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

Abstract

The application relates to a precision double-drive motion platform synchronization control method based on a composite adaptive online estimation, and relates to the field of precision motion platform cooperative control.The application solves the problems of poor task tracking performance and low synchronization performance of a double-drive motion platform.In the application, a B-spline wavelet neural network online identification model generates a neural network weight matrix through a specially designed neural network weight composite update model to update the neural network weight matrix, unknown parameters of the system are updated through a constructed system parameter composite update model, a double-drive motion platform is compensated in real time through a constructed expected compensation model, the double-drive motion platform system unmodeled dynamics and external disturbance are compensated through a constructed B-spline wavelet neural network online identification model, and then a robust feedback controller is constructed to perform robust stabilization, so that the task tracking performance and synchronization of the double-drive motion platform are improved.The application is mainly used for synchronously controlling a double-drive gantry motion platform.

Description

Technical Field

[0001] The present 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 component of high-end equipment motion systems 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 platform's task tracking capabilities and may even cause damage to the platform.

[0003] In recent years, researchers have proposed a number of control methods to address this issue, such as PID, sliding mode, and adaptive robust control methods, which have, to some extent, alleviated the problem of excessive synchronization errors during the movement of dual-drive motion platforms. However, these methods still have some limitations: First, robust control methods, such as sliding mode control, are highly conservative, which is not conducive to the high-precision target tracking pursued by the control process; second, although adaptive robust control methods are widely used because they combine the advantages of both adaptive and robust control methods, many researchers have pointed out that the adaptive performance of model parameters of this method in time-varying environments is significantly reduced, which is very disadvantageous in actual industrial applications.

[0004] In addition, the linear motor is subjected to the nonlinear factors such as cogging force and end effect, the load variation encountered by the platform in the movement process and external disturbance, and the like, which are a great challenge to the precise motion control. The traditional control method mostly adopts to improve the control gain to suppress the disturbance, but this method is not completely applicable to the precise motion control, and the excessively 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 of the neural networks have the problem of excessive calculation due to the complex structure, which is not conducive to guarantee the high real-time performance of the precise motion control. Therefore, the relevant researchers propose a B-spline wavelet neural network, which can improve the calculation efficiency by designing a special activation function, and can adjust the parameters according to the characteristics of the platform, thereby providing a basis for the network structure design. Although the above progress has been made in compensating for the nonlinear factors such as the 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 approximation to the nonlinear factors, which will lead to the increase of the approximation error and affect the compensation performance of the neural network, thereby ultimately reducing the synchronization control performance.

[0005] The proposal of the composite adaptive control method provides a new solution to the synchronization control problem of the double-drive motion platform. Unlike the traditional adaptive method which only relies on the tracking error to update the parameters, the composite adaptive control uses the tracking error and the parameter prediction error to drive the update of the unknown parameters of the system, thereby improving the tracking ability of the model parameters in the time-varying environment. However, the existing composite adaptive control is a fragile adaptive control with poor robustness, and under strong external disturbance, the synchronization control performance will be reduced, therefore, the above problems need to be solved. SUMMARY

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

[0007] The precise double-drive motion platform synchronization control method based on composite adaptive online estimation is realized 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 comprises an expected compensation model, a B-spline wavelet neural network online identification model and a robust feedback controller; the method comprises the following steps:

[0008] Step one, a rigid-flexible coupling dynamics model of the double-drive motion platform is established, and the initial values of each parameter in the unknown parameter vector of the rigid-flexible coupling dynamics model at the initial time and the virtual control vector at the initial time are set;

[0009] Step 2: The neural network weight composite 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 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 composite 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 acquired 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 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 (t) is superimposed, and the actual control vector τ is calculated based on the obtained virtual control vector τ(t) u (t), controls 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 derivative of ρ(t-1);

[0022] Step 2-3: Based on 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 the 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 are the hidden layer activation functions of the neural network in the neural network weight composite 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 under the beam motion direction and beam rotation direction, respectively. y (·) and Proj α (·) represents the projection mapping function in the direction of beam motion and beam rotation, 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 in the direction of beam rotation at time t-1 respectively.

[0036] Preferably,

[0037]

[0038] b wy and b wα are the upper bounds of the neural network weights in the beam motion direction and the beam rotation direction, 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, and 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: Based on ρ(t-1) and ξ(t-1), obtain the rate of change of the unknown parameters of the system at time t-1

[0051] Step 2, 2, 3, Perform integration processing 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 rate of change of the unknown parameters 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 time Ω θ represents a set of closures that restrict the unknown parameter vector, and Represents 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] Generate feedforward compensation signal τ using B-spline wavelet neural network online identification model 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 motion direction in the hidden layer of the B-spline wavelet neural network, is the ordinate number of the node in the hidden layer of the B-spline wavelet neural network marked as the direction of beam movement, 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 The translation factor of the beam rotation angle α in (t), 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 beam motion direction in the hidden layer of the B-spline wavelet neural network;

[0071] is the activation function value of the node marked as the beam rotation direction 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] Where 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 present invention designs a method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation. The method is based on a robust feedback controller, a B-spline wavelet neural network online identification model with a composite update model of neural network weights, and an expected compensation model with a composite update model of system parameters. The method of the present invention constructs a composite adaptive robust controller based on composite adaptive online estimation. 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 the 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 a constructed system parameter composite update model; the dual-drive motion platform is compensated in real time through a constructed expected compensation model; the unmodeled dynamics and external disturbances of the dual-drive motion platform system are compensated through a constructed B-spline wavelet neural network online identification model; and 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 use of this method to design a new B-spline wavelet neural network can also achieve high-precision compensation for nonlinear factors and interference while ensuring the real-time performance of the system.

[0081] 3. The precise 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 when the dual-drive motion platform system faces complex unmodeled dynamics and unknown interference in actual industrial production. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 Schematic diagram of the principle of the precision dual-drive motion platform synchronization control method based on composite adaptive online estimation according to 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 Schematic diagram of the internal principle of the system parameter composite update model;

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

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

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

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

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

[0090] Figure 9 Comparison diagrams of the maximum crossbeam rotation angle and the root mean square of the crossbeam rotation angle 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 are shown. DETAILED DESCRIPTION

[0091] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making any creative efforts shall fall 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 1This embodiment describes a method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation. The method is implemented based on a composite adaptive robust controller, a neural network weight composite update model, and a system parameter composite update model. The composite adaptive robust controller includes an expectation 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 dynamic 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 dynamic model at the initial moment, as well as the virtual control vector at the initial moment;

[0095] Step 2: The neural network weight composite 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 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 composite 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 acquired 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 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 (t) is superimposed, and the actual control vector τ is calculated based on the obtained virtual control vector τ(t) u (t), controls the two linear motors of the dual-drive motion platform.

[0101] The present invention designs a method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation. The method is based on a robust feedback controller, a B-spline wavelet neural network online identification model with a composite update model of neural network weights, and an expected compensation model with a composite update model of system parameters. The method of the present invention constructs a composite adaptive robust controller based on composite adaptive online estimation. 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 through the expected compensation model. The unmodeled dynamics and external disturbances of the dual-drive motion platform system are compensated through the B-spline wavelet neural network online identification model. Robust stabilization is then performed through the robust feedback controller, thereby improving the task tracking and synchronous controllability of the dual-drive motion platform.

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

[0106] The obtained rigid-flexible coupling dynamics model of the double-drive motion platform is as follows:

[0107]

[0108] Wherein, 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 position of the beam mass center, is the velocity of the beam mass center, α(t) is the rotation angle of the beam, is the rotation angular velocity of the beam.

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

[0110] represents the matrix of the viscous friction force coefficient of the system, B f is the first coupling coefficient matrix of the viscous friction force of the motor M1 and M2, B g is the second coupling coefficient matrix of the viscous friction force of the motor M1 and M2, B m is the third coupling coefficient matrix of the viscous friction force of the motor M1 and M2.

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

[0112] represents the matrix of the coulomb friction coefficient of the system, A f is the first coupling coefficient matrix of the coulomb friction of the motor M1 and M2, A g is the second coupling coefficient matrix of the coulomb friction of the motor M1 and M2.

[0113] represents the matrix of the nominal value of the external disturbance of the system, τ dny is the nominal value of the external disturbance in the direction of the beam motion during the motion of the platform, 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] 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 ∏, 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 , 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 derivative of ρ(t-1);

[0139] Step 2-3: Based on 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] In specific applications, 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 are the hidden layer activation functions of the neural network in the neural network weight composite 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 under the beam motion direction and beam rotation direction respectively;

[0150] Project y (·) and Proj α (·) represents the projection mapping function in the beam motion direction and the 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 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. and Perform integral processing to obtain and

[0155] according to and get

[0156] according to and obtained

[0157]

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

[0159] Step two, according to and obtained

[0160] In the preferred embodiment, the specific process of obtaining and is given, which has the advantage of more accurate approximation of the optimal weight of the neural network under complex working conditions, and further more accurate compensation for unmodeled dynamics and external disturbances.

[0161] Referring to Figure 3 , in step two, the implementation mode of estimating the value of the system unknown parameter vector at time t includes:

[0162] Step two, according to the beam position vector p s (t-1), the speed vector the reference position vector p d (t-1) and the reference speed vector , the sliding mode surface vector p at time t-1 is calculated; wherein,

[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, and A is a 2x2 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 , the system unknown parameter prediction error vector ξ(t-1) is calculated; wherein,

[0168]

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

[0170] Step 222: Based on ρ(t-1) and ξ(t-1), obtain the rate of change 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 time Ω θ represents a set of closures that restrict the unknown parameter vector, and Represents Ω θ The boundaries and interior sets of represent The unit normal vector at time ;

[0173] Step 2, 2, 3, Perform integration processing 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 is more accurate in approximating the unknown parameters of the system, and thus more accurately performs the expected model compensation.

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

[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 a sliding mode surface vector at time t, z(t) is a system tracking error at time t, is a derivative of z(t), and Λ is a 2x2 positive definite diagonal gain matrix.

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

[0184]

[0185] ψ d (t) is a generalized regression matrix composed of a reference position vector p d (t), a reference velocity vector a reference acceleration vector .

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

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

[0188] wherein,

[0189]

[0190] τ nny (t) is a feedforward compensation signal in the beam movement direction, τ nnα (t) is a feedforward compensation signal in the beam rotation direction, i y is the horizontal coordinate serial number of the node marked as the beam movement direction in the hidden layer of the B-spline wavelet neural network, is the vertical coordinate serial number of the node marked as the beam movement 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 The translation factor of the beam rotation angle α in (t), 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 beam motion direction in the hidden layer of the B-spline wavelet neural network;

[0192] is the activation function value of the node marked as the beam rotation direction 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] Example 1:

[0195] The indirect adaptive robust control method (C1) in the prior art, the composite adaptive robust control method based on expectation compensation (C2), the control method (C3) formed by combining the composite adaptive robust controller based on expectation compensation and the direct adaptive B-spline wavelet neural network compensator, 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, with a sampling time of h = 0.25 ms.

[0196] Under a given reference trajectory, in the composite adaptive robust controller 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 the forgetting factor λ0 = 1, upper bound of the adaptive gain matrix for the composite update of the system unknown parameters Γ0 =diag(10,20,200,30,20,30,80,80,80,50), scale factor of the B-spline wavelet neural network online identification model And the translation factor The compound learning gain of neural network weights, 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 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 compound 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 the platform tracking error under the four methods are given;

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

[0202] Experimental results show that, compared with an indirect adaptive robust control method, the platform controlled by the composite adaptive robust controller proposed in this invention can reduce the RMS tracking error by 65.04% and the RMS crossbeam rotation angle by 21.55%. Compared with a composite adaptive robust control method based on expectation compensation, the RMS tracking error can be reduced by 34.4% and the RMS crossbeam rotation angle can be reduced by 11.58%. Compared with a control method formed by combining a composite adaptive robust controller based on expectation compensation with a direct adaptive B-spline wavelet neural network, the RMS tracking error can be reduced by 25.94% and the RMS crossbeam rotation angle can be reduced by 5.7%. In summary, the effectiveness of the present invention has been verified.

[0203] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with 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. The composite adaptive robust controller includes an expectation compensation model, a B-spline wavelet neural network online identification model, and a robust feedback controller. The method is characterized by: Methods include: Step 1: Establish a rigid-flexible coupling dynamic 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 dynamic model at the initial moment, as well as the virtual control vector at the initial moment; Step 2: Neural network weight composite 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 composite 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; 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 acquired 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); 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 robust feedback compensation signal τ s (t); 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); 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; Generate feedforward compensation signal τ using B-spline wavelet neural network online identification model 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 motion direction in the hidden layer of the B-spline wavelet neural network, is the ordinate number of the node in the hidden layer of the B-spline wavelet neural network marked as the direction of beam movement, 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 The translation factor of the beam rotation angle α in (t), 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 beam rotation direction in the hidden layer of the B-spline wavelet neural network; 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 τ is calculated based on the obtained virtual control vector τ(t) u (t), controls 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, 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 derivative of ρ(t-1); Step 2-3: Based on 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 direction of beam rotation 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 the 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, characterized in that: In steps 2-13, 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 are the hidden layer activation functions of the neural network in the neural network weight composite update model in the beam movement direction and the beam rotation direction respectively; k ry and k rα are the neural network prediction error weight matrices in the beam motion direction and beam rotation direction, respectively. y (·) and Proj α (·) represents the projection mapping function in the beam motion direction and the beam rotation direction, respectively, 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 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 are the upper bounds of the neural network weights in the beam motion direction and the beam rotation direction, respectively.

5. The method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation according to claim 2, 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, estimate the unknown parameter vector of the system at time t 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, and Λ is a 2×2 positive definite diagonal gain matrix; 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, τ f (t-1) is the value after filtering the virtual control vector τ(t-1); Step 222: Based on ρ(t-1) and ξ(t-1), obtain the rate of change of the unknown parameters of the system at time t-1 Step 2, 2, 3, Perform integration processing 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, characterized in that: In step 222, the rate of change 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 time Ω θ represents a set of closures that restrict the unknown parameter vector, and Represents Ω θ The boundaries and insets of .

8. The method for synchronous control of a precision dual-drive motion platform based on composite adaptive online estimation according to claim 6, 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: t u (t)=Π -1 τ(t); P=[1,K m ,-L m1 ,K m L m2 ]; Where 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.

Images