0180] z(t)=p s (t)-p d (t);

[0181]

[0182] ρ(t) is the sliding surface vector at time t, z(t) is the system tracking error at time t, is the derivative of z(t), and Λ is a 2×2 positive definite diagonal gain matrix.

[0183] The expected compensation model generates the model compensation signal τ a (t) is implemented as follows:

[0184]

[0185] ψ d (t) is the reference position vector p d (t), reference velocity vector Reference acceleration vector The generalized regression matrix.

[0186] B-spline wavelet neural network online identification model generates feedforward compensation signal τ nn (t) is implemented as follows:

[0187] τ nn (t) = [τ nny (t), τ nnα (t)] T ;

[0188] in,

[0189]

[0190] τ nny (t) is the feedforward compensation signal in the direction of beam motion, τ nnα (t) is the feedforward compensation signal in the direction of beam rotation, i y is the horizontal coordinate number of the node marked as the beam movement direction in the hidden layer of the B-spline wavelet neural network, is the ordinate number of the node marked as the beam motion direction in the hidden layer of the B-spline wavelet neural network, i αis the horizontal coordinate number of the node marked as the beam rotation direction in the hidden layer of the B-spline wavelet neural network, is the ordinate number of the node marked as the beam rotation direction in the hidden layer of the B-spline wavelet neural network, b y is the beam position vector p s (t) Center of mass position of the middle beam y G The translation factor, is the velocity vector Center of mass speed of middle beam The translation factor, b α is the beam position vector p s (t) is the translation factor for the beam rotation angle α, is the beam position vector p s (t) Angular velocity of the middle beam The translation factor, p s (t) = [y G (t),α(t)] T ,

[0191] is the activation function value of the node marked as the direction of beam movement in the hidden layer of the B-spline wavelet neural network;

[0192] is the activation function value of the node marked as the rotation direction of the beam in the hidden layer of the B-spline wavelet neural network.

[0193] The following examples are used to verify the beneficial effects of the present invention:

[0194] Embodiment 1:

[0195] The indirect adaptive robust control method (C1) in the prior art, the composite adaptive robust control method based on expected compensation (C2), the control method formed by combining the composite adaptive robust controller based on expected compensation and the direct adaptive B-spline wavelet neural network compensator (C3), and the composite adaptive online estimation precision dual-drive motion platform synchronization control method (C4) described in the present invention are respectively applied to the dual-drive motion platform system, and the sampling time h=0.25ms.

[0196] Under a given reference trajectory, in the composite adaptive robust controller in the method of the present invention, the sliding mode control gain matrix K in the robust feedback controller is ρ =diag(14,15), proportional control gain matrix K z=diag(30,20), gain matrix Λ=diag(200,900), system unknown parameter prediction error weight matrix Q=diag(2.5,2.5), upper bound of forgetting factor λ0=1, upper bound of system unknown parameter composite update adaptive gain matrix Γ0=diag(10,20,200,30,20,30,80,80,80,50), scale factor of B-spline wavelet neural network online identification model And the translation factor Neural network weight compound learning gain, χ y =0.0009, χ α =0.0002, neural network prediction error weight matrix κ r =diag(0.0045,0.0005).

[0197] In the control group, C2 lacks the compensation of B-spline wavelet neural network compared with C4. Otherwise, its controller form is the same as C4. In order to ensure the fairness of the experiment, the controller parameters are selected to be the same as C4. The controller form and parameters of C1 are the same as those of C2, but its system parameter update law is the exponential forgetting least squares method. The forgetting factor of this method is The normalization factor υ = 0.1, and the initial value of the parameter estimation learning law is set to Γ(0) = diag(10,10,10,10,10,10,10,10,10,10); Compared with C4, the controller form and parameters of C3 are exactly the same, but the B-spline wavelet neural network used is a direct adaptive neural network, whose weights are driven only by the system tracking error, and its weight update adaptive gain is set to the same as the composite learning gain in C4.

[0198] Figure 6 The trajectory tracking errors of the platform under four kinds of control are given;

[0199] Figure 7 The beam rotation angle of the platform under four control algorithms is given;

[0200] Figure 8 The maximum absolute value and root mean square of platform tracking error under four methods are given;

[0201] Fig. 9 The maximum absolute value and root mean square of the platform beam rotation angle under the four methods are given.

[0202] It can be seen from the experimental results that the platform under the control of the composite adaptive robust controller proposed by the present invention can reduce the root mean square of trajectory tracking error by 65.04% and the root mean square of beam rotation angle by 21.55% compared with the indirect adaptive robust control method; compared with the composite adaptive robust control method based on expected compensation, the root mean square of trajectory tracking error can be reduced by 34.4% and the root mean square of beam rotation angle can be reduced by 11.58%; compared with the control method formed by combining the composite adaptive robust controller based on expected compensation and the direct adaptive B-spline wavelet neural network, the root mean square of trajectory tracking error can be reduced by 25.94% and the root mean square of beam rotation angle can be reduced by 5.7%. In summary, the effectiveness of the present invention is verified.

[0203] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims

1. A precision dual-drive motion platform synchronization control method based on composite adaptive online estimation, which is implemented based on a composite adaptive robust controller, a neural network weight composite update model and a system parameter composite update model, and the composite adaptive robust controller includes an expected compensation model, a B-spline wavelet neural network online identification model and a robust feedback controller; characterized in that: Methods include: Step 1: Establish a rigid-flexible coupling dynamics model of the dual-drive motion platform, and set the initial values ​​of each parameter in the system unknown parameter vector of the rigid-flexible coupling dynamics model at the initial moment, as well as the virtual control vector at the initial moment; Step 2: Neural network weight compound update model, according to the beam position vector p of the dual-drive motion platform at time t-1 s (t-1), velocity vector Reference position vector p d (t-1), reference velocity vector And the beam position vector p at time t-2 s (t-2), velocity vector Reference position vector p d (t-2), reference velocity vector Get the neural network weight matrix at time t at the same time, The system parameter compound update model is based on the beam position vector p of the dual-drive motion platform at time t-1. s (t-1), velocity vector Reference position vector p d (t-1), reference velocity vector Virtual control vector τ(t-1) and system unknown parameter vector Estimate the unknown parameter vector of the system at time t , and sent to the expected compensation model; Step 3: Expected compensation model, based on the received reference position vector p at the current time t d (t), reference velocity vector Reference acceleration vector and the unknown system parameter vector Generate model compensation signal τ a (t); The B-spline wavelet neural network online identification model is based on the real-time acquisition of the beam position vector p of the dual-drive motion platform at the current time t. s (t), velocity vector and the neural network weight matrix Generate a feedforward compensation signal τ nn (t); The robust feedback controller is based on the real-time acquired beam position vector p of the dual-drive motion platform at the current time t s (t), velocity vector and the reference position vector p d (t) and the reference velocity vector Generate a robust feedback compensation signal τ s (t); Step 4: Compensate the model signal τ a (t), feedforward compensation signal τ nn (t) and robust feedback compensation signal τ s (t) is superimposed, and the actual control vector is calculated based on the obtained virtual control vector τ(t) Control the two linear motors of the dual-drive motion platform.

2. The method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation according to claim 1 is characterized in that: In step 2, the neural network weight matrix at time t is obtained The implementation methods include Step 2: According to the beam position vector p s (t-1), velocity vector Reference position vector p d (t-1) and the reference velocity vector Calculate the sliding surface vector ρ(t-1) at time t-1; According to the beam position vector p at time t-2 s (t-2), velocity vector Reference position vector p d (t-2), reference velocity vector Calculate the sliding surface vector ρ(t-2) at time t-2; According to the beam position vector p at time t-2 s (t-2) and the reference position vector p d (t-2), calculate the system tracking error z(t-2) at time t-2; Step 2: According to ρ(t-1), ρ(t-2) and z(t-2), the neural network prediction error vector δ(t-1) at time t-1 is obtained. Specifically, M s is the mass of the system, K ρ is the sliding mode control gain matrix, K z is the proportional control gain matrix, is the first-order derivative of ρ(t-1); Step 2-3: According to δ(t-1) and ρ(t-1), obtain the rate of change of the neural network weights in the direction of motion at time t-1 and the rate of change of the neural network weights in the beam rotation direction Step 214: and Perform integral processing to obtain and according to and get according to and get in, and are the neural network weight estimation vectors of the beam movement direction and beam rotation direction at time t-1, and are the neural network weight estimation vectors of the beam motion direction and beam rotation direction at time t respectively; Step 215: According to and get 3. The method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation according to claim 2 The method is characterized in that In step 213, we get and The implementation is: First, rewrite δ(t-1) and ρ(t-1) to obtain: δ(t-1)=[δ y (t-1),δ α (t-1)] T ; ρ(t-1)=[ρ y (t-1),p α (t-1)] T ; Secondly, according to δ y (t-1) and ρ y (t-1), get the rate of change of the neural network weights in the direction of beam movement at time t-1 According to δ α (t-1) and ρ α (t-1), get the rate of change of the neural network weights in the beam rotation direction at time t-1 in, χ y and χ α are the composite learning gains of the neural network weights in the beam motion direction and the beam rotation direction, respectively. and They are the hidden layer activation functions of the neural network of the neural network weight compound update model in the beam movement direction and the beam rotation direction respectively; κ ry and κ rα are the neural network prediction error weight matrices in the beam motion direction and beam rotation direction, respectively. y (·) and Proj α (·) represent the projection mapping function in the beam motion direction and beam rotation direction, respectively, δ y (t-1) and δ α (t-1) are the beam motion direction prediction error and beam rotation error at time t-1, ρ y (t-1) and ρ α (t-1) are the components of the sliding surface vector in the direction of beam movement and the component of the sliding surface vector in the direction of beam rotation at time t-1 respectively.

4. The method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation according to claim 3 is characterized in that: b wy and b wα They are the upper bounds of the neural network weights in the direction of beam movement and beam rotation, respectively.

5. The method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation according to claim 2 is characterized in that: In step 214, h is the system sampling time interval.

6. The method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation according to claim 1, characterized in that: In step 2, the unknown parameter vector of the system at time t is estimated The implementation methods of the value include: Step 221: According to the beam position vector p s (t-1), velocity vector Reference position vector p d (t-1) and the reference velocity vector Calculate the sliding surface vector ρ(t-1) at time t-1; where, z(t-1)=p s (t-1)-p d (t-1); is the derivative of z(t-1), z(t-1) is the system tracking error at time t-1, Λ is a 2×2 positive definite diagonal gain matrix; At the same time, according to the virtual control vector v(t-1) and the system unknown parameter vector Calculate the system unknown parameter prediction error vector ξ(t-1); where, τ f (t-1) is the value after filtering the virtual control vector τ(t-1); Step 222: According to ρ(t-1) and ξ(t-1), obtain the change rate of the unknown parameters of the system at time t-1 Step 223: Perform integration to obtain the unknown parameter vector of the system at time t-1 Step 224: According to and Get the unknown parameter vector of the system at time t 7. The method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation according to claim 6 is characterized in that: In step 222, the change rate of the unknown parameters of the system at time t-1 is obtained The implementation methods include: in, is the projection mapping function of the unknown system parameters, Γ(t-1) is the composite update adaptive gain matrix of the unknown system parameters at time t-1, ψ d (t-1) is the generalized regression matrix using the reference trajectory signal at time t-1, Q is the system unknown parameter prediction error weight matrix, is the unknown parameter estimation vector of the system, I is the identity matrix, for The unit normal vector at θ represents the set of closures that restrict the unknown parameter vector, and Respectively represent Ω θ The boundaries and interior sets of represent The unit normal vector at time .

8. The method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation according to claim 6 is characterized in that: In step 224, 9. The method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation according to claim 1, characterized in that: The robust feedback controller generates a robust feedback compensation signal τ s (t) is implemented as follows: τ s (t)=-K ρ ρ(t)-K z z(t); z(t)=p s (t)-p d (t), ρ(t) is the sliding surface vector at time t, z(t) is the system tracking error at time t, is the derivative of z(t), Λ is a 2×2 positive definite diagonal gain matrix; The expected compensation model generates the model compensation signal τ a (t) is implemented as follows: ψ d (t) is the reference position vector p d (t), reference velocity vector Reference acceleration vector The generalized regression matrix formed; B-spline wavelet neural network online identification model generates feedforward compensation signal τ nn (t) is implemented as follows: t nn (t)=[τ nny (t),τ nnα (t)] T ; in, τ nny (t) is the feedforward compensation signal in the direction of beam motion, τ nnα (t) is the feedforward compensation signal in the direction of beam rotation, i y is the horizontal coordinate number of the node marked as the beam movement direction in the hidden layer of the B-spline wavelet neural network, is the ordinate number of the node marked as the beam motion direction in the hidden layer of the B-spline wavelet neural network, i α is the horizontal coordinate number of the node marked as the beam rotation direction in the hidden layer of the B-spline wavelet neural network, is the ordinate number of the node marked as the beam rotation direction in the hidden layer of the B-spline wavelet neural network, b y is the beam position vector p s (t) Center of mass position of the middle beam y G The translation factor, is the velocity vector Center of mass speed of middle beam The translation factor, b α is the beam position vector p s (t) is the translation factor for the beam rotation angle α, is the beam position vector p s (t) Angular velocity of the middle beam The translation factor, p s (t) = [y G (t),α(t)] T , is the activation function value of the node marked as the direction of beam movement in the hidden layer of the B-spline wavelet neural network; is the activation function value of the node marked as the rotation direction of the beam in the hidden layer of the B-spline wavelet neural network.

10. The method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation according to claim 1, characterized in that: t u (t)=Π -1 τ(t); P=[1,K m ,-L m1 ,K m L m2 ]; Among them, Π is the thrust distribution matrix, K m is the ratio of the thrust coefficients of the two linear motors, L m1 and L m2 are the distances from the center of mass of the beam to the two linear motors M1 and M2 respectively.

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