CN115236974A - Composite anti-interference controller and control parameter optimization method thereof - Google Patents
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Abstract
The invention belongs to the technical field of electro-hydraulic servo control of airplane steering engines, and provides a composite anti-interference controller and a control parameter optimization method thereof, wherein the method comprises the following steps: performing Laplace transformation on the composite anti-interference controller to generate each transfer function of a frequency domain; generating a vector of parameters ρ = [ b, ω) to be optimized c ,ω o ,k f1 ,k f2 ]The system input-output relationship function of (1); defining an optimization index function; obtaining an output force signal y t (i) And a command force signal r t (i) Tracking error e of t (p) and a control input signal u t (p) determining a theoretical optimal solution of the parameter vector p to be optimized for the gradient value of the optimal parameter vector. Based on the design of a feedback controller in the composite disturbance rejection controller, the problem that the accurate model information of a controlled object is excessively depended on is solved, and meanwhile, the accuracy and the phase characteristics of the system are improved based on a feedforward controller.
Description
Technical Field
The invention relates to the technical field of electro-hydraulic servo control of airplane steering engines, in particular to a composite anti-interference controller and a control parameter optimization method thereof.
Background
The steering engine is an important driving component for controlling the control plane of the airplane and realizing the control of the flight attitude, and the control performance of the steering engine is an important determining factor for determining the flight performance, safety and reliability of the airplane. However, the performance of the steering engine of the airplane is verified through field physical tests, and a large amount of cost is needed. In order to solve the problem, an electro-hydraulic servo loading system of the airplane steering engine is generally constructed and adopted to simulate various force loads borne by the airplane in the actual flying process so as to reduce the testing cost, improve the reliability of the system and have great significance for improving the control precision of the electro-hydraulic servo system of the airplane steering engine.
An electro-hydraulic servo system of an airplane steering engine belongs to a typical nonlinear system, and the performance of model-based servo control such as a traditional PID controller is limited due to nonlinear characteristics, model uncertainty and different task working conditions in different loading task processes, so that the problems of poor stability, low control precision, slow response speed, poor tracking performance and the like are caused.
In order to solve the problem, the prior art enhances the adaptability and the servo performance of the system to different working conditions through the PID of a self-adaptive algorithm, a cluster algorithm and an intelligent algorithm and a composite control method thereof. Or introducing a robust control method such as an H infinity method to enhance the robustness of the electro-hydraulic loading system and solve the problem of uncertain model parameters.
However, the above studies require much model information, and still have a problem of strong model dependency.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a composite anti-interference controller and a control parameter optimization method thereof, and aims to solve the problem that the existing electro-hydraulic loading system has strong dependence on a model.
In a first aspect, the present invention provides a composite immunity controller, including:
comprises an extended state observer, a feedback controller, a disturbance compensator and a feedforward controller,
the extended state observer
Wherein, L = [ L = 1 ，l 2 ，l 3 ] T For expanding the observed gain of the state observer, the determination is made by means of equivalent bandwidth modulation
Wherein omega o Is the equivalent observation gain;
b 0 is the equivalent gain of the system; c = [ 10]；
The feedback controller and the disturbance compensator are
Wherein u is c As a feedback controller, u d Is an interference compensator; r is reference input, K = [ K ] 1 ，k 2 ]Determining K = [ K ] according to equivalent bandwidth adjustment method for control gain of composite disturbance rejection controller 1 ，k 2 ]＝[ω c 2 ，2ω c ]Wherein ω is c Is an equivalent control gain;
the feedforward controller
The overall control law of the composite disturbance rejection controller is
According to the technical scheme, the composite disturbance rejection controller provided by the invention solves the problem of excessive dependence on accurate model information of a controlled object based on the feedback controller, and improves the accuracy and phase characteristics of a system based on a feedforward controller.
In a second aspect, the present invention provides a method for optimizing control parameters, which is directed to the composite disturbance rejection controller of the first aspect, and includes:
performing Laplace transformation on the composite anti-interference controller to generate each transfer function of a frequency domain;
generating a vector of parameters ρ = [ b, ω) to be optimized c ，ω o ，k f1 ，k f2 ]The system input-output relationship function of (1);
defining an optimization index function;
obtaining an output force signal y t (i) And a command force signal r t (i) Tracking error e of t (p) and a control input signal u t (ρ) for the gradient value of the optimal parameter vector, determining a theoretical optimal solution of the parameter vector ρ to be optimized.
According to the technical scheme, the control parameter optimization method provided by the invention optimizes the considered control parameters through inputting and outputting test data, can automatically adapt to the task change of the environment, and has strong robustness.
Optionally, each transfer function of the frequency domain is
F(s)＝k f1 +k f2 s；
The generated system input-output relationship function is:
wherein reference is made to the input signal r t (rho) triggered control signal u t (i) Will make the system growInto a corresponding output signal y t (i) (ii) a Wherein i =0,1,2, \ 8230;, i max ，i max Representing the set maximum number of iterations.
Optionally, the optimization index function is
Wherein e is t (rho) represents the tracking error between the output force signal and the command force of the electro-hydraulic loading system, namely e t (ρ)＝y t (ρ)-r t N is the total number of samples considered and λ is a predetermined weighting parameter.
Optionally, the obtaining of tracking error e of output force signal and command force t (p) and a control input signal u t (ρ) the gradient for the optimal parameter vector is determined according to the following method comprising:
determining a gradient calculation relation according to the system input and output relation function; the gradient is calculated by the relation
The gradient values are determined according to the following tests:
test 1:
test 2:
test 3:
wherein, the reference signal r of experiment 1 1 Provided is a command force signal r t Reference signal r of experiment 2 2 Output force signal y for test 1 t 1 While the reference signal of test 3 is still set as the command force signal r t (ii) a And the system response data obtained in the three experiments were statistically independent of each other.
Alternatively, the test also needs to satisfy the following assumptions: interference signal d t Sum noise signal v t Is a weak stationary random variable signal with zero mean value, and perturbation signals including interference signals and noise signals in different experiments are independent of each other.
Optionally based on est [ w ] in test 1, test 2 and test 3 1 ]=0 and est [ w 2 ]Assumption of =0, based on estimation of the gradient under perturbation signals
And
available y t And u t Unbiased estimation of the parameter vector to be optimized is respectively
Optimizing an index function J n (p) a gradient estimate for the parameter vector p to be optimized of
Then the
In order to satisfy the optimization index function, determining the next generation updating formula of the parameter vector rho to be optimized based on the Gauss-Newton method as
Wherein the step value gamma is optimized i Determining an optimized step size for a positive real scalar; the value of the setting matrix is
Optionally, the method further comprises evaluating the optimization result, including:
if g (rho) is within a preset threshold range and g (rho) is less than or equal to psi, updating rho according to a next generation updating formula of the parameter vector to be optimized;
if g (rho) exceeds the preset threshold range, i.e. g (rho) > psi, let
Wherein alpha is a positive real constant, and then test updating is carried out again;
evaluating a function
Wherein y is t 3 (t f ，ρ i ) Indicates t in IFT test 3 f System output value at time, y c (t f ) Output response trajectory for a limited system expected empirically, beta 1 And beta 2 Is a very common and customizable number.
By adopting the technical scheme, the application has the following beneficial effects:
(1) The composite disturbance rejection controller provided by the invention solves the problem of excessive dependence on accurate model information of a controlled object based on the feedback controller, and improves the accuracy and phase characteristics of a system based on a feedforward controller.
(2) The control parameter optimization method provided by the invention optimizes the considered control parameters through inputting and outputting test data, can automatically adapt to the task change of the environment, and has strong robustness.
Drawings
In order to more clearly illustrate the detailed description of the invention or the technical solutions in the prior art, the drawings used in the detailed description or the prior art description will be briefly described below. Throughout the drawings, like elements or portions are generally identified by like reference numerals. In the drawings, elements or portions are not necessarily drawn to scale.
FIG. 1 shows a schematic diagram of an electro-hydraulic loading system for an aircraft steering engine provided by the invention;
FIG. 2 is a schematic diagram showing an overall model structure of an electro-hydraulic loading system of an aircraft steering engine provided by the invention;
FIG. 3 shows a composite control block diagram of an electro-hydraulic loading system of an aircraft steering engine provided by the invention;
FIG. 4 is an equivalent control block diagram of FIG. 3;
FIG. 5 is a flow chart illustrating a control parameter optimization method provided by an embodiment of the invention;
FIG. 6a shows a framework diagram of a system simulation AMEstim model;
FIG. 6b shows a framework diagram of a system simulation Simulink model;
FIG. 7a shows a system step response graph;
FIG. 7b shows J of the step response IFT of the system n A variation graph;
FIG. 7c shows a graph of the b-change of the system step response IFT;
FIG. 7d shows ω of the step response IFT of the system c A variation graph;
FIG. 7e shows ω of the step response IFT of the system o A variation graph;
FIG. 7f shows k for the step response IFT of the system f1 And k f2 A variation graph;
FIG. 8a shows a system tracking sinusoidal command force signal graph;
FIG. 8b illustrates J for a system tracking sinusoidal command force signal IFT provided by an embodiment of the present invention n A variation graph;
FIG. 8c shows a graph of the b variation of the system tracking sinusoidal command force signal IFT;
FIG. 8d shows the system tracking ω of the sinusoidal command force signal IFT c A variation graph;
FIG. 8e shows the system tracking ω of the sinusoidal command force signal IFT o A variation graph;
FIG. 8f shows k for the system tracking the sinusoidal command force signal IFT f1 And k f2 The graph is varied.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and therefore are only examples, and the protection scope of the present invention is not limited thereby.
It is to be noted that, unless otherwise specified, technical or scientific terms used herein shall have the ordinary meaning as understood by those skilled in the art to which the invention pertains.
The invention aims at an airplane steering engine electro-hydraulic loading system shown in figure 1, which comprises an electro-hydraulic servo valve, a valve control hydraulic cylinder, a buffer component, a force and displacement sensor, a computer control system and the like. In the work of the electro-hydraulic loading system, the controller is used as a control center, a reference input instruction signal is set, and a control instruction signal is sent out through the calculation of a control law. The control command is transmitted to the emptying hydraulic cylinder after being amplified by the electro-hydraulic servo valve so as to push the piston of the hydraulic cylinder to displace. In addition, the system is provided with a buffer component for system structure compensation. In order to measure the displacement and acting force of the piston between the valve-controlled hydraulic cylinder and the steering engine, a corresponding displacement sensor and a corresponding force sensor are deployed in the system. Finally, the sensor transmits the measurement information to the controller to form a closed loop of the control system.
The dynamic state of the electro-hydraulic servo valve in the working interval can be simplified and regarded as a first-order inertia link, and a transfer function model of the electro-hydraulic servo valve is obtained as follows:
wherein, X v Indicating displacement of the spool, U v Representing the input voltage, K, of an electrohydraulic servo valve v Indicating the gain, T, of the electrohydraulic servo valve sv Representing its time constant.
The electro-hydraulic servo valve has the function of controlling the flow of hydraulic oil in a cylinder through the displacement change of a valve core, and can present better linear characteristics in a working interval. Therefore, in the linear working range, the following linear equation of the loading valve can be established:
Q L ＝K q X v -K c P L (2)
wherein Q is L Indicating the inlet flow of the valve-controlled hydraulic cylinder, K q Indicating the slide valve flow gain, K c Indicating the slide valve flow-pressure coefficient, P L Representing the load pressure.
The continuous equation of the flow of the valve-controlled hydraulic cylinder can be further obtained as follows:
in the above formula, A p Denotes the piston area, V t Representing the total volume, beta, of the cylinder e The modulus of elasticity of the oil is shown,
represents the total leakage coefficient, and where C i Indicating the coefficient of leakage, C, in the cylinder e Indicating the outside leakage coefficient of the cylinder.
If the influences of nonlinear factors such as friction force between a piston and a cylinder and oil quality are assumed to be neglected, the following balance equation of output force and load force can be obtained:
in the above formula, m t Mass representing piston and load, B p Represents the effective viscous damping coefficient; k is a radical of formula t Representing the spring rate. F L Represents the output force of the damping member, which can be obtained by the following formula:
F L ＝k L (x p -x s ) (5)
wherein k is L Is an equivalent spring rate, x s Is the steering engine displacement.
The overall model structure of the available electro-hydraulic loading system is shown in fig. 2 by combining equations (1) to (5), and the overall dynamic transfer function model is as follows:
wherein, K ce ＝K e +C f The total pressure flow coefficient is indicated.
In the process of establishing the linear dynamic model, the influence of more nonlinear and uncertain factors is ignored. And because the uncertainty and the interference can seriously affect the operation stability and the performance of the electro-hydraulic loading system, a data-driven composite disturbance rejection controller which is not excessively dependent on a model and adapts to the environment and task change is designed.
Example 1
As shown in fig. 3, the present application provides a composite disturbance rejection controller, which includes a linear active disturbance rejection controller and a feedforward controller, wherein the linear active disturbance rejection controller is designed by using a linear active disturbance rejection method, which is advantageous in that it does not depend too much on the precision model information of the controlled object, and the feedforward controller is used to improve the precision and phase characteristics of the system.
In order to reduce the implementation difficulty of the controller, improve the operation rate of the controller and avoid unstable factors easily caused by excessive phases, the system equivalence is considered to be the integration of a second-order integral chain and uncertain interference. Therefore, a linear active disturbance rejection controller is designed, which comprises an extended state observer, a feedback controller and a disturbance compensator:
extended State Observer (ESO) design:
in the above formula, L = [ L = 1 ，l 2 ，l 3 ] T To expand the observed gain of the observer ESO, according to the equivalent bandwidth modulation method, let L = [ L ] here 1 ，l 2 ，l 3 ] T ＝[3ω o ，3ω o 2 ，ω o 3 ] T Wherein ω is o Is the equivalent observed gain. In the formula also comprises
C＝[1 0 0](ii) a Wherein, b 0 Is the equivalent gain of the system.
Designing a feedback controller and an interference compensator:
wherein u is c As a feedback controller, u d Is an interference compensator; r is the reference input of the system, K = [ K = 1 ，k 2 ]For the control gain of the active disturbance rejection controller, according to the equivalent bandwidth adjustment method, the control gain is here designed to be K = [ K ] 1 ，k 2 ]＝[ω c 2 ，2ω c ]Wherein ω is c Is an equivalent control gain.
The active disturbance rejection controller has the functions of estimating the uncertainty of the system and the multi-source disturbance received by the ESO, suppressing the disturbance by the feedback controller and the disturbance compensator, controlling the whole electro-hydraulic loading system and ensuring the closed-loop control performance of the system. On the basis, the feedforward controller is further designed in the composite disturbance rejection controller.
A feedforward controller:
in summary, the overall control law of the designed composite disturbance rejection controller is as follows:
for a linear model, ω can be chosen appropriately o And ω c The closed loop system is stabilized.
Example 2
Although the control law of the designed composite disturbance rejection controller does not depend on model information excessively, the difficulty of parameter setting and optimization of the controller is increased due to limited known model information, and the performance of the controller is seriously influenced. Therefore, a control parameter optimization method is designed, so that the setting of the control law parameters is carried out.
Firstly, laplace transformation is carried out on the composite feedback controller, so that the conversion of the control law from a time domain to a frequency domain is completed. The control block 3 may thus be changed to the form as shown in fig. 4.
Wherein, each transfer function in fig. 4 is:
F(s)＝k f1 +k f2 s (11)
let ρ = [ b, ω = c ，ω o ，k f1 ，k f2 ]For the parameter vector to be optimized, the transfer functions F(s), H(s) and C(s) of the above-mentioned controller can be written as F (ρ), H (ρ) and C (ρ). The system I/O relationship obtained from FIG. 4 is:
as can be seen from fig. 4 and equation (15), during IFT, a series of reference input signals r t (i) Where algebraic i =0,1,2, \ 8230;, i max ，i max Control input signal u, triggered representing the set maximum number of iterations t (i) Will cause the system to generate a corresponding output signal y t (i)。
In the IFT process, the following optimization index function is defined, taking into account the tracking error and the control input energy:
wherein e is t (p) represents the tracking error of the output force signal and the command force of the electro-hydraulic loading system, namely e t (ρ)＝y t (ρ)-r t N is the total number of samples considered and λ is a settable weight parameter.
Then the theoretical optimal solution of the parameter vector to be optimized is:
ρ * ＝arg min ρ J n (ρ) (17)
in the above formula, ρ * That is, the optimal value of the parameter vector ρ obtained by the data driving method.
For calculating an optimum parameter vector p * First, it is necessary to obtain e t (p) and u t (ρ) A gradient for ρ; from equations (14) and (15), the following gradient calculation relationship can be obtained:
to obtain the gradient value of each generation i, the gradient value can be calculated by the data obtained by the following three tests.
Test 1:
test 2:
test 3:
in the above three experiments, the reference signal r of experiment 1 1 Provided is a command force signal r t Reference signal r of experiment 2 2 Set is the output force signal y of test 1 t 1 While the reference signal of experiment 3 is still set to the command force signal r t . The rule set is to ensure that the system response data obtained in three experiments are statistically independent.
In addition, in the three tests described above, the added interference signal d was set t Sum noise signal v t The following assumptions are satisfied:
suppose that: interference signal d t And a noise signal v t Is a weak stationary random variable signal of zero mean, anThese perturbation signals, including interference and noise, in different experiments are independent of each other.
Therefore, the unbiased estimation of the considered control parameter vector to be optimized can be further calculated according to the input and output test data of the system as follows:
wherein,
and
for the estimation of the gradient under perturbation, and w 1 And w 2 Representing the estimated residual. From hypothesis 1, est [ w ] is known 1 ]=0 and est [ w [) 2 ]＝0。
Thus, y can be obtained t And u t The gradient for the control parameter p to be optimized is:
in addition, the index function J is optimized n (p) a gradient estimate for the parameter vector p to be optimized of
From the random estimation theory and hypothesis 1, it can be seen that
Is a gradient
Unbiased estimation of (d), i.e.:
then, to satisfy equation (17), using the gauss-newton method, the next generation of updated equations for the parameters to be optimized can be obtained as:
wherein, γ i Is a positive real scalar quantity which determines the optimized step length; and R is i Is a proper setting matrix, and the value is as follows:
in the update formula of the formula (29), the optimization step value γ i Is a key factor in balancing convergence speed and convergence stability.
If gamma is i And R i Poor selection of (a) will result in poor optimization and non-convergence of the optimization process, which in turn may even lead to poor and unstable overall system performance. In order to improve the system performance and enhance the reliability of the optimization process, a limited optimization updating strategy is designed in the IFT optimizing process. Based on the method, the application also provides an evaluation method of the parameter vector rho to be optimized.
First, an evaluation function g (ρ) is defined as:
wherein y is c 3 (t f ，ρ i ) Denotes t in IFT trial 3 f The system output value at the time. y is c (t f ) The response trajectory is output for the limited system as empirically expected. And beta is 1 And beta 2 Is a very common and customizable number.
After each optimization calculation is finished, evaluating the optimization result, and if g (rho) is within a set threshold range and g (rho) is less than or equal to psi, updating the parameter rho according to the formula (29); if g (rho) exceeds the set threshold, i.e. g (rho) > psi, let
Wherein alpha is a positive real constant, and then the test is updated again.
In summary, a flowchart for optimizing and setting parameters of the composite disturbance rejection controller by using IFT shown in fig. 5 is formed, specifically:
1) And (6) initializing. Let i =0, determine the initial value rho of the parameter vector to be optimized 0 Initializing the system controller and determining an optimization index function J n (ρ)。
2) Three experiments of IFT were performed according to formulas (20) to (22).
3) Calculating the gradient according to equations (25) and (26)
And
further, the calculation is performed according to the equations (27) and (30)
And Hessian matrix R i 。
4) Rho is calculated by the equation (29) i+1 。
5) The g (p) value is calculated and checked. If g (rho) is less than or equal to psi, turning to step 6); otherwise make
Updating the step size, and returning to the step 4) for recalculation.
6) Through rho i+1 ＝ρ i Update controlAnd updating the composite disturbance rejection controller accordingly.
7) Judgment index function J n Delta or i is less than or equal to max If not, making i = i +1, and jumping to the step 2) to enter the next generation of TFT process; otherwise, the IFT process ends.
In order to verify the effectiveness of the control method provided by the embodiment, a combined simulation test of MATLAB/Simulink and AMESim is performed. The system parameters used in the simulation are shown in table 1.
TABLE 1
| Name (R) | Unit of | Numerical value |
| Gain of servo valve | m 3 /A·s | 0.25 |
| Flow amplification factor of servo valve | m 2 /s | 5.7735 |
| Flow pressure coefficient of servo valve | m 3 /(s·Pa) | 11.2×10 -12 |
| Total volume of two cavities of hydraulic cylinder | m 3 | 0.0036 |
| Coefficient of leakage in hydraulic cylinder | m 3 /(s·Pa) | 0 |
| Modulus of elasticity of oil | N/m 2 | 6.9×10 8 |
| Load mass | kg | 200 |
| Effective working area of hydraulic cylinder | m 2 | 0.012 |
| Stiffness of the buffer spring | T/mm | 2.4 |
| Density of hydraulic oil | kg/m 3 | 870 |
| Coefficient of loading force | T/ |
2 |
In addition, the initial parameters of the system composite disturbance rejection controller in the simulation and the parameter values in the TFT method optimization process are respectively set as: b =900, ω c ＝20πrad/s，ω o ＝60πrad/s，γ 0 ＝0.5，λ＝10 -12 ，
δ＝10 -18 ，i max =20, framework and model for co-simulation as shown in fig. 6a and 6 b.
In addition, in order to further verify the control performance and robustness of the proposed method, the present embodiment also compares the proposed method with a PID controller in a joint simulation test.
First, the constant value step response test of the system is considered in the joint simulation. In the test, the amplitude of the reference command force was set to 1N, and harmonic interference was added to the system at 1.2 s. The simulation results are shown in fig. 7a-7 f. As can be seen from fig. 7a, the IFT optimized composite immunity control performance is greatly improved compared to the pre-optimization, the settling time is reduced by about 52%, the overshoot is reduced by about 62%, the steady state error is reduced by about 20% and 0-furthermore, compared to the PID controller, the proposed method is reduced by 8% in overshoot, the settling time is reduced by 92%, and the tracking error is reduced by 32%. In addition, from fig. 7b-f, the control parameters have undergone about 11 generations of iterative optimization in the proposed IFT to converge to an optimal state.
The system's tracking sinusoidal command force signal trial is then considered in the joint simulation. In the experiment, the tracking amplitude is set to be 1N, the frequency is set to be 10Hz, and harmonic interference is added to the system at the time of 0.4 s. The simulation results are shown in fig. 8a-8 f. As can be seen from fig. 8a, compared with the conventional PID controller and the control effect before optimization, the proposed method reduces the tracking error by at least about 73%, and the optimization performance is significant. From fig. 8b-8f, the control parameters have undergone approximately 9 generations of iterative optimization in the proposed IFT to converge to an optimal state.
The above embodiments are only used to describe the technical solutions of the present application in detail, but the above embodiments are only used to help understanding the method of the embodiments of the present invention, and should not be construed as limiting the embodiments of the present invention. Modifications and substitutions that may be readily apparent to those skilled in the art are intended to be included within the scope of embodiments of the present invention.
Claims (8)
1. A composite disturbance rejection controller is characterized by comprising an extended state observer, a feedback controller, a disturbance compensator and a feedforward controller,
the extended state observer
Wherein, L = [ L = 1 ,l 2 ,l 3 ] T For expanding the observed gain of the state observer, the determination is made according to the equivalent bandwidth modulation method
Wherein ω is o Is the equivalent observation gain;
b 0 is the equivalent gain of the system; c = [ 10]；
The feedback controller and the disturbance compensator are
Wherein u is c As a feedback controller, u d Is an interference compensator; r is reference input, K = [ K = 1 ,k 2 ]Determining K = [ K ] according to equivalent bandwidth adjustment method for control gain of composite immunity controller 1 ,k 2 ]＝[ω c 2 ,2ω c ]Wherein ω is c Is an equivalent control gain;
the feedforward controller
The overall control law of the composite disturbance rejection controller is
2. A control parameter optimization method for the composite disturbance rejection controller of claim 1, comprising:
performing Laplace transformation on the composite anti-interference controller to generate each transfer function of a frequency domain;
generating a vector of parameters ρ = [ b, ω) to be optimized c ,ω o ,k f1 ,k f2 ]The system input-output relationship function of (1);
defining an optimization index function;
obtaining an output force signal y t (i) And a command force signal r t (i) Tracking error e of t (p) and a control input signal u t (ρ) for the gradient value of the optimal parameter vector, determining a theoretical optimal solution of the parameter vector ρ to be optimized.
3. The optimization method according to claim 2, wherein each transfer function of the frequency domain is
F(s)＝k f1 +k f2 s；
The generated system input-output relationship function is:
wherein reference is made to an input signal r t (rho) triggered control signal u t (i) Will cause the system to generate a corresponding output signal y t (i) (ii) a Wherein i =0,1,2, \ 8230;, i max ，i max Representing the set maximum number of iterations.
4. The optimization method according to claim 2, wherein the optimization indicator function is
Wherein e is t (p) represents the tracking error of the output force signal and the command force of the electro-hydraulic loading system, namely e t (ρ)＝y t (ρ)-r t N is the total number of samples considered and λ is a predetermined weighting parameter.
5. The optimization method according to claim 4, wherein the obtaining of the tracking error e of the output force signal and the command force t (p) and a control input signal u t (ρ) the gradient for the optimal parameter vector is determined according to the following method comprising:
determining a gradient calculation relational expression according to the system input and output relational function; the gradient is calculated by the relation
The gradient values are determined according to the following tests:
test 1:
test 2:
test 3:
wherein, the reference signal r of experiment 1 1 Provided is a command force signal r t Reference signal r of experiment 2 2 Output force signal y for test 1 t 1 While the reference signal of test 3 is still set as the command force signal r t (ii) a And the system response data obtained in the three experiments are statistically independent of each other.
6. The optimization method according to claim 5, wherein the test further satisfies the following assumptions: interference signal d t And a noise signal v t Is a weak stationary random variable signal with zero mean value, and perturbation signals including interference signals and noise signals in different experiments are independent of each other.
7. The optimization method according to claim 6, characterized in that it is based on est [ w ] in trial 1, trial 2 and trial 3 1 ]=0 and est [ w 2 ]Assumption of =0, based on estimation of the gradient under perturbation signals
And
available y t And u t Unbiased estimation of a parameter vector to be optimizedAre respectively as
Optimizing an index function J n (p) a gradient estimate with respect to the parameter vector p to be optimized of
Then the
In order to satisfy the optimization index function, determining the next generation updating formula of the parameter vector rho to be optimized based on the Gauss-Newton method as
Wherein the step value gamma is optimized i Determining an optimized step size for a real scalar; the value of the setting matrix is
8. The optimization method of claim 7, further comprising evaluating the optimization results, comprising:
if g (rho) is within a preset threshold range and g (rho) is less than or equal to psi, updating rho according to a next generation updating formula of the parameter vector to be optimized;
if g (rho) exceeds the preset threshold range, i.e. g (rho)>Psi, order
Wherein alpha is a positive real constant, and then test updating is carried out again;
evaluating a function
Wherein y is t 3 (t f ,ρ i ) Indicates t in IFT test 3 f System output value of time of day, y c (t f ) Output response trajectory for a limited system expected empirically, beta 1 And beta 2 Is a very common and customizable number.
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