A dual-loop high-performance control method based on desired trajectory constrained optimization

Abstract

The present invention discloses a dual-loop high-performance control method based on constrained optimization of desired trajectories. The method comprises: establishing a dual-loop system of a linear motor; inputting the actual position and actual speed of the output shaft of the linear motor into the inner loop system, outputting an equivalent compensation term, and inputting the actual position and actual speed of the output shaft of the linear motor and the preset desired trajectory of the output shaft of the linear motor into the outer loop system, outputting the optimized equivalent compensation term and the optimized trajectory of the desired trajectory of the output shaft of the linear motor; inputting into the inner loop system through an interpolator, the inner loop system outputs the input of the linear motor in real time, and realizes constrained optimization control of the linear motor. The present invention ensures that the linear motor system can not only comply with the state and input constraints in the presence of parameter uncertainty and external interference, but also has fast transient response performance and high steady-state tracking accuracy by designing the control structure of the inner and outer loops.

Description

Technical Field

[0001] The invention relates to a dual-loop high-performance control method, and in particular to a dual-loop high-performance control method based on desired trajectory constrained optimization. Background Art

[0002] With the increasing demand for industrial applications, the need for high-speed and high-precision motion tracking control is becoming more and more urgent. However, most actual systems are subject to state and input constraints, which increases the difficulty of controller design. There are often model uncertainties in actual systems. If the influence of these uncertainties on the system is ignored to design the controller, it may lead to poor system motion performance or even cause the system to be unable to operate stably. In addition, most actual systems are subject to state and input constraints, such as workspace, operating speed, and limited actuator performance. If the system does not comply with these constraints, problems such as reduced control accuracy and system instability will also occur. Among the existing control algorithms, the control strategies used to solve parameter uncertainty and external interference are: adaptive control, Smith predictive control, disturbance observer control, and neural network control; the methods used to deal with system state and input constraints are: barrier Leapu function, nonlinear mapping, predictive performance control, and optimization control. However, so far, there is no practical method that can make the system not only comply with state and input constraints, but also have fast transient response performance and high steady-state tracking accuracy when there are parameter uncertainties and external interference. Summary of the invention

[0003] In order to solve the problems existing in the background technology, the present invention provides a dual-loop high-performance control method based on constrained optimization of expected trajectories. The method is based on the inner loop adaptive neural synovial controller working at a high sampling rate to ensure that the linear motor system has strong robustness. The outer loop system based on the prediction model control works at a lower sampling rate, which effectively reduces the computational complexity. At the same time, the outer loop system re-optimizes the expected trajectory according to the state and input constraints to obtain the optimized trajectory that complies with the constraints and transmits it to the inner loop system to ensure that the system complies with the constraints. The interpolator between the inner and outer loops ensures that the result of the outer loop input to the inner loop has the same sampling rate as the inner loop. At the same time, since the outer loop uses the neural equivalent compensation term in the inner loop controller as the prediction model, the conservatism is effectively reduced. The method can ensure that the linear motor system can not only comply with the state and input constraints in the presence of parameter uncertainty and external interference, but also has fast transient response performance and high steady-state tracking accuracy.

[0004] The technical solution adopted by the present invention is:

[0005] The dual-loop high-performance control method of the present invention comprises the following steps:

[0006] Step 1: Establish a dual-loop system of the linear motor, wherein the dual-loop system includes an inner loop system, an interpolator, and an outer loop system connected in sequence.

[0007] Step 2, obtain the actual position and actual speed of the current output shaft of the linear motor, input the actual position and actual speed of the current output shaft of the linear motor into the inner loop system, and the inner loop system outputs the equivalent compensation item; the inner loop system inputs the equivalent compensation item into the outer loop system, and at the same time inputs the actual position and actual speed of the output shaft of the linear motor and the preset expected trajectory of the output shaft of the linear motor into the outer loop system, and the outer loop system outputs the optimized equivalent compensation item and the optimized trajectory of the expected trajectory of the output shaft of the linear motor.

[0008] In step 3, the outer loop system inputs the optimized equivalent compensation term and the optimized trajectory of the expected trajectory of the output shaft of the linear motor into the inner loop system through the interpolator. The inner loop system outputs the input of the linear motor in real time to achieve restricted optimization control of the linear motor. At the same time, the inner loop system outputs the updated value of the optimized equivalent compensation term to replace the equivalent compensation term before optimization in step 2 and input it into the outer loop system to perform the next cycle to achieve closed-loop control.

[0009] The inner loop system inputs the input of the linear motor into the linear motor system through the saturation effect of the saturator. The linear motor system controls the position and speed according to the input of the linear motor, and outputs the actual position and actual speed of the output shaft of the linear motor after control, which are then input into the dual loop system as the actual position and actual speed of the output shaft of the current linear motor, and then perform the next cycle to realize closed-loop control.

[0010] The desired trajectory constrained optimization control means that when the linear motor has state and input constraints, the desired trajectory of the output shaft of the linear motor is optimized by the outer loop system to obtain the optimized trajectory that satisfies the state and input constraints. The position and speed of the output shaft of the linear motor are controlled by the controller designed by the inner loop system, so that the actual position and actual speed of the output shaft of the controlled linear motor can track the desired trajectory of the output shaft of the linear motor as quickly as possible while satisfying the state and input constraints, thereby achieving optimal control of the trajectory of the output shaft of the linear motor.

[0011] The saturation performance of the linear motor actuator can be regarded as the input of the designed input result after the saturation effect of the saturator is obtained and then it is actually input to the linear motor system. This may cause a deviation between the designed input and the actual input, resulting in poor control performance or even instability of the linear motor system. In order to avoid these phenomena, the saturator is added to the outer loop system as an input constraint of the outer loop system, and then the input of the linear motor is designed without exceeding the saturator constraint boundary.

[0012] In step 1, the inner loop system is an adaptive neural synovial membrane controller, which is as follows:

[0013]

[0014] f(x r1 ,x r2 )=v *T Φ * (x r ,δ * ,α * ,β * )+Δ

[0015] u=u a +u s

[0016]

[0017] u s =u s1 +u s2

[0018] u s1 =-k s1 s

[0019] u s2 =-k s2 sat(s)

[0020] Among them, x r is the optimized trajectory of the desired trajectory of the output shaft of the linear motor, x r =[x r1 ,x r2 ] T , x r1 is the optimized position of the desired position of the output shaft of the linear motor, x r2 is the optimized speed of the desired speed of the output shaft of the linear motor; f() is a smooth unknown nonlinear function representing the unknown nonlinearity of the linear motor; is the estimate of the smooth unknown nonlinear function f(); v * is the optimal value of the control input v of the linear motor, is the optimal value v of the control input of the linear motor * The estimated value of *T Φ * () is the optimal recurrent neural network, is the estimate of the optimal recurrent neural network, Φ * () is the optimal parameter vector of the hidden layer output vector Φ() of the recurrent neural network obtained by inputting the actual trajectory x of the output shaft of the linear motor into the recurrent neural network, is the optimal parameter vector Φ *() estimation vector; δ * , α * and β * are the optimal values ​​of the width δ, center α of the Gaussian basis function of the recurrent neural network and the cyclic weight β of the recurrent neural network, respectively. and They are the width and center of the Gaussian basis function of the recurrent neural network and the optimal value of the recurrent weight of the recurrent neural network δ * , α * and β * The estimated value of; Δ is the smooth unknown nonlinear function f() and the optimal recurrent neural network v *T Φ * () approximate error; u is the input of the linear motor; u a is the neural equivalent compensation control term of the linear motor input, u s is the robust control feedback term of the linear motor input; M is the load mass of the linear motor; is the optimized acceleration of the desired acceleration of the output shaft of the linear motor; s1 is the nominal system stability term, u s2 is the uncertainty attenuation term; k s1 and k s2 are the first control gain and the second control gain of the inner loop adaptive neural synovial controller respectively; s is the synovial surface of the inner loop adaptive neural synovial controller, e is the actual position x1 and the optimized position x1 of the output shaft of the linear motor r1 The position tracking error between 1r , The actual speed x2 and the optimized speed x of the output shaft of the linear motor r2 The position tracking error between c1 is a positive constant parameter to be designed for the inner loop adaptive neural synovial membrane controller.

[0021] sat(s) is the saturation function of the synovial surface s in the inner loop adaptive neural synovial controller, as follows:

[0022]

[0023] Neural equivalent compensation control term u a For estimating dynamic system models Robust control feedback term u s Used to eliminate the influence of the estimated error χ and the unknown disturbance d of the linear motor.

[0024] The inner loop system satisfies the following constraints:

[0025] a) State constraints:

[0026] x 1min ≤x1≤x 1max

[0027] x 2min ≤x2≤x 2max

[0028] Among them, x 1max and x 1min are the upper and lower boundaries of the actual position x1 of the output shaft of the linear motor; 2max and x 2min They are the upper and lower limits of the actual speed of the output shaft of the linear motor respectively.

[0029] b) Input constraints:

[0030] |u|≤u max

[0031] Among them, u max is the maximum control input of the linear motor.

[0032] Before establishing the inner and outer loop systems, it is necessary to establish a state space model of the linear motor that takes into account state constraints and input constraints, as follows:

[0033]

[0034]

[0035] Where d is the unknown disturbance of the linear motor, including uncertain nonlinearity and external disturbance.

[0036] The smooth unknown nonlinear function f(x1,x2) is as follows:

[0037] f(x1,x2)=-Bx2-AS(x2)

[0038] Among them, B is the viscous friction coefficient, Bx2 is the viscous friction force on the output shaft of the linear motor; A is the Coulomb friction coefficient, S(x2) is a smooth function of the actual speed x2 of the output shaft of the linear motor, and AS(x2) is the Coulomb friction force on the output shaft of the linear motor.

[0039] The linear motor system is as follows:

[0040]

[0041] By defining the state variable Convert the linear motor system into a state-space model.

[0042] The smooth unknown nonlinear function f(x1,x2) describes the uncertainty of the parameters in the state-space model; the uncertain nonlinearity of the unknown disturbance d of the linear motor includes the external influence of the linear motor and the modeling error when the linear motor system is converted into a state-space model.

[0043] The first control gain k of the inner loop adaptive neural synovial controller is s1 and the second control gain k s2 The following constraints are met:

[0044]

[0045] k s2 ≥K+d+ρ

[0046] Where k is the first control gain k s1 Any positive constant parameter, ρ is the second control gain k s2 A sufficiently small positive constant parameter of .

[0047] In step 1, the outer loop system includes a state observer and an optimization target model, which are as follows:

[0048] a) State Observer:

[0049]

[0050]

[0051] u1=u a1 +u s

[0052]

[0053]

[0054] |u1|=|u a1 +u s |≤|u a1 |+|u s |≤u amax +u smax ≤|u max |

[0055]

[0056] in, is the observed value of the actual position x1 of the output shaft of the linear motor, that is, the observed position; and is the observed value of the actual speed x2 of the output shaft of the linear motor, i.e., the observed speed; is the observed value of the actual acceleration of the output shaft of the linear motor, that is, the observed acceleration; u1 is the optimized input of the linear motor; z1 is the actual position x1 of the output shaft of the linear motor and the observed position The observation error, and z2 are the actual speed x2 and the observed speed of the output shaft of the linear motor The observation error, The actual speed x2 of the output shaft of the linear motor and the observed speed The first derivative of the observation error; u smax is the robust control feedback term u s The maximum value of u amax is the equivalent compensation term u a1 The maximum value of the equivalent compensation term u a1 The maximum value of the neural equivalent compensation control term u a The maximum value of is the same; γ is a sufficiently small positive constant parameter of the optimized input u1 of the linear motor; χ is the estimation error between the smooth unknown nonlinear function of the linear motor and its estimation, that is, the difference between the two.

[0057] The equivalent compensation term u is obtained through the state observer a1 The maximum value u amax , so that the robust control feedback term u s The maximum value u smax and equivalent compensation term u a1 The maximum value u amax Can be reasonably allocated, constraining the equivalent compensation item u a1 .

[0058] It can be seen By estimating the smooth unknown nonlinear function f(x1,x2) The estimated error and the unknown disturbance d of the linear motor are composed of the robust control feedback term u s The role of is to eliminate the influence of these two on the linear motor.

[0059] b) Optimize the target model for each sampling period of the linear motor as follows:

[0060]

[0061]

[0062]

[0063] x 1 min ≤x r1 ≤x 1 max

[0064] x 2 min ≤xr2 ≤x 2 max

[0065]

[0066] x r1 (t0) = x1(t0)

[0067] x r2 (t0) = x2(t0)

[0068] Among them, t0 is the initial time of the sampling period, τ is the prediction time domain; x d is the desired trajectory of the linear motor; Q is the optimized trajectory x of the output shaft of the linear motor r and the expected trajectory x d The weighted matrix norm of the difference between a1 The weighted matrix norm of ; is the optimized speed of the desired speed of the output shaft of the linear motor, u a1 is an equivalent compensation term, specifically, the neural equivalent compensation control term u a It is approximated as the neural equivalent compensation control term without the unknown disturbance d of the linear motor, that is, the equivalent compensation term u is obtained a1 ;x r1 (t0) is the optimized position of the linear motor at time t0, and x1(t0) is the actual position of the linear motor at time t0; r2 (t0) is the optimized speed of the linear motor at time t0, and x2(t0) is the actual speed of the linear motor at time t0.

[0069] The optimization problem of the outer loop system based on the optimization target model is a nonlinear model prediction problem, which can be solved using the ParNMPC toolkit in Matlab to obtain the optimized trajectory x of the optimized linear motor. r and equivalent compensation term u a1 , and input this result into the inner loop system. Optimizing the target model can make the overall system have fast transient capability and high steady-state accuracy.

[0070] in, is the state constraint of the outer loop system, |u a1 |≤|u amax | is the input constraint of the outer loop system.

[0071] In the step 2, the actual position and actual speed of the output shaft of the current linear motor are obtained, specifically by measuring the output shaft of the linear motor through a position speed sensor preset inside the linear motor to obtain the actual position and actual speed of the output shaft of the linear motor.

[0072] In step 2, the actual position x1 and actual speed x2 of the output shaft of the current linear motor are input into the inner loop system, specifically, input into the inner loop adaptive neural synovial membrane controller, and the updated neural equivalent compensation control item u is obtained in the inner loop adaptive neural synovial membrane controller. a , and then through the neural equivalent compensation control term u a Get equivalent compensation u a1 And output;

[0073] The inner loop system will compensate the equivalent term u a1 Input the outer loop system, and at the same time, the actual position x1 and actual speed x2 of the output shaft of the linear motor and the expected trajectory x2 of the output shaft of the linear motor are input. d Input the outer loop system, specifically input the actual position x1 and actual speed x2 of the output shaft of the linear motor into the state observer, and output the equivalent compensation term u through the state observer a1 The maximum value u amax For equivalent compensation item u a1 Constraints are made; the equivalent compensation term u a1 and the desired trajectory x of the linear motor d Input the optimization target model and use the model prediction method to output the optimized trajectory x of the desired trajectory of the output shaft of the linear motor r and the optimized equivalent compensation term.

[0074] In step 3, the outer loop system optimizes the equivalent compensation term and the optimized trajectory x of the desired trajectory of the output shaft of the linear motor. r The optimized equivalent compensation term and the optimized trajectory x of the desired trajectory of the output shaft of the linear motor are input into the inner loop system through the interpolator. r The sampling rate is converted to the same as the sampling rate of the inner loop system through the interpolator and then output to the inner loop adaptive neural synovial membrane controller in the inner loop system. The inner loop adaptive neural synovial membrane controller outputs the input u of the linear motor in real time to achieve constrained optimization control of the desired trajectory of the output shaft of the linear motor.

[0075] Since the optimization problem of the outer loop system has a very high computational complexity and can only work at a low sampling rate, and the inner loop system needs to work at a high sampling rate to ensure that the entire system has strong robustness, the inner and outer loop systems have different sampling rates. The interpolator between the inner and outer loop systems ensures that the optimization result of the outer loop system input to the inner loop system has the same sampling rate as the inner loop system.

[0076] The beneficial effects of the present invention are:

[0077] 1. The dual-loop high-performance control method proposed in the present invention can simultaneously ensure that the controlled linear motor system meets the constraints and has fast transient response performance and high steady-state tracking accuracy.

[0078] 2. The conservatism is effectively reduced by converting the neural equivalent compensation term in the inner-loop controller into a prediction model in the outer-loop optimizer.

[0079] 3. The inner and outer loops use different sampling rates, which effectively reduces the computational complexity while ensuring that the controlled system has strong robust stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 is a control flow chart of the present invention;

[0081] Figure 2 It is a schematic diagram of the position tracking trajectory of the present invention;

[0082] Figure 3 It is a transient schematic diagram of the position tracking error of the present invention;

[0083] Figure 4 It is a schematic diagram of the steady state of the position tracking error of the present invention;

[0084] Figure 5 It is a schematic diagram of the speed tracking trajectory of the present invention;

[0085] Figure 6 Schematic diagram of control signals of the present invention. DETAILED DESCRIPTION

[0086] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0087] like Figure 1 As shown, the dual-loop high-performance control method of the present invention comprises the following steps:

[0088] Step 1: Establish a dual-loop system of the linear motor, wherein the dual-loop system includes an inner loop system, an interpolator, and an outer loop system connected in sequence.

[0089] In step 1, the inner loop system is an adaptive neural synovial membrane controller, which is as follows:

[0090]

[0091] f(x r1 ,x r2 )=v *T Φ * (x r ,δ * ,α * ,β * )+Δ

[0092] u=u a +u s

[0093]

[0094] u s =u s1 +u s2

[0095] u s1 =-k s1 s

[0096] u s2 =-k s2 sat(s)

[0097] Among them, x r is the optimized trajectory of the desired trajectory of the output shaft of the linear motor, x r =[x r1 ,x r2 ] T , x r1 is the optimized position of the desired position of the output shaft of the linear motor, x r2 is the optimized speed of the desired speed of the output shaft of the linear motor; f() is a smooth unknown nonlinear function representing the unknown nonlinearity of the linear motor; is the estimate of the smooth unknown nonlinear function f(); v * is the optimal value of the control input v of the linear motor, is the optimal value v of the control input of the linear motor * The estimated value of *T Φ * () is the optimal recurrent neural network, is the estimate of the optimal recurrent neural network, Φ * () is the optimal parameter vector of the hidden layer output vector Φ() of the recurrent neural network obtained by inputting the actual trajectory x of the output shaft of the linear motor into the recurrent neural network, is the optimal parameter vector Φ * () estimation vector; δ * , α * and β * are the optimal values ​​of the width δ, center α of the Gaussian basis function of the recurrent neural network and the cyclic weight β of the recurrent neural network, respectively. and They are the width and center of the Gaussian basis function of the recurrent neural network and the optimal value of the recurrent weight of the recurrent neural network δ * , α * and β * The estimated value of; Δ is the smooth unknown nonlinear function f() and the optimal recurrent neural network v *T Φ * () approximate error; u is the input of the linear motor; u ais the neural equivalent compensation control term of the linear motor input, u s is the robust control feedback term of the linear motor input; M is the load mass of the linear motor; is the optimized acceleration of the desired acceleration of the output shaft of the linear motor; s1 is the nominal system stability term, u s2 is the uncertainty attenuation term; k s1 and k s2 are the first control gain and the second control gain of the inner loop adaptive neural synovial controller respectively; s is the synovial surface of the inner loop adaptive neural synovial controller, e is the actual position x1 and the optimized position x1 of the output shaft of the linear motor r1 The position tracking error between 1r , The actual speed x2 and the optimized speed x of the output shaft of the linear motor r2 The position tracking error between c1 is a positive constant parameter to be designed for the inner loop adaptive neural synovial membrane controller.

[0098] sat(s) is the saturation function of the synovial surface s in the inner loop adaptive neural synovial controller, as follows:

[0099]

[0100] Neural equivalent compensation control term u a For estimating dynamic system models Robust control feedback term u s Used to eliminate the influence of the estimated error χ and the unknown disturbance d of the linear motor.

[0101] The inner loop system satisfies the following constraints:

[0102] a) State constraints:

[0103] x 1 min ≤x1≤x 1 max

[0104] x 2 min ≤x2≤x 2 max

[0105] Among them, x 1 max and x 1 min are the upper and lower boundaries of the actual position x1 of the output shaft of the linear motor; 2 max and x 2 min They are the upper and lower limits of the actual speed of the output shaft of the linear motor respectively.

[0106] b) Input constraints:

[0107] |u|≤umax

[0108] Among them, u max is the maximum control input of the linear motor.

[0109] Before establishing the inner and outer loop systems, it is necessary to establish a state space model of the linear motor that takes into account state constraints and input constraints, as follows:

[0110]

[0111]

[0112] Where d is the unknown disturbance of the linear motor, including uncertain nonlinearity and external disturbance.

[0113] The smooth unknown nonlinear function f(x1,x2) is as follows:

[0114] f(x1,x2)=-Bx2-AS(x2)

[0115] Among them, B is the viscous friction coefficient, Bx2 is the viscous friction force on the output shaft of the linear motor; A is the Coulomb friction coefficient, S(x2) is a smooth function of the actual speed x2 of the output shaft of the linear motor, and AS(x2) is the Coulomb friction force on the output shaft of the linear motor.

[0116] The linear motor system is as follows:

[0117]

[0118] By defining the state variable Convert the linear motor system into a state-space model.

[0119] The smooth unknown nonlinear function f(x1,x2) describes the uncertainty of the parameters in the state-space model; the uncertain nonlinearity of the unknown disturbance d of the linear motor includes the external influence of the linear motor and the modeling error when the linear motor system is converted into a state-space model.

[0120] The first control gain k of the inner loop adaptive neural synovial controller s1 and the second control gain k s2 The following constraints are met:

[0121]

[0122] k s2 ≥K+d+ρ

[0123] Where k is the first control gain k s1 Any positive constant parameter, ρ is the second control gain k s2A sufficiently small positive constant parameter of .

[0124] In step 1, the outer loop system includes a state observer and an optimization target model, as follows:

[0125] a) State Observer:

[0126]

[0127]

[0128] u1=u a1 +u s

[0129]

[0130]

[0131] |u1|=|u a1 +u s |≤|u a1 |+|u s |≤u amax +u smax ≤|u max |

[0132]

[0133] in, is the observed value of the actual position x1 of the output shaft of the linear motor, that is, the observed position; and is the observed value of the actual speed x2 of the output shaft of the linear motor, i.e., the observed speed; is the observed value of the actual acceleration of the output shaft of the linear motor, that is, the observed acceleration; u1 is the optimized input of the linear motor; z1 is the actual position x1 of the output shaft of the linear motor and the observed position The observation error, and z2 are the actual speed x2 and the observed speed of the output shaft of the linear motor The observation error, The actual speed x2 of the output shaft of the linear motor and the observed speed The first derivative of the observation error; u smax is the robust control feedback term u s The maximum value of u amax is the equivalent compensation term u a1 The maximum value of the equivalent compensation term u a1 The maximum value of the neural equivalent compensation control term u aThe maximum value of is the same; γ is a sufficiently small positive constant parameter of the optimized input u1 of the linear motor; χ is the estimation error between the smooth unknown nonlinear function of the linear motor and its estimation, that is, the difference between the two.

[0134] The equivalent compensation term u is obtained through the state observer a1 The maximum value u amax , so that the robust control feedback term u s The maximum value u smax and equivalent compensation term u a1 The maximum value u amax Can be reasonably allocated, constraining the equivalent compensation item u a1 .

[0135] It can be seen By estimating the smooth unknown nonlinear function f(x1,x2) The estimated error and the unknown disturbance d of the linear motor are composed of the robust control feedback term u s The role of is to eliminate the influence of these two on the linear motor.

[0136] b) Optimize the target model for each sampling period of the linear motor as follows:

[0137]

[0138]

[0139]

[0140] x 1 min ≤x r1 ≤x 1 max

[0141] x 2 min ≤x r2 ≤x 2 max

[0142]

[0143] x r1 (t0) = x1(t0)

[0144] x r2 (t0) = x2(t0)

[0145] Among them, t0 is the initial time of the sampling period, τ is the prediction time domain; x d is the desired trajectory of the linear motor; Q is the optimized trajectory x of the output shaft of the linear motor r and the expected trajectory x d The weighted matrix norm of the difference between a1The weighted matrix norm of ; is the optimized speed of the desired speed of the output shaft of the linear motor, u a1 is an equivalent compensation term, specifically, the neural equivalent compensation control term u a It is approximated as the neural equivalent compensation control term without the unknown disturbance d of the linear motor, that is, the equivalent compensation term u is obtained a1 ;x r1 (t0) is the optimized position of the linear motor at time t0, and x1(t0) is the actual position of the linear motor at time t0; r2 (t0) is the optimized speed of the linear motor at time t0, and x2(t0) is the actual speed of the linear motor at time t0.

[0146] The optimization problem of the outer loop system based on the optimization target model is a nonlinear model prediction problem, which can be solved using the ParNMPC toolkit in Matlab to obtain the optimized trajectory x of the optimized linear motor. r and equivalent compensation terms, and input this result into the inner loop system.

[0147] Optimizing the target model can make the overall system have fast transient capability and high steady-state accuracy.

[0148] in, is the state constraint of the outer loop system, |u a1 |≤|u amax | is the input constraint of the outer loop system.

[0149] Step 2, obtain the actual position and actual speed of the current output shaft of the linear motor, input the actual position and actual speed of the current output shaft of the linear motor into the inner loop system, and the inner loop system outputs the equivalent compensation item; the inner loop system inputs the equivalent compensation item into the outer loop system, and at the same time inputs the actual position and actual speed of the output shaft of the linear motor and the preset expected trajectory of the output shaft of the linear motor into the outer loop system, and the outer loop system outputs the optimized equivalent compensation item and the optimized trajectory of the expected trajectory of the output shaft of the linear motor.

[0150] In step 2, the actual position and actual speed of the output shaft of the current linear motor are obtained, specifically, the output shaft of the linear motor is measured by a position and speed sensor preset inside the linear motor to obtain the actual position and actual speed of the output shaft of the linear motor.

[0151] In step 2, the actual position x1 and actual speed x2 of the output shaft of the current linear motor are input into the inner loop system, specifically, into the inner loop adaptive neural synovial membrane controller, and the updated neural equivalent compensation control item u is obtained in the inner loop adaptive neural synovial membrane controller. a , and then through the neural equivalent compensation control term u aGet equivalent compensation u a1 And output.

[0152] The inner loop system will compensate the equivalent term u a1 Input the outer loop system, and at the same time, the actual position x1 and actual speed x2 of the output shaft of the linear motor and the expected trajectory x2 of the output shaft of the linear motor are input. d Input the outer loop system, specifically input the actual position x1 and actual speed x2 of the output shaft of the linear motor into the state observer, and output the equivalent compensation term u through the state observer a1 The maximum value u amax For equivalent compensation item u a1 Constraints are made; the equivalent compensation term u a1 and the desired trajectory x of the linear motor d Input the optimization target model and use the model prediction method to output the optimized trajectory x of the desired trajectory of the output shaft of the linear motor r and the optimized equivalent compensation term.

[0153] In step 3, the outer loop system inputs the optimized equivalent compensation term and the optimized trajectory of the expected trajectory of the output shaft of the linear motor into the inner loop system through the interpolator. The inner loop system outputs the input of the linear motor in real time to achieve restricted optimization control of the linear motor. At the same time, the inner loop system outputs the updated value of the optimized equivalent compensation term to replace the equivalent compensation term before optimization in step 2 and input it into the outer loop system to perform the next cycle to achieve closed-loop control.

[0154] The inner loop system inputs the input of the linear motor into the linear motor system through the saturation effect of the saturator. The linear motor system controls the position and speed according to the input of the linear motor, and outputs the actual position and actual speed of the output shaft of the linear motor after control, which are then input into the dual loop system as the actual position and actual speed of the output shaft of the current linear motor, and then perform the next cycle to realize closed-loop control.

[0155] The desired trajectory constrained optimization control means that when the linear motor has state and input constraints, the desired trajectory of the output shaft of the linear motor is optimized by the outer loop system to obtain the optimized trajectory that satisfies the state and input constraints. The position and speed of the output shaft of the linear motor are controlled by the controller designed by the inner loop system, so that the actual position and actual speed of the output shaft of the controlled linear motor can track the desired trajectory of the output shaft of the linear motor as quickly as possible while satisfying the state and input constraints, thereby achieving optimal control of the trajectory of the output shaft of the linear motor.

[0156] The saturation performance of the linear motor actuator can be regarded as the input of the designed input result after the saturation effect of the saturator is obtained and then it is actually input to the linear motor system. This may cause a deviation between the designed input and the actual input, resulting in poor control performance or even instability of the linear motor system. In order to avoid these phenomena, the saturator is added to the outer loop system as an input constraint of the outer loop system, and then the input of the linear motor is designed without exceeding the saturator constraint boundary.

[0157] In step 3, the outer loop system optimizes the equivalent compensation term and the optimized trajectory x of the desired trajectory of the output shaft of the linear motor. r The optimized equivalent compensation term and the optimized trajectory x of the desired trajectory of the output shaft of the linear motor are input into the inner loop system through the interpolator. r The sampling rate is converted to the same as the sampling rate of the inner loop system through the interpolator and then output to the inner loop adaptive neural synovial membrane controller in the inner loop system. The inner loop adaptive neural synovial membrane controller outputs the input u of the linear motor in real time to achieve constrained optimization control of the desired trajectory of the output shaft of the linear motor.

[0158] Since the optimization problem of the outer loop system has a very high computational complexity and can only work at a low sampling rate, and the inner loop system needs to work at a high sampling rate to ensure that the entire system has strong robustness, the inner and outer loop systems have different sampling rates. The interpolator between the inner and outer loop systems ensures that the optimization result of the outer loop system input to the inner loop system has the same sampling rate as the inner loop system.

[0159] In order to verify the effectiveness and superiority of the method of the present invention, the following control methods are simulated and compared, and the specific embodiments are as follows:

[0160] M1: Reference governor based on PID, with a design control rate of:

[0161]

[0162] Among them, u(t) is the input of the linear motor at time t, K p is the first control parameter, K i is the second control parameter; x(t) is the position of the output shaft of the linear motor at time t, v(t) is the preset control input of the linear motor at time t; K d is the third control parameter; is the speed of the output shaft of the linear motor at time t, The first-order derivative of the preset control input of the linear motor at time t.

[0163] Among them, the preset control input v(t) of the linear motor at time t is obtained through the following optimization problem:

[0164]

[0165] stv(t)=v(t-1)+κ(x 1d (t)-v(t-1))

[0166] Among them, κ is the optimization parameter, κ(t) is the maximum value of the optimization parameter κ at time t; v(t-1) is the preset control input of the linear motor at time t-1; the control parameter is set to: K p =480,K i =3200,K d =23.4, sampling rate is 5khz.

[0167] M2: Adaptive neural synovial control, designed control rate is:

[0168] u s =u a +u s1 +u s2

[0169] u s1 =-k s1 s

[0170]

[0171]

[0172] in is the desired acceleration of the linear motor; set the control parameter to: k s1 =5, The sampling rate is 5khz.

[0173] M3: Model predictive control method, the prediction model is constructed as:

[0174]

[0175]

[0176] Among them, θ1, θ2, θ3, θ4 are the predicted values ​​of M, B, A, and d respectively, and the design control rate is:

[0177]

[0178]

[0179]

[0180] x 1 min ≤x1≤x 1 max

[0181] x 2 min ≤x2≤x 2 max

[0182] |u|≤|u max |

[0183] Among them, the initial state of the linear motor is selected as x1(0)=x2(0)=0, the parameters are selected as θ1=0.35, θ2=0.66, θ3=0.25, θ4=0, and the sampling rate is 1 khz.

[0184] M4: The dual-loop high-performance control method based on desired trajectory constrained optimization proposed in this invention has a control rate as shown below, and the control parameters are set as follows: k s1 =5, The sampling rate of the inner loop system is 5khz, and the sampling rate of the outer loop system is 1khz.

[0185] Set the parameters in the linear motor system to: M = 0.4, B = 0.6, A = 0.2,

[0186] The expected trajectory, initial state, total state constraints, and total input constraints of the linear motor system in the above simulation experiment are set as follows:

[0187] Expected trajectory:

[0188]

[0189] Initial state:

[0190] x1(0)=x2(0)=0

[0191] Total state input and total input constraints:

[0192] u max =10

[0193] -0.43≤x1≤0.43

[0194] -2.05≤x2≤2.05

[0195] Figure 2 Schematic diagram of the position tracking trajectory of the linear motor system under different control methods. Figure 3 and Figure 4 They are respectively the transient and steady-state schematic diagrams of position tracking error, Figure 5 It is a schematic diagram of the speed tracking trajectory of the linear motor system under different control methods. Figure 6 Schematic diagram of control signals for different control methods.

[0196] Depend on Figure 3 and Figure 5It can be seen that the simple recurrent neural network control (M2) not only cannot handle the state constraints, but also the system convergence speed is slow; and although the model predictive control (M3) can ensure that the state constraints are not violated, it does not have the ability to handle parameter uncertainty and external interference, so the controlled system has a poor steady-state error; although the PID-based Reference governor (M1) can ensure that the state constraints are not violated and has good transient performance, the steady-state error is also unsatisfactory; and the dual-loop high-performance control method based on expected trajectory constrained optimization (M4) not only ensures that the system complies with the state constraints, but also has fast transient response performance and high steady-state tracking accuracy.

[0197] The above contents are only the technical ideas of the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical ideas proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A dual-loop high-performance control method based on desired trajectory constrained optimization, which has the following characteristics: Step 1, establishing a dual-loop system of the linear motor, the dual-loop system comprising an inner loop system, an interpolator and an outer loop system connected in sequence; Step 2, obtaining the actual position and actual speed of the output shaft of the current linear motor, inputting the actual position and actual speed of the output shaft of the current linear motor into the inner loop system, and the inner loop system outputs an equivalent compensation item; the inner loop system inputs the equivalent compensation item into the outer loop system, and at the same time inputs the actual position and actual speed of the output shaft of the linear motor and the preset expected trajectory of the output shaft of the linear motor into the outer loop system, and the outer loop system outputs the optimized equivalent compensation item and the optimized trajectory of the expected trajectory of the output shaft of the linear motor; Step 3, the outer loop system inputs the optimized equivalent compensation term and the optimized trajectory of the desired trajectory of the output shaft of the linear motor into the inner loop system through an interpolator, and the inner loop system outputs the input of the linear motor in real time to achieve restricted optimization control of the linear motor; In step 1, the inner loop system is an adaptive neural synovial membrane controller, which is as follows: f(x r1 ,x r2 )=v *T F * (x r ,d * ,a * ,b * )+D in=in a +in s in s =in s1 +in s2 u s1 =-k s1 s u s2 =-k s2 sat(s) in, x r is the optimized trajectory of the desired trajectory of the output shaft of the linear motor, x r =[x r1 ,x r2 ] T , x r1 is the optimized position of the desired position of the output shaft of the linear motor, x r2 is the optimized speed of the desired speed of the output shaft of the linear motor; f() is a smooth unknown nonlinear function representing the unknown nonlinearity of the linear motor; is the estimate of the smooth unknown nonlinear function f(); v * is the optimal value of the control input v of the linear motor, is the optimal value v of the control input of the linear motor * The estimated value of *T Φ * () is the optimal recurrent neural network, is the estimate of the optimal recurrent neural network, Φ * () is the optimal parameter vector of the hidden layer output vector Φ() of the recurrent neural network obtained by inputting the actual trajectory x of the output shaft of the linear motor into the recurrent neural network, is the optimal parameter vector Φ * () estimation vector; δ * , α * and β * are the optimal values ​​of the width δ, center α of the Gaussian basis function of the recurrent neural network and the cyclic weight β of the recurrent neural network, respectively. and are the width and center of the Gaussian basis function of the recurrent neural network and the optimal value of the recurrent weight of the recurrent neural network δ * , α * and β * The estimated value of; Δ is the smooth unknown nonlinear function f() and the optimal recurrent neural network v *T Φ * () approximate error; u is the input of the linear motor; u a is the neural equivalent compensation control term, u s is the robust control feedback term of the linear motor input; M is the load mass of the linear motor; is the optimized acceleration of the desired acceleration of the output shaft of the linear motor; s1 is the nominal system stability term, u s2 is the uncertainty attenuation term; k s1 and k s2 are the first control gain and the second control gain of the inner loop adaptive neural synovial controller respectively; s is the synovial surface of the inner loop adaptive neural synovial controller, e is the actual position x1 and the optimized position x1 of the output shaft of the linear motor r1 The position tracking error between 1r , The actual speed x2 and the optimized speed x of the output shaft of the linear motor r2 The position tracking error between c1 is the positive constant parameter of the inner loop adaptive neural synovial membrane controller; sat(s) is the saturation function of the synovial surface s in the inner loop adaptive neural synovial controller, as follows: The inner loop system satisfies the following constraints: a) State constraints: x 1min ≤x1≤x 1max x 2min ≤x2≤x 2max Among them, x 1max and x 1min are the upper and lower boundaries of the actual position x1 of the output shaft of the linear motor; 2max and x 2min They are the upper and lower limits of the actual speed of the output shaft of the linear motor respectively; b) Input constraints: |in|≤in max Among them, u max is the maximum control input of the linear motor; The first control gain k of the inner loop adaptive neural synovial controller is s1 and the second control gain k s2 The following constraints are met: k s2 ≥K+d+ρ Where k is the first control gain k s1 The positive constant parameter, ρ is the second control gain k s2 A positive constant parameter of ; In step 1, the outer loop system includes a state observer and an optimization target model, which are as follows: a) State Observer: u1=u a1 +u s |u1|=|u a1 +u s |≤|u a1 |+|u s |≤u amax +u smax ≤|u max | in, is the observed value of the actual position x1 of the output shaft of the linear motor, that is, the observed position; and is the observed value of the actual speed x2 of the output shaft of the linear motor, i.e., the observed speed; is the observed value of the actual acceleration of the output shaft of the linear motor, that is, the observed acceleration; u1 is the optimized input of the linear motor; z1 is the actual position x1 of the output shaft of the linear motor and the observed position The observation error, and z2 are the actual speed x2 and the observed speed of the output shaft of the linear motor The observation error, The actual speed x2 of the output shaft of the linear motor and the observed speed The first derivative of the observation error; u smax is the robust control feedback term u s The maximum value of u amax is the equivalent compensation term u a1 The maximum value of the equivalent compensation term u a1 The maximum value of the neural equivalent compensation control term u a The maximum value of is the same; γ is the positive constant parameter of the optimized input u1 of the linear motor; χ is the estimated error between the smooth unknown nonlinear function of the linear motor and its estimation, that is, the difference between the two; The equivalent compensation term u is obtained through the state observer a1 The maximum value u amax , constrained equivalent compensation term u a1 ; b) Optimize the target model for each sampling period of the linear motor as follows: x 1min ≤x r1 ≤x 1max x 2min ≤x r2 ≤x 2max x r1 (t0)=x1(t0) x r2 (t0)=x2(t0) Among them, t0 is the initial time of the sampling period, τ is the prediction time domain; x d is the desired trajectory of the linear motor; Q is the optimized trajectory x of the output shaft of the linear motor r and the expected trajectory x d The weighted matrix norm of the difference between a1 The weighted matrix norm of ; is the optimized speed of the desired speed of the output shaft of the linear motor, u a1 is an equivalent compensation term, specifically, the neural equivalent compensation control term u a It is approximated as the neural equivalent compensation control term without the unknown disturbance d of the linear motor, that is, the equivalent compensation term u is obtained a1 ;x r1 (t0) is the optimized position of the linear motor at time t0, and x1(t0) is the actual position of the linear motor at time t0; r2 (t0) is the optimized speed of the linear motor at time t0, and x2(t0) is the actual speed of the linear motor at time t0; in, is the state constraint of the outer loop system, |u a1 |≤|u amax | is the input constraint of the outer loop system; In the step 2, the actual position and actual speed of the output shaft of the current linear motor are obtained, specifically, the output shaft of the linear motor is measured by a position and speed sensor preset inside the linear motor to obtain the actual position and actual speed of the output shaft of the linear motor; In step 2, the actual position x1 and actual speed x2 of the output shaft of the current linear motor are input into the inner loop system, specifically, input into the inner loop adaptive neural synovial membrane controller, and the neural equivalent compensation control item u is obtained in the inner loop adaptive neural synovial membrane controller. a , and then through the neural equivalent compensation control term u a Get equivalent compensation u a1 And output; The inner loop system will compensate the equivalent term u a1 Input the outer loop system, and at the same time, the actual position x1 and actual speed x2 of the output shaft of the linear motor and the expected trajectory x2 of the output shaft of the linear motor are input. d Input the outer loop system, specifically input the actual position x1 and actual speed x2 of the output shaft of the linear motor into the state observer, and output the equivalent compensation term u through the state observer a1 The maximum value u amax For equivalent compensation item u a1 Constraints are made; the equivalent compensation term u a1 and the desired trajectory x of the linear motor d Input the optimization target model and use the model prediction method to output the optimized trajectory x of the desired trajectory of the output shaft of the linear motor r and the optimized equivalent compensation term; In step 3, the outer loop system optimizes the equivalent compensation term after optimization and the optimized trajectory x of the desired trajectory of the output shaft of the linear motor. r The optimized equivalent compensation term and the optimized trajectory x of the desired trajectory of the output shaft of the linear motor are input into the inner loop system through the interpolator. r The sampling rate is converted to the same as the sampling rate of the inner loop system through the interpolator and then output to the inner loop adaptive neural synovial membrane controller in the inner loop system. The inner loop adaptive neural synovial membrane controller outputs the input u of the linear motor in real time to achieve constrained optimization control of the desired trajectory of the output shaft of the linear motor.

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