CN115128951A - Double-loop high-performance control method based on expected track limited optimization - Google Patents
Double-loop high-performance control method based on expected track limited optimization Download PDFInfo
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Abstract
The invention discloses a double-loop high-performance control method based on expected track limited optimization. The method comprises the following steps: establishing a double-ring system of the linear motor; inputting the actual position and the actual speed of an output shaft of the linear motor into an inner ring system, outputting an equivalent compensation term, inputting the actual position and the actual speed of the output shaft of the linear motor and a preset expected track of the output shaft of the linear motor into an outer ring system, and outputting an optimized equivalent compensation term and an optimized track of the expected track of the output shaft of the linear motor; the linear motor is input into the inner ring system through the interpolator, and the inner ring system outputs the input of the linear motor in real time, so that the limited optimization control of the linear motor is realized. According to the invention, through designing the control structures of the inner ring and the outer ring, the linear motor system is ensured to not only obey the state and the input constraint, but also have quick transient response performance and high steady-state tracking precision under the condition of parameter uncertainty and external interference.
Description
Technical Field
The invention relates to a double-ring high-performance control method, in particular to a double-ring high-performance control method based on expected track limited optimization.
Background
As the demand for industrial applications increases, the need for high speed and high precision motion tracking control becomes more stringent, however most practical systems are constrained by state and input, which adds difficulty to the controller design. Model uncertain parts often exist in an actual system, and if the influence of the uncertain parts on the system is ignored to design a controller, the motion performance of the system can be deteriorated, and even the system can not run stably. In addition, most practical systems are subject to state and input constraints such as limited workspace, operating speed, actuator performance, etc. If the system does not comply with these constraints, problems such as reduced control accuracy, system instability, etc. may also occur. In the existing control algorithm, the control strategies for solving the parameter uncertainty and the external interference are as follows: self-adaptive control, Smith prediction control, disturbance observer control and neural network control; the method for processing system state and input constraints is as follows: barrier Lyapunov function, nonlinear mapping, prediction performance control and optimization control. However, to date, there is no feasible method for a system to comply with not only state and input constraints but also fast transient response performance and high steady-state tracking accuracy in the presence of parameter uncertainty and external interference.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides a double-loop high-performance control method based on expected track limited optimization. The method is based on the inner-ring self-adaptive neural synovial controller, the linear motor system is guaranteed to have strong robustness, the outer-ring system based on the prediction model control works at a low sampling rate, the calculation complexity is effectively reduced, meanwhile, the outer-ring system conducts re-optimization on the expected track according to the state and the input constraint to obtain an optimized track which complies with the constraint and transmits the optimized track to the inner-ring system, and the system is guaranteed to comply with the constraint. The interpolator between the inner and outer rings ensures that the results input to the inner ring by the outer ring have the same sampling rate as the inner ring. Meanwhile, the outer ring adopts a neural equivalent compensation term in the inner ring controller as a prediction model, so that the conservation is effectively reduced. The method can ensure that the linear motor system can not only obey state and input constraint but also have quick transient response performance and high steady-state tracking accuracy under the condition of parameter uncertainty and external interference.
The technical scheme adopted by the invention is as follows:
the double-ring high-performance control method comprises the following steps:
And 3, inputting the optimized equivalent compensation item and the optimized track of the expected track of the output shaft of the linear motor into the inner ring system by the outer ring system through an interpolator, outputting the input of the linear motor by the inner ring system in real time to realize the limited optimization control of the linear motor, outputting the updated value of the optimized equivalent compensation item by the inner ring system to replace the equivalent compensation item before optimization in the step 2, inputting the equivalent compensation item into the outer ring system, and circulating the next step to realize closed-loop control.
The inner ring system inputs the input of the linear motor into the linear motor system again through the saturation effect of the saturator, the linear motor system controls the position and the speed according to the input of the linear motor, outputs the actual position and the actual speed of the output shaft of the linear motor after control, and inputs the actual position and the actual speed of the output shaft of the linear motor into the double-ring system as the actual position and the actual speed of the output shaft of the linear motor at present to carry out next circulation, so that closed-loop control is realized.
The method comprises the following steps of optimizing the expected trajectory of an output shaft of the linear motor by an outer ring system under the condition that the linear motor has state and input constraints to obtain the optimized trajectory meeting the state and the input constraints, and controlling the position and the speed of the output shaft of the linear motor by a controller designed by an inner ring system, so that the expected trajectory of the output shaft of the linear motor can be tracked as fast as possible on the premise that the actual position and the actual speed of the output shaft of the controlled linear motor meet the state and the input constraints, and the optimized control of the trajectory of the output shaft of the linear motor is realized.
The saturation performance of the linear motor actuator can be regarded as that the designed input result is actually input into the linear motor system after the saturation effect of the saturator, so that the designed input and the actual input may have deviation, and the linear motor system has the phenomena of poor control performance, even instability and the like.
In the step 1, the inner ring system is an adaptive neural synovial membrane controller, and specifically comprises the following steps:
f(x r1 ,x r2 )＝v *T Φ * (x r ,δ * ,α * ,β * )+Δ
u＝u a +u s
u s ＝u s1 +u s2
u s1 ＝-k s1 s
u s2 ＝-k s2 sat(s)
wherein x is r Optimized for the desired trajectory of the output shaft of the linear motor, x r ＝[x r1 ,x r2 ] T ，x r1 For optimum position of desired position of output shaft of linear motor, x r2 An optimized speed for a desired speed of an output shaft of the linear motor; f () is a smooth unknown nonlinear function representing the unknown nonlinearity of the linear motor;
an estimate that is a smooth unknown nonlinear function f (); v. of * For an optimized value of the control input v of the linear motor,
optimized value v for the control input of a linear motor * An estimated value of (d); v. of *T Φ * () In order to optimize the recurrent neural network,
for estimation of the optimal recurrent neural network, phi * () In order to obtain the optimal parameter vector of the hidden layer output vector phi () of the recurrent neural network after inputting the actual track x of the output shaft of the linear motor into the recurrent neural network,
for the optimal parameter vector phi * () The estimated vector of (2); delta. for the preparation of a coating * 、α * And beta * Respectively are the optimal values of the width delta and the center alpha of the Gaussian function of the recurrent neural network and the recurrent weight beta of the recurrent neural network,
and
the width and the center of the Gaussian function of the recurrent neural network and the optimal value delta of the recurrent weight of the recurrent neural network * 、α * And beta * An estimated value of (d); delta is a smooth unknown nonlinear function f () and an optimal recurrent neural network v *T Φ * () The approximation error therebetween; u is the input of the linear motor; u. of a For neuroequivalent compensation of the input of a linear motor control term u s A robust control feedback term that is an input to the linear motor; m is the load mass of the linear motor;
an optimized acceleration for a desired acceleration of an output shaft of the linear motor; u. of s1 Is a nominal system stability term, u s2 Is an uncertainty attenuation term; k is a radical of s1 And k s2 A first control gain and a second control gain of the inner loop adaptive neural synovial controller respectively; s is the synovial surface of the inner ring self-adaptive neural synovial controller,
e is the actual position x of the output shaft of the linear motor 1 And an optimum position x r1 Position tracking error of (e) x 1 -x 1r ，
Is the actual speed x of the output shaft of the linear motor 2 And optimizing the speed x r2 The position tracking error between the two or more position tracking errors,
c 1 the inner loop is adapted with the positive constant parameter to be designed for the neural synovial controller.
sat(s) is a saturation function for synovial surface s in the inner-loop adaptive neural synovial controller, specifically as follows:
neuroequivalent compensation control term u a For estimating dynamic system models
Robust control feedback term u s The method is used for eliminating the influence of the estimation error x and the unknown interference d of the linear motor.
The inner ring system satisfies the following constraints:
a) and (3) state constraint:
x 1min ≤x 1 ≤x 1max
x 2min ≤x 2 ≤x 2max
wherein x is 1max And x 1min Respectively the actual position x of the output shaft of the linear motor 1 The upper and lower boundaries of (c); x is the number of 2max And x 2min Respectively, the upper and lower boundaries of the actual speed of the output shaft of the linear motor.
b) Inputting a constraint:
|u|≤u max
wherein u is max Is the maximum control input of the linear motor.
Before establishing the inner ring system and the outer ring system, a state space model of the linear motor considering state constraint and input constraint needs to be established, which specifically comprises the following steps:
wherein d is unknown interference of the linear motor, including uncertain nonlinearity and external interference.
Smooth unknown non-linear function f (x) 1 ,x 2 ) The method comprises the following steps:
f(x 1 ,x 2 )＝-Bx 2 -AS(x 2 )
wherein B is the coefficient of viscous friction, Bx 2 The viscous friction force is applied to the output shaft of the linear motor; a Coulomb coefficient of friction, S (x) 2 ) About the output shaft of the linear motorActual speed x 2 Is a smooth function, AS (x) 2 ) Is the coulomb friction force applied to the output shaft of the linear motor.
The linear motor system is as follows:
by defining state variables
And converting the linear motor system into a state space model.
Smooth unknown non-linear function f (x) 1 ,x 2 ) Describing the uncertainty of the parameters in the state space model; the uncertain nonlinearity of the unknown disturbance d of the linear motor comprises the external influence of the linear motor and the modeling error when a linear motor system is converted into a state space model.
The inner ring self-adaptive neural synovium controller has a first control gain k s1 And a second control gain k s2 The following constraints are satisfied:
k s2 ≥K+d+ρ
where k is the first control gain k s1 P is the second control gain k s2 Sufficiently small positive constant parameter.
In the step 1, the outer loop system includes a state observer and an optimization target model, which are specifically as follows:
a) a state observer:
u 1 ＝u a1 +u s
|u 1 |＝|u a1 +u s |≤|u a1 |+|u s |≤u amax +u smax ≤|u max |
wherein the content of the first and second substances,
is the actual position x of the output shaft of the linear motor 1 The observed value of (a), i.e. the observed position;
and
is the actual speed x of the output shaft of the linear motor 2 The observed value of (a), namely the observation speed;
the actual acceleration of the output shaft of the linear motor is observed, namely the observed acceleration; u. of 1 Inputting the optimized linear motor; z is a radical of 1 Is the actual position x of the output shaft of the linear motor 1 And observation position
The error of the observation of (2) is,
and z 2 Is the actual speed x of the output shaft of the linear motor 2 And the observed speed
The error of observation of (2) is,
is the actual speed x of the output shaft of the linear motor 2 And the observed speed
The first derivative of the observation error of (1); u. of smax Controlling a feedback term u for robustness s Maximum value of (d); u. of amax Is an equivalent compensation term u a1 Maximum value of (d), equivalent compensation term u a1 Maximum value of (c) and a neuroequivalent compensation control term u a The maximum values of (a) are the same; gamma is the optimized input u of the linear motor 1 Sufficiently small positive constant parameter; χ is the estimation error between the smooth unknown nonlinear function of the linear motor and its estimation, i.e. the difference between them.
Obtaining an equivalent compensation term u by a state observer a1 Maximum value u of amax So that the feedback term u is robustly controlled s Maximum value u of smax And an equivalent compensation term u a1 Maximum value u of amax Can reasonably distribute and constrain equivalent compensation terms u a1 。
It can be seen that
By estimating a smooth unknown non-linear function f (x) 1 ,x 2 ) Is estimated by
And the unknown disturbance d of the linear motor, and a robust control feedback term u s The effect of (1) is to eliminate the influence of the two on the linear motor.
b) Optimizing an objective model, specifically for each sampling period of the linear motor as follows:
x 1 min ≤x r1 ≤x 1 max
x 2 min ≤x r2 ≤x 2 max
x r1 (t 0 )＝x 1 (t 0 )
x r2 (t 0 )＝x 2 (t 0 )
wherein, t 0 Is the initial time of the sampling period, tau is the prediction time domain; x is the number of d Is the expected track of the linear motor; q is the optimized track x of the output shaft of the linear motor r And a desired trajectory x d A weighted matrix norm of the difference between; r is an equivalent compensation term u a1 The weighted matrix norm of (a);
optimized speed for the desired speed of the output shaft of the linear motor u a1 For the equivalent compensation term, in particular by compensating the neuroequivalent of the control term u a Approximating a neuroequivalent compensation control term that does not contain the unknown disturbance d of the linear motor, i.e. obtaining an equivalent compensation term u a1 ；x r1 (t 0 ) Is t 0 Optimum position of the linear motor at time, x 1 (t 0 ) Is t 0 Time linear electricityThe actual position of the machine; x is the number of r2 (t 0 ) Is t 0 Optimized speed, x, of a linear motor at a time 2 (t 0 ) Is t 0 The actual speed of the linear motor at that time.
The optimization problem of the outer ring system based on the optimization target model is a nonlinear model prediction problem, and can be solved by using a ParNMPC toolkit in Matlab to obtain the optimized track x of the linear motor r And an equivalent compensation term u a1 And inputs the result into the inner loop system. The optimization objective model can enable the whole system to have fast transient capability and high steady-state accuracy.
Wherein the content of the first and second substances,
for the state constraint of the outer loop system, | u a1 |≤|u amax And | is the input constraint of the outer loop system.
In the step 2, the current actual position and the actual speed of the output shaft of the linear motor are obtained, specifically, the actual position and the actual speed of the output shaft of the linear motor are obtained by measuring the output shaft of the linear motor through a position and speed sensor preset in the linear motor.
In the step 2, the current actual position x of the output shaft of the linear motor is determined 1 And the actual speed x 2 Inputting into an inner ring system, specifically inputting into an inner ring adaptive neural synovium controller, and obtaining an updated neural equivalent compensation control item u from the inner ring adaptive neural synovium controller a And then compensating the control term u through the neural equivalence a Obtaining an equivalent compensation term u a1 And outputting;
the inner loop system will be equivalent to the compensation term u a1 Inputting the actual position x of the output shaft of the linear motor into an outer ring system 1 And the actual speed x 2 And a preset expected trajectory x of the output shaft of the linear motor d Inputting an outer ring system, in particular the actual position x of the output shaft of the linear motor 1 And actual speed x 2 Inputting into a state observer, outputting equivalent compensation terms by the state observeru a1 Maximum value u of amax To equivalent compensation term u a1 Carrying out constraint; will be equivalent to the compensation term u a1 And the desired trajectory x of the linear motor d Inputting the optimized target model, and outputting an optimized locus x of an expected locus of an output shaft of the linear motor by using a model prediction method r And an optimized equivalent compensation term.
In step 3, the outer ring system optimizes the equivalent compensation term and the optimized track x of the expected track of the output shaft of the linear motor r Inputting the equivalent compensation term and the optimized track x of the expected track of the output shaft of the linear motor into the inner ring system through an interpolator r The sampling rate is changed to be the same as that of the inner ring system through the interpolator and then is output to the inner ring adaptive neural synovial controller in the inner ring system, the inner ring adaptive neural synovial controller outputs the input u of the linear motor in real time, and the limited optimization control of the expected track of the output shaft of the linear motor is realized.
Because the optimization problem of the outer ring system has strong computational complexity and can only work under a low sampling rate, and the inner ring system needs to work under a high sampling rate to ensure that the whole system has strong robustness, the inner ring system and the outer ring system have different sampling rates, and an interpolator between the inner ring system and the outer ring system ensures that the optimization result input into the inner ring system by the outer ring system has the same sampling rate as the inner ring system.
The invention has the beneficial effects that:
1. the double-ring high-performance control method provided by the invention can simultaneously ensure that a controlled linear motor system meets the constraint and has quick transient response performance and high steady-state tracking precision.
2. The conservative property is effectively reduced by using a method of converting the neural equivalent compensation term in the inner loop controller into a prediction model in the outer loop optimizer.
3. The inner ring and the outer ring adopt different sampling rates, and the calculation complexity is effectively reduced on the premise of ensuring that the controlled system has strong robustness and stability.
Drawings
FIG. 1 is a control flow diagram of the present invention;
FIG. 2 is a schematic diagram of the position tracking trajectory of the present invention;
FIG. 3 is a schematic diagram of a position tracking error transient of the present invention;
FIG. 4 is a steady state diagram of the position tracking error of the present invention;
FIG. 5 is a schematic diagram of the velocity tracking trajectory of the present invention;
FIG. 6 is a schematic diagram of control signals according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
As shown in fig. 1, the dual-loop high-performance control method of the present invention includes the following steps:
In step 1, the inner ring system is an adaptive neural synovial membrane controller, which comprises the following specific steps:
f(x r1 ,x r2 )＝v *T Φ * (x r ,δ * ,α * ,β * )+Δ
u＝u a +u s
u s ＝u s1 +u s2
u s1 ＝-k s1 s
u s2 ＝-k s2 sat(s)
wherein x is r Optimized for the desired trajectory of the output shaft of the linear motor, x r ＝[x r1 ,x r2 ] T ，x r1 Is the advantage of the expected position of the output shaft of the linear motorPosition of change, x r2 An optimized speed for a desired speed of an output shaft of the linear motor; f () is a smooth unknown nonlinear function representing the unknown nonlinearity of the linear motor;
estimation of an unknown nonlinear function f () which is smooth; v. of * For an optimized value of the control input v of the linear motor,
optimized value v for the control input of a linear motor * An estimated value of (d); v. of *T Φ * () In order to optimize the recurrent neural network,
for estimation of the optimal recurrent neural network, phi * () In order to obtain the optimal parameter vector of the hidden layer output vector phi () of the recurrent neural network after inputting the actual track x of the output shaft of the linear motor into the recurrent neural network,
for the optimal parameter vector phi * () The estimated vector of (2); delta * 、α * And beta * Respectively are the optimal values of the width delta and the center alpha of the Gaussian function of the recurrent neural network and the recurrent weight beta of the recurrent neural network,
and
the width and the center of the Gaussian function of the recurrent neural network and the optimal value delta of the recurrent weight of the recurrent neural network * 、α * And beta * An estimated value of (d); delta is a smooth unknown nonlinear function f () and an optimal recurrent neural network v *T Φ * () The approximation error therebetween; u is the input of the linear motor; u. of a For neuroequivalent compensation of the input of a linear motor control term u s Is a linear electricityA robust control feedback term for the input to the machine; m is the load mass of the linear motor;
an optimized acceleration for a desired acceleration of an output shaft of the linear motor; u. u s1 Is a nominal system stability term, u s2 Is an uncertainty attenuation term; k is a radical of s1 And k s2 A first control gain and a second control gain of the inner loop adaptive neural synovial controller respectively; s is the synovial surface of the inner-ring adaptive neural synovial controller,
e is the actual position x of the output shaft of the linear motor 1 And an optimum position x r1 Position tracking error between, e ═ x 1 -x 1r ，
Is the actual speed x of the output shaft of the linear motor 2 And optimizing the speed x r2 The position tracking error between the two or more position tracking errors,
c 1 the inner loop is adapted with the positive constant parameter to be designed for the neural synovial controller.
sat(s) is a saturation function for synovial surface s in the inner-loop adaptive neural synovial controller, specifically as follows:
neuroequivalent compensation control term u a For estimating dynamic system models
Robust control feedback term u s The method is used for eliminating the influence of the estimation error x and the unknown interference d of the linear motor.
The inner ring system satisfies the following constraints:
a) and (3) state constraint:
x 1 min ≤x 1 ≤x 1 max
x 2 min ≤x 2 ≤x 2 max
wherein x is 1 max And x 1 min Respectively the actual position x of the output shaft of the linear motor 1 The upper and lower boundaries of (c); x is the number of 2 max And x 2 min Respectively, the upper and lower boundaries of the actual speed of the output shaft of the linear motor.
b) Inputting constraints:
|u|≤u max
wherein u is max Is the maximum control input of the linear motor.
Before establishing the inner ring system and the outer ring system, a state space model of the linear motor considering state constraint and input constraint needs to be established, which specifically comprises the following steps:
wherein d is unknown interference of the linear motor, including uncertain nonlinearity and external interference.
Smooth unknown non-linear function f (x) 1 ,x 2 ) The method comprises the following steps:
f(x 1 ,x 2 )＝-Bx 2 -AS(x 2 )
wherein B is the coefficient of viscous friction, Bx 2 The viscous friction force is applied to the output shaft of the linear motor; a Coulomb coefficient of friction, S (x) 2 ) Is related to the actual speed x of the output shaft of the linear motor 2 Of, AS (x) 2 ) Is the coulomb friction force applied to the output shaft of the linear motor.
The linear motor system is specifically as follows:
by defining state variables
And converting the linear motor system into a state space model.
Smooth unknown non-linear function f (x) 1 ,x 2 ) Describing the uncertainty of the parameters in the state space model; the uncertain nonlinearity of the unknown disturbance d of the linear motor comprises the external influence of the linear motor and the modeling error when a linear motor system is converted into a state space model.
First control gain k of inner-loop adaptive neural synovial controller s1 And a second control gain k s2 The following constraints are satisfied:
k s2 ≥K+d+ρ
where k is the first control gain k s1 P is the second control gain k s2 Sufficiently small positive constant parameter.
In step 1, the outer loop system includes a state observer and an optimized target model, specifically as follows:
a) a state observer:
u 1 ＝u a1 +u s
|u 1 |＝|u a1 +u s |≤|u a1 |+|u s |≤u amax +u smax ≤|u max |
wherein the content of the first and second substances,
is the actual position x of the output shaft of the linear motor 1 The observed value of (a), i.e. the observed position;
and
is the actual speed x of the output shaft of the linear motor 2 The observed value of (a), namely the observation speed;
the actual acceleration of the output shaft of the linear motor is observed, namely the observed acceleration; u. of 1 Inputting the optimized linear motor; z is a radical of formula 1 Is the actual position x of the output shaft of the linear motor 1 And observation position
The error of observation of (2) is,
and z 2 Is the actual speed x of the output shaft of the linear motor 2 And the observed speed
Observation error of，
Is the actual speed x of the output shaft of the linear motor 2 And the observed speed
The first derivative of the observation error of (1); u. u smax Controlling a feedback term u for robustness s Maximum value of (d); u. of amax Is an equivalent compensation term u a1 Maximum value of (d), equivalent compensation term u a1 Maximum value of (d) and neuroequivalent compensation control term u a The maximum values of (a) are the same; gamma is the optimized input u of the linear motor 1 A sufficiently small positive constant parameter; χ is the estimation error between the smooth unknown nonlinear function of the linear motor and its estimation, i.e. the difference between them.
Obtaining an equivalent compensation term u by a state observer a1 Maximum value u of amax So that the robust control feedback term u s Maximum value u of smax And an equivalent compensation term u a1 Maximum value u of amax Can reasonably distribute and constrain equivalent compensation terms u a1 。
It can be seen that
By estimating a smooth unknown non-linear function f (x) 1 ,x 2 ) Is estimated by
And the unknown disturbance d of the linear motor, and a robust control feedback term u s The effect of (1) is to eliminate the influence of the two on the linear motor.
b) Optimizing an objective model, specifically for each sampling period of the linear motor as follows:
x 1 min ≤x r1 ≤x 1 max
x 2 min ≤x r2 ≤x 2 max
x r1 (t 0 )＝x 1 (t 0 )
x r2 (t 0 )＝x 2 (t 0 )
wherein, t 0 Is the initial time of the sampling period, tau is the prediction time domain; x is the number of d Is the expected track of the linear motor; q is the optimized track x of the output shaft of the linear motor r And a desired trajectory x d A weighted matrix norm of the difference between; r is an equivalent compensation term u a1 The weighted matrix norm of (a);
optimized speed for the desired speed of the output shaft of the linear motor u a1 For the equivalent compensation term, in particular by compensating the neuroequivalent of the control term u a Approximating a neuroequivalent compensation control term that does not contain the unknown disturbance d of the linear motor, i.e. obtaining an equivalent compensation term u a1 ；x r1 (t 0 ) Is t 0 Optimum position of the linear motor at time, x 1 (t 0 ) Is t 0 The actual position of the linear motor at the moment; x is the number of r2 (t 0 ) Is t 0 Optimized speed, x, of a linear motor at a time 2 (t 0 ) Is t 0 The actual speed of the linear motor at that time.
The optimization problem of the outer loop system based on the optimization target model is a nonlinear model prediction problemThe optimized trajectory x of the linear motor can be obtained by solving with a ParNMPC toolkit in Matlab r And an equivalent compensation term, and inputs the result into the inner loop system.
The optimization objective model can enable the whole system to have fast transient capability and high steady-state accuracy.
Wherein the content of the first and second substances,
for the state constraint of the outer loop system, | u a1 |≤|u amax And | is the input constraint of the outer loop system.
In step 2, the current actual position and actual speed of the output shaft of the linear motor are obtained, specifically, the actual position and actual speed of the output shaft of the linear motor are obtained by measuring the output shaft of the linear motor through a position and speed sensor preset in the linear motor.
In step 2, the current actual position x of the output shaft of the linear motor is calculated 1 And the actual speed x 2 Inputting the data into an inner ring system, specifically inputting the data into an inner ring adaptive neural synovium controller, and obtaining an updated neural equivalent compensation control item u from the inner ring adaptive neural synovium controller a And then compensating the control term u through the neural equivalence a Obtaining an equivalent compensation term u a1 And output.
The inner loop system will be equivalent to the compensation term u a1 Inputting the actual position x of the output shaft of the linear motor into an outer ring system 1 And the actual speed x 2 And presetDesired trajectory x of the output shaft of the linear motor d Inputting an outer ring system, in particular the actual position x of the output shaft of the linear motor 1 And the actual speed x 2 Inputting into a state observer, outputting equivalent compensation term u through the state observer a1 Maximum value u of amax To equivalent compensation term u a1 Carrying out constraint; will be equivalent to the compensation term u a1 And the desired trajectory x of the linear motor d Inputting the optimized target model, and outputting an optimized locus x of an expected locus of an output shaft of the linear motor by using a model prediction method r And an optimized equivalent compensation term.
And 3, inputting the optimized equivalent compensation item and the optimized track of the expected track of the output shaft of the linear motor into the inner ring system by the outer ring system through an interpolator, outputting the input of the linear motor by the inner ring system in real time to realize the limited optimization control of the linear motor, outputting the updated value of the optimized equivalent compensation item by the inner ring system to replace the equivalent compensation item before optimization in the step 2, inputting the equivalent compensation item into the outer ring system, and circulating the next step to realize the closed-loop control.
The inner ring system inputs the input of the linear motor into the linear motor system again through the saturation effect of the saturator, the linear motor system controls the position and the speed according to the input of the linear motor, outputs the actual position and the actual speed of the output shaft of the linear motor after control, and inputs the actual position and the actual speed of the output shaft of the linear motor into the double-ring system as the actual position and the actual speed of the output shaft of the linear motor at present to carry out next circulation, so that closed-loop control is realized.
The method comprises the following steps of optimizing the expected trajectory of an output shaft of the linear motor by an outer ring system under the condition that the linear motor has state and input constraints to obtain the optimized trajectory meeting the state and the input constraints, and controlling the position and the speed of the output shaft of the linear motor by a controller designed by an inner ring system, so that the expected trajectory of the output shaft of the linear motor can be tracked as fast as possible on the premise that the actual position and the actual speed of the output shaft of the controlled linear motor meet the state and the input constraints, and the optimized control of the trajectory of the output shaft of the linear motor is realized.
The saturation performance of the linear motor actuator can be regarded as that the designed input result is actually input into the linear motor system after the saturation effect of the saturator, so that the designed input and the actual input may have deviation, and the linear motor system has the phenomena of poor control performance, even instability and the like.
In step 3, the outer ring system optimizes the equivalent compensation term and the optimized track x of the expected track of the output shaft of the linear motor r Inputting the equivalent compensation term and the optimized track x of the expected track of the output shaft of the linear motor into the inner ring system through an interpolator r The sampling rate is changed to be the same as that of the inner ring system through the interpolator and then is output to the inner ring adaptive neural synovial controller in the inner ring system, the inner ring adaptive neural synovial controller outputs the input u of the linear motor in real time, and the limited optimization control of the expected track of the output shaft of the linear motor is realized.
Because the optimization problem of the outer ring system has strong computational complexity and can only work under a low sampling rate, and the inner ring system needs to work under a high sampling rate to ensure that the whole system has strong robustness, the inner ring system and the outer ring system have different sampling rates, and the interpolator between the inner ring system and the outer ring system ensures that the optimization result input into the inner ring system by the outer ring system has the same sampling rate as the inner ring system.
In order to verify the effectiveness and superiority of the method, the following control methods are simulated and compared, and the specific embodiments are as follows:
m1: PID-based Reference governor (Reference regulator), the design control rate is as follows:
wherein u (t) is the input of the linear motor at time t, K p Is the first controlSystem parameter, K i Is a second control parameter; x (t) is the position of the output shaft of the linear motor at the time t, and v (t) is the preset control input quantity of the linear motor at the time t; k d Is a third control parameter;
is the speed of the output shaft of the linear motor at time t,
the first derivative of the preset control input of the linear motor at time t.
The preset control input quantity v (t) of the linear motor at the time t is obtained by the following optimization problem:
s.t.v(t)＝v(t-1)+κ(x 1d (t)-v(t-1))
wherein, kappa is an optimization parameter, and kappa (t) is the maximum value of the optimization parameter kappa at the moment t; v (t-1) is the preset control input quantity of the linear motor at the time of t-1; setting the control parameters as follows: k p ＝480,K i ＝3200,K d The sampling rate was 23.4 at 5 khz.
M2: the adaptive neural synovium control has the design control rate as follows:
u s ＝u a +u s1 +u s2
u s1 ＝-k s1 s
wherein
Is the desired acceleration of the linear motor; setting the control parameters as follows: k is a radical of s1 ＝5,
The sampling rate was 5 khz.
M3: the model prediction control method comprises the following steps of:
wherein, theta 1 ,θ 2 ,θ 3 ,θ 4 The predicted values of M, B, A and d are respectively, and the design control rate is as follows:
x 1 min ≤x 1 ≤x 1 max
x 2 min ≤x 2 ≤x 2 max
|u|≤|u max |
wherein the initial state of the linear motor is selected as x 1 (0)＝x 2 (0) 0, the parameter is selected as theta 1 ＝0.35,θ 2 ＝0.66,θ 3 ＝0.25,θ 4 The sampling rate is 1khz at 0.
M4: the double-loop high-performance control method based on expected track limited optimization provided by the invention is used at a control rateAs shown, the control parameters are set as follows: k is a radical of s1 ＝5,
The sampling rate of the inner loop system is 5khz, and the sampling rate of the outer loop system is 1 khz.
The parameters in the linear motor system are set as follows: m is 0.4, B is 0.6, a is 0.2,
the expected track, the initial state, the total state constraint and the total input constraint of the linear motor system in the simulation experiment are set as follows:
the expected trajectory:
initial state:
x 1 (0)＝x 2 (0)＝0
total state input and total input constraints:
u max ＝10
-0.43≤x 1 ≤0.43
-2.05≤x 2 ≤2.05
fig. 2 is a schematic diagram of a position tracking trajectory of a linear motor system under different control methods, fig. 3 and 4 are schematic diagrams of a transient state and a steady state of a position tracking error, respectively, fig. 5 is a schematic diagram of a speed tracking trajectory of the linear motor system under different control methods, and fig. 6 is a schematic diagram of control signals of different control methods.
As can be seen from fig. 3 and 5, the simple recurrent neural network control (M2) cannot handle the state constraint, and the convergence speed of the system is slow; the model predictive control (M3) can ensure that the state constraint is not violated, but does not have the capability of processing parameter uncertainty and external interference, so that the controlled system has poor steady-state error; the Reference governor (M1) based on PID, although able to guarantee that the state constraints are not violated and has better transient performance, is also unsatisfactory for steady state errors; and the double-loop high-performance control method (M4) based on the expected track limited optimization not only ensures that the system complies with the state constraint, but also has quick transient response performance and high steady-state tracking accuracy.
The above-mentioned contents are only technical ideas of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical ideas proposed by the present invention fall within the protection scope of the claims of the present invention.
Claims (7)
1. A double-loop high-performance control method based on expected track limited optimization is characterized by comprising the following steps:
step 1, establishing a double-ring system of the linear motor, wherein the double-ring system comprises an inner ring system, an interpolator and an outer ring system which are sequentially connected;
step 2, acquiring the actual position and the actual speed of the output shaft of the current linear motor, inputting the actual position and the actual speed of the output shaft of the current linear motor into an inner ring system, and outputting an equivalent compensation term by the inner ring system; the inner ring system inputs the equivalent compensation item into the outer ring system, and simultaneously inputs the actual position and the actual speed of the output shaft of the linear motor and the preset expected track of the output shaft of the linear motor into the outer ring system, and the outer ring system outputs the optimized equivalent compensation item and the optimized track of the expected track of the output shaft of the linear motor;
and 3, inputting the optimized equivalent compensation item and the optimized track of the expected track of the output shaft of the linear motor into the inner ring system by the outer ring system through the interpolator, and outputting the input of the linear motor by the inner ring system in real time to realize the limited optimized control of the linear motor.
2. The dual-loop high-performance control method based on the desired trajectory-limited optimization of claim 1, characterized in that:
in the step 1, the inner ring system is an adaptive neural synovial membrane controller, and specifically comprises the following steps:
f(x r1 ,x r2 )＝v *T Φ * (x r ,δ * ,α * ,β * )+Δ
u＝u a +u s
u s ＝u s1 +u s2
u s1 ＝-k s1 s
u s2 ＝-k s2 sat(s)
wherein x is r Optimized for the desired trajectory of the output shaft of the linear motor, x r ＝[x r1 ,x r2 ] T ，x r1 For optimum position of desired position of output shaft of linear motor, x r2 An optimized speed for a desired speed of an output shaft of the linear motor; f () is a smooth unknown nonlinear function representing the unknown nonlinearity of the linear motor;
an estimate that is a smooth unknown nonlinear function f (); v. of * For an optimized value of the control input v of the linear motor,
optimized value v for the control input of a linear motor * An estimated value of (d); v. of *T Φ * () In order to optimize the recurrent neural network,
for estimation of the optimal recurrent neural network, phi * () The hidden layer output direction of the recurrent neural network is obtained after the actual track x of the output shaft of the linear motor is input into the recurrent neural networkThe optimal parameter vector of the quantity phi (),
for the optimal parameter vector phi * () The estimated vector of (2); delta. for the preparation of a coating * 、α * And beta * Respectively are the optimal values of the width delta and the center alpha of the Gaussian function of the recurrent neural network and the recurrent weight beta of the recurrent neural network,
and
the width and the center of the Gaussian function of the recurrent neural network and the optimal value delta of the recurrent weight of the recurrent neural network * 、α * And beta * An estimated value of (d); delta is a smooth unknown nonlinear function f () and an optimal recurrent neural network v *T Φ * () The approximation error therebetween; u is the input of the linear motor; u. of a Compensating the control term for neuroequivalence u s A robust control feedback term that is an input to the linear motor; m is the load mass of the linear motor;
an optimized acceleration for a desired acceleration of an output shaft of the linear motor; u. of s1 Is a nominal system stability term, u s2 Is an uncertainty attenuation term; k is a radical of s1 And k s2 A first control gain and a second control gain of the inner loop adaptive neural synovial controller respectively; s is the synovial surface of the inner ring self-adaptive neural synovial controller,
e is the actual position x of the output shaft of the linear motor 1 And an optimum position x r1 Position tracking error between, e ═ x 1 -x 1r ，
Is the actual speed x of the output shaft of the linear motor 2 And optimizing the speed x r2 The position tracking error between the two sensors,
c 1 adapting the positive constant parameter of the neural synovial controller for the inner loop;
sat(s) is a saturation function for synovial surface s in the inner-loop adaptive neural synovial controller, specifically as follows:
the inner ring system satisfies the following constraints:
a) and (3) state constraint:
x 1min ≤x 1 ≤x 1max
x 2min ≤x 2 ≤x 2max
wherein x is 1max And x 1min Respectively the actual position x of the output shaft of the linear motor 1 The upper and lower boundaries of (c); x is a radical of a fluorine atom 2max And x 2min Upper and lower boundaries of the actual speed of the output shaft of the linear motor, respectively;
b) inputting constraints:
|u|≤u max
wherein u is max Is the maximum control input of the linear motor.
3. The dual-loop high-performance control method based on the desired trajectory limited optimization of claim 2, characterized in that:
the first control gain k of the inner-ring self-adaptive neural synovial controller s1 And a second control gain k s2 The following constraints are satisfied:
k s2 ≥K+d+ρ
where k is the first control gain k s1 P is the second control gain k s2 A positive constant parameter.
4. The dual-loop high-performance control method based on the desired trajectory-limited optimization of claim 1, characterized in that:
in the step 1, the outer loop system includes a state observer and an optimization target model, which are specifically as follows:
a) a state observer:
u 1 ＝u a1 +u s
|u 1 |＝|u a1 +u s |≤|u a1 |+|u s |≤u amax +u smax ≤|u max |
wherein the content of the first and second substances,
is the actual position x of the output shaft of the linear motor 1 The observed value of (a), i.e. the observed position;
and
is the actual speed x of the output shaft of the linear motor 2 The observed value of (a), namely the observation speed;
the actual acceleration of the output shaft of the linear motor is observed, namely the observed acceleration; u. of 1 Inputting the optimized linear motor; z is a radical of 1 Is the actual position x of the output shaft of the linear motor 1 And observation position
The error of observation of (2) is,
and z 2 Is the actual speed x of the output shaft of the linear motor 2 And the observed speed
The error of observation of (2) is,
is the actual speed x of the output shaft of the linear motor 2 And the observed speed
The first derivative of the observation error of (1); u. u smax Controlling a feedback term u for robustness s The maximum value of (a); u. of amax Is an equivalent compensation term u a1 Maximum value of (d), equivalent compensation term u a1 Maximum value of (d) and neuroequivalent compensation control term u a The maximum values of (a) are the same; gamma is the optimized input u of the linear motor 1 A positive constant parameter of; χ is a smooth unknown nonlinear function of the linear motor and an estimation error between estimation of the function, namely a difference value between the function and the estimation error;
obtaining an equivalent compensation term u by a state observer a1 Maximum value u of amax Constraining the equivalent compensation term u a1 ；
b) Optimizing an objective model, specifically for each sampling period of the linear motor as follows:
x 1min ≤x r1 ≤x 1max
x 2min ≤x r2 ≤x 2max
x r1 (t 0 )＝x 1 (t 0 )
x r2 (t 0 )＝x 2 (t 0 )
wherein, t 0 Is the initial time of the sampling period, tau is the prediction time domain; x is a radical of a fluorine atom d Is a straight lineA desired trajectory of the motor; q is the optimized track x of the output shaft of the linear motor r And a desired trajectory x d A weighted matrix norm of the difference between; r is an equivalent compensation term u a1 The weighted matrix norm of (a);
optimized speed, u, for the desired speed of the output shaft of the linear motor a1 For the equivalent compensation term, in particular by compensating the neuroequivalent of the control term u a Approximating a neuroequivalent compensation control term that does not contain the unknown disturbance d of the linear motor, i.e. obtaining an equivalent compensation term u a1 ；x r1 (t 0 ) Is t 0 Optimum position of the linear motor at time, x 1 (t 0 ) Is t 0 The actual position of the linear motor at the moment; x is the number of r2 (t 0 ) Is t 0 Optimized speed, x, of a linear motor at a time 2 (t 0 ) Is t 0 The actual speed of the linear motor at the moment;
wherein the content of the first and second substances,
for the state constraint of the outer loop system, | u a1 |≤|u amax And | is the input constraint of the outer loop system.
5. The dual-loop high-performance control method based on the desired trajectory-limited optimization of claim 1, characterized in that:
in the step 2, the current actual position and the actual speed of the output shaft of the linear motor are obtained, specifically, the actual position and the actual speed of the output shaft of the linear motor are obtained by measuring the output shaft of the linear motor through a position and speed sensor preset in the linear motor.
6. The dual-loop high-performance control method based on the desired trajectory-limited optimization of claim 1, characterized in that:
in the step 2, the current actual position of the output shaft of the linear motor is determinedx 1 And the actual speed x 2 Inputting the data into an inner ring system, particularly inputting the data into an inner ring adaptive neural synovium controller, and obtaining a neural equivalent compensation control item u from the inner ring adaptive neural synovium controller a And then compensating the control term u through the neural equivalence a Obtaining an equivalent compensation term u a1 And outputting;
the inner loop system will be equivalent to the compensation term u a1 Inputting the actual position x of the output shaft of the linear motor into an outer ring system 1 And the actual speed x 2 And a preset expected track x of the output shaft of the linear motor d Inputting an outer ring system, in particular the actual position x of the output shaft of the linear motor 1 And the actual speed x 2 Inputting into a state observer, outputting equivalent compensation term u by the state observer a1 Maximum value u of amax To equivalent compensation term u a1 Carrying out constraint; will be equivalent to the compensation term u a1 And the desired trajectory x of the linear motor d Inputting the optimized target model, and outputting an optimized locus x of an expected locus of an output shaft of the linear motor by using a model prediction method r And an optimized equivalent compensation term.
7. The dual-loop high-performance control method based on the desired trajectory-limited optimization of claim 1, characterized in that: in the step 3, the outer ring system optimizes the equivalent compensation term and the optimized track x of the expected track of the output shaft of the linear motor r Inputting the equivalent compensation term and the optimized track x of the expected track of the output shaft of the linear motor into the inner ring system through an interpolator r The sampling rate is changed to be the same as that of the inner ring system through the interpolator and then is output to the inner ring adaptive neural synovial controller in the inner ring system, the inner ring adaptive neural synovial controller outputs the input u of the linear motor in real time, and the limited optimization control of the expected track of the output shaft of the linear motor is realized.
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