Three-ring control method and system suitable for six-degree-of-freedom parallel platform in high-dynamic environment

Abstract

The invention belongs to the technical field of engineering equipment control, and discloses a three-ring control method and system suitable for a six-degree-of-freedom parallel platform in a high-dynamic environment, and the method comprises the steps: employing a self-adaptive sliding mode control method of a disturbance observer in a position ring, and carrying out the quick estimation and compensation of the motion and posture of a parallel stable platform; a linear active-disturbance-rejection control method of a radial basis function neural network is applied to a speed ring, so that stable speed regulation can be provided and sufficient adaptivity can be ensured; and the inner current loop adopts internal model control to adjust the stator current and electromagnetic torque of the motor. The three layers of control rings cooperatively work in a nested mode from inside to outside, a three-ring nested control method composed of self-adaptive sliding mode control of a novel disturbance observer, linear active disturbance rejection control of a radial basis function neural network and internal model control is provided, the platform tracking precision and stability are improved, the contradiction between rapidity and stability in a classic PI method is overcome, and the stability of the platform is improved. Accurate tracking of expected motion of the tail end platform is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of engineering equipment control, and relates to a three-loop control method and system suitable for a six-degree-of-freedom parallel platform in a high-dynamic environment. Background Art

[0002] In highly dynamic environments, when payloads perform precision operations, system stability and control accuracy are often significantly affected by factors such as attitude disturbances, structural vibrations, and coupled nonlinearities. This not only restricts the precision control of sensing and measurement equipment but also places higher demands on the safety of material transportation, payload operations, and high-risk missions. To improve the attitude stability and mission execution accuracy of equipment in complex dynamic environments, six-degree-of-freedom parallel stabilized platforms, as a key technology for active disturbance isolation, have shown broad application prospects in many high-dynamic scenarios. They can effectively mitigate the effects of external disturbances and significantly improve the overall dynamic response performance and mission completion efficiency of the system. From a structural perspective, parallel mechanisms, due to their high stiffness, high load capacity, and excellent dynamic response characteristics, are more suitable than traditional series structures for deploying high-precision instruments and actuators in space-constrained, high-disturbance environments. This makes them a major development direction for six-degree-of-freedom platforms. The PSU configuration, as a parallel mechanism with a compact structure and superior kinematic performance, holds particular promise for application in high-dynamic control platforms. Currently, the main control strategies for this type of platform include traditional PID control, adaptive control and robust control. Although PID control is simple to implement, it is difficult to cope with typical dynamic characteristics such as nonlinearity, strong coupling and parameter perturbation. Although adaptive and robust control have certain anti-interference capabilities, they are highly dependent on the accuracy of system modeling. When there are modeling errors, the overall control performance is likely to degrade. Therefore, there is an urgent need to design a general six-degree-of-freedom parallel platform control method with high precision, strong robustness and adaptability to complex disturbance environments to meet the stability control needs of future high-end marine equipment and aerospace vehicles in complex dynamic scenarios. Summary of the Invention

[0003] The purpose of the present invention is to solve the problems that the existing technology is difficult to cope with typical dynamic characteristics such as nonlinearity, strong coupling and parameter perturbation, is highly dependent on the accuracy of system modeling, and the overall control performance is easily reduced when there are modeling errors. The present invention provides a three-loop control method and system for a six-degree-of-freedom parallel platform suitable for high-dynamic environments.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] A three-loop control method for a six-degree-of-freedom parallel platform in a high-dynamic environment, comprising:

[0006] Based on the six-degree-of-freedom parallel platform, an electromechanical coupled nonlinear dynamic model of the six-degree-of-freedom parallel stable platform was constructed; the components of the six-degree-of-freedom parallel platform were modeled to determine the position loop, velocity loop, and current loop;

[0007] Based on the nonlinear dynamic model, a nested control structure consisting of current loop, speed loop and position loop is constructed;

[0008] Based on the nested control structure consisting of current loop, speed loop and position loop, the position and posture of the permanent magnet synchronous motor are tracked and disturbance compensation is performed.

[0009] A further improvement of the present invention is:

[0010] Furthermore, the electromechanical coupling nonlinear dynamic model of the six-degree-of-freedom parallel stabilized platform is constructed as follows:

[0011] According to Kane's formula, the electromechanical coupling nonlinear dynamic model of the six-degree-of-freedom parallel stabilized platform is established as follows:

[0012]

[0013] Among them, M(X) represents the inertia matrix, are the Coriolis force and centrifugal force matrices, G(X) represents the gravity matrix, is the friction force; J qi is the Jacobian matrix of the slider velocity, F pi is the force vector provided by the permanent magnet synchronous motor in the vertical direction; is the generalized acceleration, is the generalized speed.

[0014] Furthermore, the nested control structure composed of the current loop, speed loop and position loop is used to track and compensate for the position and posture of the permanent magnet synchronous motor, specifically:

[0015] The position loop uses adaptive sliding mode control with disturbance observer to perform disturbance compensation on attitude and position errors;

[0016] The current loop adopts internal model control to achieve fast dynamic adjustment of the actuator current;

[0017] The speed loop uses a linear active disturbance rejection control (LADRC) optimized by a radial basis function neural network (RBF-NN) to achieve robust and stable control of the motor speed.

[0018] Furthermore, the position loop uses adaptive sliding mode control with disturbance observer to perform disturbance compensation on attitude and position errors, specifically:

[0019] Based on the mechanical motion equation of the permanent magnet synchronous motor, the rotation angle of the permanent magnet synchronous motor is used as the observation variable to obtain the tracking error of the rotation angle and angular velocity of the permanent magnet synchronous motor, and then the error control equation of the rotation angle and angular velocity is obtained;

[0020] Based on the error control equation and the sliding surface of sliding mode control, the control quantity of traditional sliding mode control is obtained;

[0021] Adaptive sliding mode control and the introduction of disturbance observer are used to optimize the control quantity of traditional sliding mode control, and then disturbance compensation is performed on the attitude and position errors.

[0022] Furthermore, based on the mechanical motion equation of the permanent magnet synchronous motor, the rotation angle of the permanent magnet synchronous motor is used as an observation variable to obtain the tracking error of the rotation angle and angular velocity of the permanent magnet synchronous motor, and then obtain the error control equation of the rotation angle and angular velocity, which is specifically:

[0023] Using the rotor magnetic field oriented control method, the mechanical motion equation of the permanent magnet synchronous motor is obtained as follows:

[0024]

[0025] Among them, θ m is the rotor position angle; ω m is the mechanical angular velocity; J m is the equivalent inertia moment of the motor, transmission device, ball screw and parallel mechanism; B m is the viscous friction coefficient of the system; T L is the load torque of the parallel mechanism; T e is the electromagnetic torque;

[0026] The electromagnetic torque equation of the permanent magnet synchronous motor is Therefore, formula (2) gives

[0027]

[0028] Among them, the position control gain b0 = 3p n ψ f / 2J m Considering the changes of system parameters, we can get

[0029]

[0030] Where Δα1, Δα2 and Δα3 represent the changes in the permanent magnet synchronous motor parameters, β is the perturbation value caused by the load torque and parameters; p n is the number of pole pairs of the permanent magnet synchronous motor; ψf is the permanent magnet flux; i q The q-axis component of the stator current;

[0031] The rotation angle of the permanent magnet synchronous motor is used as the observed variable; the tracking error of the rotation angle and angular velocity of the permanent magnet synchronous motor is defined as

[0032]

[0033] Among them, θ ref is the reference rotor position angle of the motor, ω ref is the reference rotor angular velocity of the motor; x p1 is the tracking error of the permanent magnet synchronous motor rotation angle; x p2 is the tracking error of the angular velocity of the permanent magnet synchronous motor;

[0034] Taking the derivative of formula (5), the control equation of the error is expressed as

[0035]

[0036] Furthermore, the control quantity of the traditional sliding mode control is obtained based on the error control equation and the sliding mode surface of the sliding mode control, which is specifically:

[0037] In traditional sliding mode control, in order to ensure the asymptotic stability of modal motion, the sliding surface is defined as

[0038] s=c s x P1 +x P2 (7)

[0039] Among them, c s >0 is the control parameter to be designed; the exponential reaching law is written as

[0040]

[0041] Among them, k1 is the exponential gain, ε1 is the switching gain;

[0042] Therefore, the sliding surface of formula (7) depends on the state error, current and the intensity of the perturbation and is written as

[0043]

[0044] Combining formula (6), formula (7) and formula (9), the control quantity of traditional sliding mode control is expressed as

[0045]

[0046] Furthermore, the adaptive sliding mode control and the introduction of disturbance observer are used to optimize the control quantity of the traditional sliding mode control, and then the disturbance compensation of the attitude and position errors is performed, specifically:

[0047] Adaptive sliding mode control

[0048]

[0049] When |s|>ζ increases, g(x P1 ,s) ranges from 1 to 2. As |s| increases, the system state follows the speed reaching law g(x P1 ,s)tanh(s) and exponential convergence law k1s reach the sliding surface at two rates, and the convergence time is shortened; on the contrary, when |s|<ζ, g(x P1 ,s) ranges from 0 to 1. As |s| decreases, the exponential convergence rate k1s gradually approaches zero. The variable speed arrival law term plays an important role. g(x P1 ,s)tanh(s) converges to ε1|x P1 |, under the action of the sliding mode control law, the system state |x P1 | gradually approaches zero; ζ is the threshold parameter;

[0050] In order to further weaken the chattering, the sign(·) function in the traditional sliding mode control is replaced by the tanh(·) function, which is expressed as

[0051]

[0052] Where μ>0;

[0053] Substituting formula (9) into formula (11) and combining it with formula (12), the output equation of adaptive sliding mode control is obtained as follows:

[0054]

[0055] The output of the permanent magnet synchronous motor system is expressed as y P , formula (6) is expressed as

[0056]

[0057] Among them, e P1 is the angular position state tracking parameter, e P2 is the angular velocity state tracking parameter, u w Type i for the replacement system q ;

[0058] Taking β as the observation object, the observer designed based on formula (14) is

[0059]

[0060] Among them, λ1, λ2 and η are positive real numbers; is the observed disturbance term; is the observed angular position state tracking value;

[0061] definition From formulas (15) and (14), the error equation of the observer is:

[0062]

[0063] Among them, e P is the actual state tracking value; is the state tracking value of the observation; Formula (16) can be converted into the state space form of the following form

[0064]

[0065] in, For the designed observer, if the eigenvalues ​​of the matrix M are all less than zero, the state error will converge to zero asymptotically;

[0066] For the proposed adaptive sliding mode control function, the total observed disturbance is considered to be Substituting into formula (17), the position loop input is expressed as

[0067]

[0068] From equation (18), parameter changes and load disturbances are adopted as feedforward compensation.

[0069] Furthermore, the speed loop uses the linear active disturbance rejection control (LADRC) optimized by radial basis function neural network (RBF-NN) to achieve robust and stable control of the motor speed, specifically:

[0070] The mathematical model of the permanent magnet synchronous motor in the dq coordinate system is expressed as

[0071]

[0072] Among them, L s is the stator inductance; Rs is the resistance of the stator winding; i d is the d-axis component of the stator current; Pn is the number of pole pairs of the three-phase permanent magnet synchronous motor;

[0073] When using i d = 0, the rotor field oriented control method, formula (19) is simplified to

[0074]

[0075] Among them, ω m is the mechanical angular velocity; J m is the equivalent inertia moment of the motor, transmission device, ball screw and parallel mechanism; B m is the viscous friction coefficient of the system; T L is the load torque of the parallel mechanism; T eis the electromagnetic torque; u q is the axial component of the stator voltage q;

[0076] The state variable is defined as x V1 =ω m , The output of the permanent magnet synchronous motor system affected by the speed loop is expressed as y ω , expand the total disturbance into a new state variable x V3 ; Then transform formula (20) into the following extended state space

[0077]

[0078] Convert Equation (21) into the extended state space equation

[0079]

[0080] in,

[0081] For a second-order system, the third-order linear active disturbance rejection control can be expressed as

[0082]

[0083] Among them, z1, z2 and z3 are estimated state variables respectively; by selecting appropriate observer gains β1, β2 and β3, linear active disturbance rejection control can achieve real-time tracking of system variables with a small steady-state error, i.e. z3→x V1 ,z2→x V2 ,z1→x V3 ;

[0084] Compensate the observed disturbance value into a control signal

[0085] u ω =(u0-z1) / b0 (24)

[0086] Where u0 is the error feedback variable; considering the steady state is f = z1, the following conditions can be obtained:

[0087]

[0088] Therefore, when linear ADRC is used, the updated input is defined as

[0089] u0=k p (ω ref -z3)-k d z2 (26)

[0090] Among them, ω ref is the reference input of the speed loop; similar to PD control, the controller parameters are

[0091]

[0092] The key parameters of the linear active disturbance rejection controller are ω0 and ω c , in practical applications, ω0=(3~5)ω c In order to expand the bandwidth ω0 of the observer, the intelligent optimization algorithm of radial basis function neural network is embedded in the linear active disturbance rejection controller to obtain the optimal bandwidth;

[0093] Assume that the output of the permanent magnet synchronous motor and the input vector of the network are u ω and y ω The network input vector is E=[u ω y ω ] T , then the output of the entire uncertainty process is expressed as

[0094]

[0095] Where h j (E) is the output vector of the hidden node neural network weight coefficient, b j and c j are width and center vector respectively, j is the number of hidden layer nodes, is the output vector of the hidden node, w is the weight coefficient vector in the neural network, and χ is the output vector of the hidden node;

[0096] For the optimal weight coefficient, the error function is defined as

[0097]

[0098] in, is the optimal weight for online tuning, is the weight coefficient error, ε is the approximate error vector; when the sampling step is t, the indicator function expression is

[0099]

[0100] When the index function of the radial basis function neural network reaches the minimum value, the gradient descent method is used to find the parameters. The update process is as follows

[0101]

[0102] Among them, η is the learning rate, α is the momentum coefficient; w j (t) is the weight coefficient vector in the neural network; b ji (t) is the center vector of the jth hidden node on the i-th input dimension; h j is the output vector of the hidden node neural network weight coefficients.

[0103] Furthermore, the current loop uses internal model control to achieve fast dynamic adjustment of the actuator current, specifically:

[0104] The internal model controller is transformed to obtain an equivalent controller, which is:

[0105]

[0106] Where I is the identity matrix; is the internal model, G(s) is the controlled object, and C(s) is the internal model controller; if the internal model is accurate, that is, G(s) = G(s), then there is no feedback link in the system, and the system transfer function is

[0107] G c (s)=G(s)C(s) (33)

[0108] As long as G(s) and C(s) are stable, the closed-loop control must be stable; considering C(s) = G -1 (s), G c (s) = I can be obtained, thus simplifying the analysis of system stability;

[0109] G(s) has no pure delay and its right half plane is zero. In order to optimize the control parameters, improve the control performance and ensure the stability of the control, a low-pass filter L(s) is added, which is defined as

[0110]

[0111] Where, L(s) = αI / (s+α), α is the design parameter;

[0112] Substituting formula (34) into formula (32) forms the internal model controller expression

[0113]

[0114] From equations (34) and (35), we know that the controller adjustment parameters are reduced from 2 to 1, which reduces the difficulty of parameter adjustment and satisfies the following relationship:

[0115]

[0116] A three-loop control system for a six-degree-of-freedom parallel platform in a high-dynamic environment, comprising:

[0117] A determination module, wherein the determination module constructs an electromechanical coupling nonlinear dynamic model of the six-degree-of-freedom parallel stable platform based on the six-degree-of-freedom parallel platform; models the components of the six-degree-of-freedom parallel platform and determines three loops: a position loop, a velocity loop, and a current loop;

[0118] A building module, wherein the building module builds a nested control structure consisting of a current loop, a speed loop, and a position loop based on a nonlinear dynamic model;

[0119] The compensation module tracks and compensates for disturbances of the permanent magnet synchronous motor based on a nested control structure consisting of a current loop, a speed loop, and a position loop.

[0120] Compared with the prior art, the present invention has the following beneficial effects:

[0121] The present invention uses an adaptive sliding mode control method with a disturbance observer in the position loop to rapidly estimate and compensate for the motion and attitude of a parallel stable platform. A linear anti-disturbance control method with a radial basis function neural network is used in the velocity loop to provide stable speed regulation and ensure sufficient adaptability. Internal model control is used in the inner current loop to regulate the motor's stator current and electromagnetic torque. The three control loops are nested and work together from the inside out. The proposed three-loop nested control method, consisting of a novel adaptive sliding mode control with a disturbance observer, linear anti-disturbance control with a radial basis function neural network, and internal model control, effectively improves platform tracking accuracy and smoothness, overcomes the contradiction between rapidity and stability in the classic PI method, and achieves precise tracking of the desired motion of the terminal platform. BRIEF DESCRIPTION OF THE DRAWINGS

[0122] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0123] Figure 1 Schematic diagram of the flow of the three-loop control method of the six-degree-of-freedom parallel platform applicable to a high-dynamic environment of the present invention;

[0124] Figure 2 Schematic diagram of the topology of the three-loop control method of the present invention applicable to a six-degree-of-freedom parallel platform in a high-dynamic environment;

[0125] Figure 3 This is a schematic diagram of the speed loop control method;

[0126] Figure 4 (a) is a typical internal model control block diagram;

[0127] Figure 4 (b) for Figure 4 (a) Block diagram of internal model control principle obtained by equivalent transformation;

[0128] Figure 5Schematic diagram of the structure of the three-loop control method of the present invention suitable for a six-degree-of-freedom parallel platform in a high dynamic environment. DETAILED DESCRIPTION

[0129] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of 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. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0130] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0131] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0132] In the description of the embodiments of the present invention, it should be noted that if the terms "upper," "lower," "horizontal," "inner," etc. appear, the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the inventive product is typically placed when in use. These terms are merely for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first," "second," etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0133] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0134] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0135] The present invention is described in further detail below with reference to the accompanying drawings:

[0136] Based on the electromechanical coupling dynamics model of the shipborne stabilized platform, the relationship between the drive input signal and the output motion of the terminal platform is established. However, the geometric nonlinearity of the parallel stabilized platform and the electromechanical nonlinearity of the actuator will significantly induce drive errors. These nonlinear factors have prompted the development of corresponding control methods to achieve the required precise motion. In order to improve the control performance, the present invention discloses a three-loop control method for a six-degree-of-freedom parallel platform in a high-dynamic environment. The specific process is as follows: Figure 1 shown.

[0137] S101: Based on a six-degree-of-freedom parallel platform, an electromechanical coupled nonlinear dynamic model of the six-degree-of-freedom parallel stabilized platform is constructed; the components of the six-degree-of-freedom parallel platform are modeled to determine the position loop, velocity loop, and current loop.

[0138] See also Figure 2 , construct the electromechanical coupling nonlinear dynamic model of the six-degree-of-freedom parallel stabilized platform, specifically:

[0139] According to Kane's formula, the electromechanical coupling nonlinear dynamic model of the six-degree-of-freedom parallel stabilized platform is established as follows:

[0140]

[0141] Among them, M(X) represents the inertia matrix, are the Coriolis force and centrifugal force matrices, G(X) represents the gravity matrix, is the friction force; J qi is the Jacobian matrix of the slider velocity, F pi is the force vector provided by the permanent magnet synchronous motor in the vertical direction; is the generalized acceleration, is the generalized speed.

[0142] S102, based on the nonlinear dynamic model, construct a nested control structure consisting of a current loop, a speed loop, and a position loop;

[0143] S103 , based on the nested control structure consisting of the current loop, the speed loop, and the position loop, the position and posture of the permanent magnet synchronous motor are tracked and disturbance compensation is performed.

[0144] S103.1, the position loop uses adaptive sliding mode control with a disturbance observer to perform disturbance compensation on attitude and position errors;

[0145] Based on the mechanical motion equation of the permanent magnet synchronous motor, the rotation angle of the permanent magnet synchronous motor is used as the observation variable to obtain the tracking error of the rotation angle and angular velocity of the permanent magnet synchronous motor, and then the error control equation of the rotation angle and angular velocity is obtained;

[0146] Based on the error control equation and the sliding surface of sliding mode control, the control quantity of traditional sliding mode control is obtained;

[0147] Adaptive sliding mode control and the introduction of disturbance observer are used to optimize the control quantity of traditional sliding mode control, and then disturbance compensation is performed on the attitude and position errors.

[0148] Based on the mechanical motion equation of the permanent magnet synchronous motor, the rotation angle of the permanent magnet synchronous motor is used as the observation variable to obtain the tracking error of the rotation angle and angular velocity of the permanent magnet synchronous motor, and then the error control equation of the rotation angle and angular velocity is obtained, which is specifically:

[0149] Using the rotor magnetic field oriented control method, the mechanical motion equation of the permanent magnet synchronous motor is obtained as follows:

[0150]

[0151] Among them, θ m is the rotor position angle; ω m is the mechanical angular velocity; J m is the equivalent inertia moment of the motor, transmission device, ball screw and parallel mechanism; B m is the viscous friction coefficient of the system; T L is the load torque of the parallel mechanism; T e is the electromagnetic torque;

[0152] The electromagnetic torque equation of the permanent magnet synchronous motor is Therefore, formula (2) gives

[0153]

[0154] Among them, the position control gain b0 = 3p n ψ f / 2J m Considering the changes of system parameters, we can get

[0155]

[0156] Where Δα1, Δα2 and Δα3 represent the changes in the permanent magnet synchronous motor parameters, β is the perturbation value caused by the load torque and parameters; p n is the number of pole pairs of the permanent magnet synchronous motor; f is the permanent magnet flux; i q The q-axis component of the stator current;

[0157] The rotation angle of the permanent magnet synchronous motor is used as the observed variable; the tracking error of the rotation angle and angular velocity of the permanent magnet synchronous motor is defined as

[0158]

[0159] Among them, θ ref is the reference rotor position angle of the motor, ω ref is the reference rotor angular velocity of the motor; x p1 is the tracking error of the permanent magnet synchronous motor rotation angle; x p2 is the tracking error of the angular velocity of the permanent magnet synchronous motor;

[0160] Taking the derivative of formula (5), the control equation of the error is expressed as

[0161]

[0162] The control quantity of the traditional sliding mode control is obtained based on the error control equation and the sliding mode surface of the sliding mode control, which is specifically:

[0163] In traditional sliding mode control, in order to ensure the asymptotic stability of modal motion, the sliding surface is defined as

[0164] s=c s x P1 +x P2 (7)

[0165] Among them, c s >0 is the control parameter to be designed; the exponential reaching law is written as

[0166]

[0167] Among them, k1 is the exponential gain, ε1 is the switching gain;

[0168] Therefore, the sliding surface of formula (7) depends on the state error, current and the intensity of the perturbation and is written as

[0169]

[0170] Combining formula (6), formula (7) and formula (9), the control quantity of traditional sliding mode control is expressed as

[0171]

[0172] Adaptive sliding mode control and the introduction of disturbance observer are used to optimize the control quantity of traditional sliding mode control, and then disturbance compensation is performed on the attitude and position errors. Specifically:

[0173] Adaptive sliding mode control

[0174]

[0175] When |s|>ζ increases, g(x P1 ,s) ranges from 1 to 2. As |s| increases, the system state follows the speed reaching law g(x P1 ,s)tanh(s) and exponential convergence law k1s reach the sliding surface at two rates, and the convergence time is shortened; on the contrary, when |s|<ζ, g(x P1 ,s) ranges from 0 to 1. As |s| decreases, the exponential convergence rate k1s gradually approaches zero. The variable speed arrival law term plays an important role. g(x P1 ,s)tanh(s) converges to ε1|x P1 |, under the action of the sliding mode control law, the system state |x P1 | gradually approaches zero; ζ is the threshold parameter;

[0176] In order to further weaken the chattering, the sign(·) function in the traditional sliding mode control is replaced by the tanh(·) function, which is expressed as

[0177]

[0178] Where μ>0;

[0179] Substituting formula (9) into formula (11) and combining it with formula (12), the output equation of adaptive sliding mode control is obtained as follows:

[0180]

[0181] The output of the permanent magnet synchronous motor system is expressed as y P , formula (6) is expressed as

[0182]

[0183] Among them, e P1 is the angular position state tracking parameter, e P2 is the angular velocity state tracking parameter, u w Type i for the replacement system q ;

[0184] Taking β as the observation object, the observer designed based on formula (14) is

[0185]

[0186] Among them, λ1, λ2 and η are positive real numbers; is the observed disturbance term; is the observed angular position state tracking value;

[0187] definition From formulas (15) and (14), the error equation of the observer is:

[0188]

[0189] Among them, e P is the actual state tracking value; is the state tracking value of the observation; Formula (16) can be converted into the state space form of the following form

[0190]

[0191] in, For the designed observer, if the eigenvalues ​​of the matrix M are all less than zero, the state error will converge to zero asymptotically;

[0192] For the proposed adaptive sliding mode control function, the total observed disturbance is considered to be Substituting into formula (17), the position loop input is expressed as

[0193]

[0194] From equation (18), parameter changes and load disturbances are adopted as feedforward compensation.

[0195] S103.2, the speed loop uses a linear active disturbance rejection control (LADRC) optimized by a radial basis function neural network (RBF-NN) to achieve robust and stable control of the motor speed.

[0196] The speed loop uses the linear active disturbance rejection control (LADRC) optimized by radial basis function neural network (RBF-NN) to achieve robust and stable control of the motor speed. Specifically:

[0197] The mathematical model of the permanent magnet synchronous motor in the dq coordinate system is expressed as

[0198]

[0199] Among them, L s is the stator inductance; Rs is the resistance of the stator winding; i d is the d-axis component of the stator current; Pn is the number of pole pairs of the three-phase permanent magnet synchronous motor;

[0200] When using i d = 0, the rotor field oriented control method, formula (19) is simplified to

[0201]

[0202] Among them, ω m is the mechanical angular velocity; J mis the equivalent inertia moment of the motor, transmission device, ball screw and parallel mechanism; B m is the viscous friction coefficient of the system; T L is the load torque of the parallel mechanism; T e is the electromagnetic torque; u q is the axial component of the stator voltage q;

[0203] The state variable is defined as x V1 =ω m , The output of the permanent magnet synchronous motor system affected by the speed loop is expressed as y ω , expand the total disturbance into a new state variable x V3 ; Then transform formula (20) into the following extended state space

[0204]

[0205] Convert Equation (21) into the extended state space equation

[0206]

[0207] in,

[0208] For a second-order system, the third-order linear active disturbance rejection control can be expressed as

[0209]

[0210] Among them, z1, z2 and z3 are estimated state variables respectively; by selecting appropriate observer gains β1, β2 and β3, linear active disturbance rejection control can achieve real-time tracking of system variables with a small steady-state error, i.e. z3→x V1 ,z2→x V2 ,z1→x V3 ;

[0211] Compensate the observed disturbance value into a control signal

[0212] u ω =(u0-z1) / b0 (24)

[0213] Where u0 is the error feedback variable; considering the steady state is f = z1, the following conditions can be obtained:

[0214]

[0215] Therefore, when linear ADRC is used, the updated input is defined as

[0216] u0=k p (ω ref -z3)-kd z2 (26)

[0217] Among them, ω ref is the reference input of the speed loop; similar to PD control, the controller parameters are

[0218]

[0219] The key parameters of the linear active disturbance rejection controller are ω0 and ω c , in practical applications, ω0=(3~5)ω c ; In order to expand the bandwidth ω0 of the observer, the intelligent optimization algorithm of the radial basis function neural network is embedded in the linear active disturbance rejection controller to obtain the optimal bandwidth; Figure 3 shown.

[0220] Assume that the output of the permanent magnet synchronous motor and the input vector of the network are u ω and y ω The network input vector is E=[u ω y ω ] T , then the output of the entire uncertainty process is expressed as

[0221]

[0222] Where h j (E) is the output vector of the hidden node neural network weight coefficient, b j and c j are width and center vector respectively, j is the number of hidden layer nodes, ω * c is the output vector of the hidden node, w is the weight coefficient vector in the neural network, and χ is the output vector of the hidden node;

[0223] For the optimal weight coefficient, the error function is defined as

[0224]

[0225] in, is the optimal weight for online tuning, is the weight coefficient error, ε is the approximate error vector; when the sampling step is t, the indicator function expression is

[0226]

[0227] When the index function of the radial basis function neural network reaches the minimum value, the gradient descent method is used to find the parameters. The update process is as follows

[0228]

[0229] Among them, η is the learning rate, α is the momentum coefficient; w j (t) is the weight coefficient vector in the neural network; b ji (t) is the center vector of the jth hidden node on the i-th input dimension; h j is the output vector of the hidden node neural network weight coefficients.

[0230] S103.2, the current loop uses internal model control to achieve rapid dynamic adjustment of the actuator current;

[0231] The function of the current loop controller is to achieve fast dynamic adjustment of torque. In order to facilitate the design of the current loop controller, the voltage equation of the permanent magnet synchronous motor in the dq coordinate system is rewritten as a state equation with dq current as the state variable.

[0232]

[0233] From formula (32), we can see that the stator current i d and i q Cross-coupled electromotive forces will be generated in the d-axis and q-axis directions respectively.

[0234] If i d and i q For complete decoupling, equation (32) is changed to

[0235]

[0236] Where: u d0 and u q0 are the voltages in the d-axis and q-axis directions after current decoupling.

[0237] After Laplace transforming Equation (33), we can get

[0238] Y(s)=G(s)U(s) (34)

[0239] Where:

[0240] Using the conventional PI regulator combined with the feedforward decoupling control method, the voltage of the dq axis can be obtained as

[0241]

[0242] Among them, K pd and K pq are the proportional gain of the PI controller, K id and K iq are the integral gains of the PI controller, and are the reference current values ​​of the dq axes respectively.

[0243] As shown in equation (35), when the feedforward decoupling control method is used, although the parameters of the PI controller can be designed according to the typical system in the automatic control theory, the cross-coupling electromotive force can only be completely decoupled when the actual parameters of the motor match the model parameters. However, due to the existence of the salient pole effect of the built-in three-phase permanent magnet synchronous motor, the impact of the model error on the system cannot be ignored, so this decoupling method cannot achieve complete decoupling. In order to solve this problem, a control method with low model accuracy requirements and insensitive to parameter changes should be selected. The internal model controller has the advantages of simple structure, single parameters and convenient online calculation, so it can be used. Figure 4 The internal model control method shown is used for parameter design. Figure 4 (a) shows a typical internal model control block diagram, where: is the internal model, G(s) is the controlled object, and C(s) is the internal model controller. According to the classical automatic control principle, Figure 4 (a) By performing appropriate equivalent transformation, we can obtain Figure 4 (b) shows the principle block diagram, and its equivalent controller is specifically:

[0244]

[0245] Where I is the identity matrix; is the internal model, G(s) is the controlled object, and C(s) is the internal model controller; if the internal model is accurate, that is, G(s) = G(s), then there is no feedback link in the system, and the system transfer function is

[0246] G c (s)=G(s)C(s) (37)

[0247] As long as G(s) and C(s) are stable, the closed-loop control must be stable; considering C(s) = G -1 (s), G c (s) = I can be obtained, thus simplifying the analysis of system stability;

[0248] G(s) has no pure delay and its right half plane is zero. In order to optimize the control parameters, improve the control performance and ensure the stability of the control, a low-pass filter L(s) is added, which is defined as

[0249]

[0250] Where, L(s) = αI / (s+α), α is the design parameter;

[0251] Substituting formula (38) into formula (36) forms the internal model controller expression

[0252]

[0253] From equations (38) and (39), we know that the controller adjustment parameters are reduced from 2 to 1, which reduces the difficulty of parameter adjustment and satisfies the following relationship:

[0254]

[0255] See also Figure 5 The present invention discloses a three-loop control system suitable for a six-degree-of-freedom parallel platform in a high-dynamic environment, comprising:

[0256] A determination module, wherein the determination module constructs an electromechanical coupling nonlinear dynamic model of the six-degree-of-freedom parallel stable platform based on the six-degree-of-freedom parallel platform; models the components of the six-degree-of-freedom parallel platform and determines three loops: a position loop, a velocity loop, and a current loop;

[0257] A building module, wherein the building module builds a nested control structure consisting of a current loop, a speed loop, and a position loop based on a nonlinear dynamic model;

[0258] The compensation module tracks and compensates for disturbances of the permanent magnet synchronous motor based on a nested control structure consisting of a current loop, a speed loop, and a position loop.

[0259] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A three-loop control method for a six-degree-of-freedom parallel platform in a high-dynamic environment, characterized in that: include: Based on the six-degree-of-freedom parallel platform, an electromechanical coupled nonlinear dynamic model of the six-degree-of-freedom parallel stable platform was constructed; the components of the six-degree-of-freedom parallel platform were modeled to determine the position loop, velocity loop, and current loop; Based on the nonlinear dynamic model, a nested control structure consisting of current loop, speed loop and position loop is constructed; Based on the nested control structure consisting of current loop, speed loop and position loop, the position and posture of the permanent magnet synchronous motor are tracked and disturbance compensation is performed.

2. The three-loop control method for a six-degree-of-freedom parallel platform in a high-dynamic environment according to claim 1, characterized in that: The electromechanical coupling nonlinear dynamic model of the six-degree-of-freedom parallel stabilized platform is constructed as follows: According to Kane's formula, the electromechanical coupling nonlinear dynamic model of the six-degree-of-freedom parallel stabilized platform is established as follows: Among them, M(X) represents the inertia matrix, are the Coriolis force and centrifugal force matrices, G(X) represents the gravity matrix, is the friction force; J qi is the Jacobian matrix of the slider velocity, F pi is the force vector provided by the permanent magnet synchronous motor in the vertical direction; is the generalized acceleration, is the generalized speed.

3. The three-loop control method for a six-degree-of-freedom parallel platform in a high-dynamic environment according to claim 2, characterized in that: The nested control structure composed of the current loop, speed loop and position loop is used to track and compensate for the position and posture of the permanent magnet synchronous motor. Specifically, The position loop uses adaptive sliding mode control with disturbance observer to perform disturbance compensation on attitude and position errors; The current loop adopts internal model control to achieve fast dynamic adjustment of the actuator current; The speed loop uses a linear active disturbance rejection control (LADRC) optimized by a radial basis function neural network (RBF-NN) to achieve robust and stable control of the motor speed.

4. The three-loop control method for a six-degree-of-freedom parallel platform in a high-dynamic environment according to claim 3, characterized in that: The position loop uses adaptive sliding mode control with disturbance observer to compensate for the attitude and position errors. Specifically: Based on the mechanical motion equation of the permanent magnet synchronous motor, the rotation angle of the permanent magnet synchronous motor is used as the observation variable to obtain the tracking error of the rotation angle and angular velocity of the permanent magnet synchronous motor, and then the error control equation of the rotation angle and angular velocity is obtained; Based on the error control equation and the sliding surface of sliding mode control, the control quantity of traditional sliding mode control is obtained; Adaptive sliding mode control and the introduction of disturbance observer are used to optimize the control quantity of traditional sliding mode control, and then disturbance compensation is performed on the attitude and position errors.

5. The three-loop control method for a six-degree-of-freedom parallel platform in a high-dynamic environment according to claim 4, characterized in that: Based on the mechanical motion equation of the permanent magnet synchronous motor, the rotation angle of the permanent magnet synchronous motor is used as the observation variable to obtain the tracking error of the rotation angle and angular velocity of the permanent magnet synchronous motor, and then obtain the error control equation of the rotation angle and angular velocity, which is specifically: Using the rotor magnetic field oriented control method, the mechanical motion equation of the permanent magnet synchronous motor is obtained as follows: Among them, θ m is the rotor position angle; ω m is the mechanical angular velocity; J m is the equivalent inertia moment of the motor, transmission device, ball screw and parallel mechanism; B m is the viscous friction coefficient of the system; T L is the load torque of the parallel mechanism; T e is the electromagnetic torque; The electromagnetic torque equation of the permanent magnet synchronous motor is Therefore, formula (2) gives Among them, the position control gain b0 = 3p n ψ f / 2J m Considering the changes of system parameters, we can get Where Δα1, Δα2 and Δα3 represent the changes in the permanent magnet synchronous motor parameters, β is the perturbation value caused by the load torque and parameters; p n is the number of pole pairs of the permanent magnet synchronous motor; f is the permanent magnet flux; i q The q-axis component of the stator current; The rotation angle of the permanent magnet synchronous motor is used as the observed variable; the tracking error of the rotation angle and angular velocity of the permanent magnet synchronous motor is defined as Among them, θ ref is the reference rotor position angle of the motor, ω ref is the reference rotor angular velocity of the motor; x p1 is the tracking error of the permanent magnet synchronous motor rotation angle; x p2 is the tracking error of the angular velocity of the permanent magnet synchronous motor; Taking the derivative of formula (5), the control equation of the error is expressed as 6. The three-loop control method for a six-degree-of-freedom parallel platform in a high-dynamic environment according to claim 5, characterized in that: The control quantity of the traditional sliding mode control is obtained based on the error control equation and the sliding mode surface of the sliding mode control, which is specifically: In traditional sliding mode control, in order to ensure the asymptotic stability of modal motion, the sliding surface is defined as s=c s x P1 +x P2 (7) Among them, c s >0 is the control parameter to be designed; the exponential reaching law is written as Among them, k1 is the exponential gain, ε1 is the switching gain; Therefore, the sliding surface of formula (7) depends on the state error, current and the intensity of the perturbation and is written as Combining formula (6), formula (7) and formula (9), the control quantity of traditional sliding mode control is expressed as 7. The three-loop control method for a six-degree-of-freedom parallel platform in a high-dynamic environment according to claim 6, characterized in that: The adaptive sliding mode control and the introduction of disturbance observer are used to optimize the control quantity of the traditional sliding mode control, and then the disturbance compensation of the attitude and position errors is performed. Specifically: Adaptive sliding mode control When |s|>ζ increases, g(x P1 ,s) ranges from 1 to 2. As |s| increases, the system state follows the speed reaching law g(x P1 ,s)tanh(s) and exponential convergence law k1s reach the sliding surface at two rates, and the convergence time is shortened; on the contrary, when |s|<ζ, g(x P1 ,s) ranges from 0 to 1. As |s| decreases, the exponential convergence rate k1s gradually approaches zero. The variable speed arrival law term plays an important role. g(x P1 ,s)tanh(s) converges to ε1|x P1 |, under the action of the sliding mode control law, the system state |x P1 | gradually approaches zero; v is the threshold parameter; In order to further weaken the chattering, the sign(·) function in the traditional sliding mode control is replaced by the tanh(·) function, which is expressed as Where μ>0; Substituting formula (9) into formula (11) and combining it with formula (12), the output equation of adaptive sliding mode control is obtained as follows: The output of the permanent magnet synchronous motor system is expressed as y P , formula (6) is expressed as Among them, e P1 is the angular position state tracking parameter, e P2 is the angular velocity state tracking parameter, u w Type i for the replacement system q ; Taking β as the observation object, the observer designed based on formula (14) is Among them, λ1, λ2 and η are positive real numbers; is the observed disturbance term; is the observed angular position state tracking value; definition From formulas (15) and (14), the error equation of the observer is: Among them, e P is the actual state tracking value; is the state tracking value of the observation; Formula (16) can be converted into the state space form of the following form in, For the designed observer, if the eigenvalues ​​of the matrix M are all less than zero, the state error will converge to zero asymptotically; For the proposed adaptive sliding mode control function, the total observed disturbance is considered to be Substituting into formula (17), the position loop input is expressed as From equation (18), parameter changes and load disturbances are adopted as feedforward compensation.

8. The three-loop control method for a six-degree-of-freedom parallel platform in a high-dynamic environment according to claim 7, characterized in that: The speed loop uses the linear active disturbance rejection control (LADRC) optimized by radial basis function neural network (RBF-NN) to achieve robust and stable control of the motor speed, specifically: The mathematical model of the permanent magnet synchronous motor in the dq coordinate system is expressed as Among them, L s is the stator inductance; Rs is the resistance of the stator winding; i d is the d-axis component of the stator current; Pn is the number of pole pairs of the three-phase permanent magnet synchronous motor; When using i d = 0, the rotor field oriented control method, formula (19) is simplified to Among them, ω m is the mechanical angular velocity; J m is the equivalent inertia moment of the motor, transmission device, ball screw and parallel mechanism; B m is the viscous friction coefficient of the system; T L is the load torque of the parallel mechanism; T e is the electromagnetic torque; u q is the axial component of the stator voltage q; The state variable is defined as x V1 =ω m , The output of the permanent magnet synchronous motor system affected by the speed loop is expressed as y ω , expand the total disturbance into a new state variable x V3 ; Then transform formula (20) into the following extended state space Convert Equation (21) into the extended state space equation in, C=(1 0 0), For a second-order system, the third-order linear active disturbance rejection control can be expressed as Among them, z1, z2 and z3 are estimated state variables respectively; by selecting appropriate observer gains β1, β2 and β3, linear active disturbance rejection control can achieve real-time tracking of system variables with a small steady-state error, i.e. z3→x V1 ,z2→x V2 ,z1→x V3 ; Compensate the observed disturbance value into a control signal in ω =(u0-z1) / b0 (24) Where u0 is the error feedback variable; considering the steady state is f = z1, the following conditions can be obtained: Therefore, when linear ADRC is used, the updated input is defined as u0=k p (oh ref -z3)-k d z2 (26) Among them, ω ref is the reference input of the speed loop; similar to PD control, the controller parameters are The key parameters of the linear active disturbance rejection controller are ω0 and ω c , in practical applications, ω0=(3~5)ω c In order to expand the bandwidth ω0 of the observer, the intelligent optimization algorithm of radial basis function neural network is embedded in the linear active disturbance rejection controller to obtain the optimal bandwidth; Assume that the output of the permanent magnet synchronous motor and the input vector of the network are u ω and y ω The network input vector is E=[u ω y ω ] T , then the output of the entire uncertainty process is expressed as Where h j (E) is the output vector of the hidden node neural network weight coefficient, b j and c j are width and center vector respectively, j is the number of hidden layer nodes, is the output vector of the hidden node, w is the weight coefficient vector in the neural network, and χ is the output vector of the hidden node; For the optimal weight coefficient, the error function is defined as in, is the optimal weight for online tuning, is the weight coefficient error, ε is the approximate error vector; when the sampling step is t, the indicator function expression is When the index function of the radial basis function neural network reaches the minimum value, the gradient descent method is used to find the parameters. The update process is as follows Among them, η is the learning rate, α is the momentum coefficient; w j (t) is the weight coefficient vector in the neural network; b ji (t) is the center vector of the jth hidden node on the i-th input dimension; h j is the output vector of the hidden node neural network weight coefficients.

9. The three-loop control method for a six-degree-of-freedom parallel platform in a high-dynamic environment according to claim 8, characterized in that: The current loop uses internal model control to achieve fast dynamic adjustment of the actuator current, specifically: The internal model controller is transformed to obtain an equivalent controller, which is: Where I is the identity matrix; is the internal model, G(s) is the controlled object, and C(s) is the internal model controller; if the internal model is accurate, that is, G(s) = G(s), then there is no feedback link in the system, and the system transfer function is G c (s)=G(s)C(s) (33) As long as G(s) and C(s) are stable, the closed-loop control must be stable; considering C(s) = G -1 (s), G c (s) = I can be obtained, thus simplifying the analysis of system stability; G(s) has no pure delay and its right half plane is zero. In order to optimize the control parameters, improve the control performance and ensure the stability of the control, a low-pass filter L(s) is added, which is defined as Where, L(s) = αI / (s+α), α is the design parameter; Substituting formula (34) into formula (32) forms the internal model controller expression From equations (34) and (35), we know that the controller adjustment parameters are reduced from 2 to 1, which reduces the difficulty of parameter adjustment and satisfies the following relationship:

10. A three-loop control system for a six-degree-of-freedom parallel platform in a high-dynamic environment, characterized in that: include: A determination module, wherein the determination module constructs an electromechanical coupling nonlinear dynamic model of the six-degree-of-freedom parallel stable platform based on the six-degree-of-freedom parallel platform; models the components of the six-degree-of-freedom parallel platform and determines three loops: a position loop, a velocity loop, and a current loop; A building module, wherein the building module builds a nested control structure consisting of a current loop, a speed loop, and a position loop based on a nonlinear dynamic model; The compensation module tracks and compensates for disturbances of the permanent magnet synchronous motor based on a nested control structure consisting of a current loop, a speed loop, and a position loop.

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