CN113189880B - Extreme value search optimization active disturbance rejection control method of electro-hydraulic servo system - Google Patents
Extreme value search optimization active disturbance rejection control method of electro-hydraulic servo system Download PDFInfo
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Abstract
The invention belongs to the technical field of electro-hydraulic servo systems, and provides an extremum search optimization active disturbance rejection control method of an electro-hydraulic servo system. The method comprises the following steps: s1: acquiring an expansion state system according to a state space model of the electro-hydraulic servo system; s2: establishing an extended state observer, an interference compensator and a feedback controller according to the extended state system; s3: and carrying out iterative updating on the control parameters of the extended state observer, the interference compensator and the feedback controller by using an extremum searching method. The invention adopts an extremum search algorithm to carry out data-based optimization on the control parameters of the designed extended state observer, the designed interference compensator and the designed feedback controller, the optimization process does not depend on interference and a system model, and an optimal automatic setting method of the control parameters is provided, so that the interference on the system is estimated and compensated, and the control on the electro-hydraulic servo system is realized.
Description
Technical Field
The invention relates to the technical field of electro-hydraulic servo systems, in particular to an extremum searching optimization active disturbance rejection control method of an electro-hydraulic servo system.
Background
The electro-hydraulic servo system has the advantages of high system transmission efficiency, high response speed, high output power, high control accuracy and the like, and becomes an important execution device in the field of aircraft brake, undercarriage and control system under the development trend of multi-electric/full-electric aircraft. In recent years, with the pursuit of limited performance of aircrafts, the research on electro-hydraulic servo systems is further focused by domestic and overseas workers, and deep discussion and remarkable optimization are obtained in the aspects of mechanism improvement, performance analysis, control design and the like.
In control design, the servo capability of the electro-hydraulic system directly influences the performance index of the electro-hydraulic system in an airplane, so that a great deal of research is focused on how to inhibit interference and enable the tracking performance of the system on a specific signal to reach the expected index. The electro-hydraulic servo system is a typical multi-source interference system and is influenced by multi-source internal and external disturbances such as self-strong nonlinearity, model uncertainty, leakage interference, friction torque disturbance, external load torque disturbance and the like in work. This presents new challenges to the control and disturbance compensator design of electro-hydraulic servo systems. Although advanced control schemes such as sliding mode control, robust adaptive control and backstepping adaptive control are available to solve the interference on the system, the control schemes all need more accurate system model information, and the improvement of the control performance of the electro-hydraulic servo system is limited.
Aiming at the problem of interference suppression of the electro-hydraulic servo system, a method based on interference/uncertainty estimation and compensation is a new choice for solving the multi-source disturbance of the electro-hydraulic servo system in the near term. The method mainly comprises the following steps: a sliding mode control scheme of the disturbance observer based on frequency domain information; and an active disturbance rejection control method which does not depend on a model and utilizes an extended state observer to carry out active estimation and compensation on system lumped disturbance becomes a mainstream method for improving the control performance of the electro-hydraulic servo system. However, it should be noted that the strong nonlinearity of the electro-hydraulic servo system makes the tuning and optimization of the control parameters of the active disturbance rejection method face significant challenges.
Disclosure of Invention
In view of this, the embodiment of the present invention provides an extremum search optimization active disturbance rejection control method for an electro-hydraulic servo system, which at least partially solves the problems in the prior art.
The embodiment of the invention provides an extremum searching optimization active disturbance rejection control method of an electro-hydraulic servo system, which comprises the following steps:
s1: acquiring an expansion state system according to a state space model of the electro-hydraulic servo system;
s2: establishing an extended state observer, an interference compensator and a feedback controller according to the extended state system;
s3: and carrying out iterative updating on the control parameters of the extended state observer, the interference compensator and the feedback controller by using an extremum searching method.
According to a specific implementation manner of the embodiment of the present invention, the step 3 specifically includes the following steps:
executing a track tracking experiment of the electro-hydraulic servo system and calculating a position output tracking error of the electro-hydraulic servo system;
outputting a tracking error through the position of the electro-hydraulic servo system to calculate an optimized objective function;
updating the control parameters according to the optimization objective function;
and repeatedly executing the track tracking experiment of the electro-hydraulic servo system, calculating the position output tracking error of the electro-hydraulic servo system, calculating an optimized objective function and updating the control parameters until the execution times are greater than the set times or the optimized objective function is less than the set threshold.
According to a specific implementation manner of the embodiment of the present invention, the optimization objective function satisfies J ═ w1MA+w2MSD, wherein J is an optimization objective function, MA and MSD are respectively a moving average value and a moving standard deviation, w, of the output of the electro-hydraulic servo system1And w2Weighting coefficients for balancing the high-frequency positioning performance and the low-frequency positioning performance of the electro-hydraulic servo system are respectively used.
The extreme value search optimization active disturbance rejection control method, the extreme value search optimization active disturbance rejection control device and the electronic equipment of the electro-hydraulic servo system provided by the embodiment of the invention provide a data-based extreme value search control parameter optimization method for a user, solve the design and optimization problems of a linear active disturbance rejection controller under strong nonlinearity and multi-source disturbance, and improve the control performance of the electro-hydraulic servo system. The embodiment of the invention at least has the following technical effects:
the first embodiment of the invention designs the active disturbance rejection controller of the electro-hydraulic servo system, does not depend on a system model excessively, is less influenced by system nonlinearity, and has better robustness.
Secondly, the embodiment of the invention optimizes the parameters by adopting an optimization index function combining the moving average index and the moving standard deviation index, and balances the high-frequency and low-frequency positioning performance of the electro-hydraulic servo system.
Thirdly, the embodiment of the invention adopts an extremum search algorithm to carry out data-based optimization on the control parameters of the designed active disturbance rejection controller, namely the extended state observer, the disturbance compensator and the feedback controller, the optimization process does not depend on disturbance and a system model, and an optimal automatic setting method of the control parameters is provided, so that the disturbance on the system is estimated and compensated, and the control on the electro-hydraulic servo system is realized.
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In order to more clearly illustrate the detailed description of the invention or the technical solutions in the prior art, the drawings that are needed in the detailed description of the invention or the prior art 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 is a flow chart illustrating the steps of an extremum seeking optimized active disturbance rejection control method provided by an embodiment of the present invention;
FIG. 2 illustrates an extremum seeking optimization tuning block diagram for an active disturbance rejection controller;
fig. 3 shows a flow chart of an extremum seeking optimization method.
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 first embodiment is as follows:
referring to fig. 1, an extremum search optimization active disturbance rejection control method of an electro-hydraulic servo system includes the following steps:
s1: acquiring a dynamic state space model of the electro-hydraulic servo system, and acquiring an expansion state system according to the state space model;
and acquiring a dynamic state space model of the electro-hydraulic servo system, performing differential flattening treatment on the state space model to acquire a differential flat model of the nonlinear system, and acquiring an expansion state system of the electro-hydraulic servo system from the differential flat model. The step ensures that an active disturbance rejection controller designed for the electro-hydraulic servo system does not depend on a system model excessively, is less influenced by system nonlinearity, and has better robustness.
S2: establishing an extended state observer, an interference compensator and a feedback controller according to the extended state system;
the extended state observer, the interference compensator and the feedback controller jointly form an active disturbance rejection controller, the extended state observer is used for observing lumped interference of the system, the interference compensator is used for compensating the lumped interference borne by the system, and the feedback controller is used for controlling the whole closed-loop system.
S3: the control parameters of the extended state observer, the disturbance compensator and the feedback controller are iteratively updated by using an extremum searching method, which specifically comprises the following steps:
taking the control parameter values of the current extended state observer, the interference compensator and the feedback controller as initial values;
executing a track tracking experiment of the electro-hydraulic servo system and calculating a position output tracking error of the electro-hydraulic servo system;
calculating an optimized objective function through the position output tracking error of the electro-hydraulic servo system, wherein the optimized objective function meets the condition that J is w1MA+w2MSD, wherein J is an optimization objective function, MA and MSD are respectively a moving average value and a moving standard deviation, w, of the output of the electro-hydraulic servo system1And w2Weighting coefficients for balancing the high-frequency positioning performance and the low-frequency positioning performance of the electro-hydraulic servo system are respectively set;
updating the control parameters according to the optimization objective function;
and repeating the steps of executing the track tracking experiment of the electro-hydraulic servo system, calculating the position output tracking error of the electro-hydraulic servo system, calculating the optimization objective function and updating the control parameter until the execution times are more than the set times or the optimization objective function is less than the set threshold.
The step adopts an optimization index function combining a moving average index and a moving standard deviation index to optimize the control parameters, so that the high-frequency and low-frequency positioning performance of the electro-hydraulic servo system is balanced; and simultaneously, an extremum search algorithm is adopted to carry out data-based optimization on designed parameters of the active disturbance rejection controller, the optimization process does not depend on interference and a system model, and an optimal automatic setting method of control parameters is provided, so that the interference on the system is estimated and compensated, and the control on the electro-hydraulic servo system is realized.
The steps are repeated after a period of time, and the control of the electro-hydraulic servo system is maintained.
It should be noted that, the modules are arranged according to a streaming layout, which is only one embodiment of the present invention, and may also be arranged in other manners, and the present invention is not limited to this.
The embodiment of the invention has the following technical effects:
first, the active disturbance rejection controller designed for the electro-hydraulic servo system in this embodiment does not depend on the system model excessively, is less affected by system nonlinearity, and has better robustness.
Secondly, the parameters are optimized by adopting an optimization index function combining a moving average index and a moving standard deviation index, and the high-frequency and low-frequency positioning performance of the electro-hydraulic servo system is balanced.
Thirdly, the control parameters of the designed active disturbance rejection controller, namely the extended state observer, the disturbance compensator and the feedback controller, are optimized based on data by adopting an extremum search algorithm, the optimization process does not depend on disturbance and a system model, and an optimal automatic setting method of the control parameters is provided, so that the disturbance on the system is estimated and compensated, and the control of the electro-hydraulic servo system is realized.
The second embodiment:
an extremum search optimization active disturbance rejection control method of an electro-hydraulic servo system specifically comprises the following steps:
s1: the method for acquiring the expansion state system according to the state space model of the electro-hydraulic servo system specifically comprises the following steps:
s1.1, setting a disturbed state space model of the electro-hydraulic servo system under the dynamic assumption of neglecting an electric valve:
wherein x1Indicating piston position, x, of electrohydraulic servo2Representing piston velocity, x3Representing load pressure, u input current, ApIndicating the area of the piston under pressure, PsRepresenting the supply pressure of the pump, m is the equivalent mass, k is the equivalent stiffness, c is the equivalent damping, and α, β and γ are hydraulic coefficients. In addition, d1And d2Is the interference experienced by the system and has the following form:
d1＝Fload+Ffriction+Δ1, (2)
d2＝dleakage+Δ2, (3)
wherein FloadAnd FfrictionRespectively representing the load force and the friction force, dleakageIs an internal leakage disturbance. And Δ1And Δ2Is the model uncertainty.
S1.2, carrying out differential flattening treatment on a disturbed state space model of the electro-hydraulic servo system, and specifically comprising the following steps:
s1.2.1, defining the flat output: y is x1. (4)；
S1.2.2 deriving equation (1) as a functional expression for flat output y:
wherein
S1.2.3 calculating the dynamic model of the electro-hydraulic servo system about the flat variable:
s1.2.4 definition of New variables:
s1.2.5 obtaining a differential flat model of equation (1) from equation (7):
wherein f (xi) ═ lambda1βξ1-(λ3α+λ2β+λ1)ξ2-(λ2+β)ξ3,
S1.3, acquiring an expansion state system of the electro-hydraulic servo system, which specifically comprises the following steps:
s1.3.1, writing equation (8) as follows:
wherein b is0In order to control the gain equivalently, the gain is controlled,
for lumped interference experienced by the system, d is an interference term, including d1And d2。
Defining lumped disturbances as states of expansion
An extended state system of calculation equation (9):
wherein
S2: an extended state observer, a disturbance compensator and a feedback controller are designed for an extended state system, the extended state observer, the disturbance compensator and the feedback controller jointly form an active disturbance rejection controller, and the method specifically comprises the following steps:
s2.1: designing an extended state observer for the extended state system equation (10):
wherein
For state observation, L ═ L1,l2,l3,l4]TRepresenting the gain of an observer, and selecting the observation gain as the following form by an equivalent gain adjustment method:
wherein ω isoDefining the equivalent observation bandwidth;
s2.2: designing an interference compensator and a feedback controller for the expansion state system:
considering a given tracking reference signal r of the system, an interference compensator and a feedback controller are designed for equation (10), which controls the input current as calculated as follows:
wherein u iscFor a feedback controller, the control gain is designed as
Wherein ω iscDefining as an equivalent control bandwidth; u. ofdA control input for the interference compensator controller.
S3: as shown in fig. 2 to 3, the iterative updating and optimization of the control parameters of the extended state observer, the disturbance compensator and the feedback controller in step S2 are performed by using an extremum search method, so as to obtain an optimal control parameter value, which specifically includes the following steps:
s3.1: setting a control parameter theta [ theta ] needing to be optimally set1,θ2,θ3]＝[b0,ωo,ωc](ii) a Setting a maximum number of iterations kmaxAnd optimizing the target threshold Jthreshold。
S3.2: let k equal to 0, initialize the control parameter theta (0) to be set to [ b ]0(0),ωo(0),ωc(0)]，b0(0),ω0(0),ωc(0) Is current b0,ω0,ωcThe value is obtained.
S3.3: and (3) making k equal to k +1, executing a track tracking experiment of the electro-hydraulic servo system, and calculating a position output tracking error of the electro-hydraulic servo system: e ═ r- ξ1。
S3.4: and calculating an optimization objective function.
Calculating a Moving Average (MA) index output by the electro-hydraulic servo system:
wherein, T0To optimize the window time period.
Calculating a Moving Standard Deviation (MSD) index:
calculating a control parameter optimization objective function as follows:
J＝w1 MA+w2 MSD, (15)
wherein w1And w2Weighting coefficients for balancing the high-frequency positioning performance and the low-frequency positioning performance of the electro-hydraulic servo system are respectively used.
S3.5: the optimization objective function J is sampled.
S3.6: and sequentially updating the ith (i is 1,2 and 3) control parameter according to the following formula.
Wherein
In order to be a high-frequency filter state,
for the parameter value by modulation and filtering, alphaicos(Ωik) Representing harmonic modulated signals, alphaiFor modulating the signal amplitude, ΩiFor modulating the angular frequency of the signal, h is the high-frequency filter parameter, gammaiIs the gain of the integral term.
In which step b of the extended state observer, the disturbance compensator and the feedback controller0,ω0,ωcUpdating the value to b corresponding to theta (k)0(k),ω0(k),ωc(k)。
S3.7: if k +1 is determined>kmaxOr J < JthresholdIf yes, skipping to the step 3.2 after the interval of the set time; otherwise jump to step 3.3.
It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (3)
1. An extremum search optimization active disturbance rejection control method of an electro-hydraulic servo system is characterized by comprising the following steps:
s1: the method comprises the following steps of obtaining an expansion state system according to a state space model of the electro-hydraulic servo system, specifically:
s1.1, acquiring a disturbed state space model of the electro-hydraulic servo system:
wherein x1Indicating piston position, x, of electrohydraulic servo2Representing piston velocity, x3Representing load pressure, u input current, ApIndicating the area of the piston under pressure, PsDenotes the supply pressure of the pump, m is the equivalent mass, k is the equivalent stiffness, c is the equivalent damping, and α, β and γ are hydraulic coefficients, in addition, d1And d2Is the interference experienced by the system and has the following form:
d1＝Fload+Ffriction+Δ1, (2)
d2＝dleakage+Δ2, (3)
wherein FloadAnd FfrictionRespectively representing the load force and the friction force, dleakageFor internal leakage interference, Δ1And Δ2Is the model uncertainty;
s1.2, carrying out differential flattening treatment on a disturbed state space model of the electro-hydraulic servo system, and specifically comprising the following steps:
s1.2.1, defining the flat output: y is x1, (4)
S1.2.2, deriving equation (1) as a functional expression with respect to the flat output y:
x1＝y,
wherein
S1.2.3 calculating the dynamic model of the electro-hydraulic servo system about the flat variable:
s1.2.4, define the new variables:
s1.2.5 obtaining a differential flat model of equation (1) from equation (7):
wherein
S1.3, acquiring an expansion state system of the electro-hydraulic servo system, which specifically comprises the following steps:
s1.3.1 writing equation (8) as follows:
wherein b is0In order to control the gain equivalently,
for lumped interference experienced by the system, d is an interference term, including d1And d2；
Defining lumped disturbances as expansion states
An extended state system of calculation equation (9):
wherein
S2: establishing an extended state observer, an interference compensator and a feedback controller according to the extended state system, specifically:
s2.1: establishing an extended state observer for the extended state system equation (10):
wherein
For state observation, L ═ L1,l2,l3,l4]TRepresenting the gain of an observer, and selecting the observation gain as the following form by an equivalent gain adjustment method:
wherein ω isoDefining the equivalent observation bandwidth;
s2.2: establishing an interference compensator and a feedback controller for the extended state system:
considering a given tracking reference signal r of the system, an interference compensator and a feedback controller are designed for equation (10), which controls the input current as calculated as follows:
wherein u iscFor the feedback controller, the control gain is designed to
Wherein ω iscDefining the equivalent control bandwidth; u. ofdA disturbance compensator controller control input;
s3: and performing iterative update on the control parameters of the extended state observer, the interference compensator and the feedback controller by using an extremum searching method, specifically:
executing a track tracking experiment of the electro-hydraulic servo system and calculating the position output tracking error of the electro-hydraulic servo system;
outputting a tracking error through the position of the electro-hydraulic servo system to calculate an optimized objective function;
updating the control parameters according to the optimization objective function;
and repeatedly executing the track tracking experiment of the electro-hydraulic servo system, calculating the position output tracking error of the electro-hydraulic servo system, calculating the optimized objective function and updating the control parameter until the execution times are greater than the set times or the optimized objective function is less than the set threshold.
2. The extremum seeking optimized active disturbance rejection control method of claim 1, wherein: the optimization objective function satisfies J ═ w1MA+w2MSD, wherein J is the optimization objective function, MA and MSD scoresMoving mean and moving standard deviation, w, of the electrohydraulic servo system output1And w2Weighting coefficients for balancing the high-frequency positioning performance and the low-frequency positioning performance of the electro-hydraulic servo system are respectively used.
3. The extremum seeking optimization active disturbance rejection control method according to claim 2, wherein the step S3 specifically comprises:
s3.1: obtaining a control parameter theta [ theta ] needing to be optimized and set1,θ2,θ3]＝[b0,ωo,ωc](ii) a Obtaining the maximum iteration number kmaxAnd optimizing the target threshold Jthreshold；
S3.2: let k equal to 0, initialize the control parameter theta (0) to be set to [ b ]0(0),ωo(0),ωc(0)]，b0(0),ω0(0),ωc(0) Is current b0,ω0,ωcA value;
s3.3: and (3) making k equal to k +1, executing a track tracking experiment of the electro-hydraulic servo system, and calculating a position output tracking error of the electro-hydraulic servo system: e ═ r- ξ1；
S3.4: calculating an optimization objective function:
calculating the moving average index output by the electro-hydraulic servo system:
wherein, T0To optimize the window time period;
calculating a mobile standard deviation index:
calculating a control parameter optimization objective function as follows:
J＝w1MA+w2MSD, (15)
wherein w1And w2Respectively balancing the electric liquidWeighting coefficients of high-frequency and low-frequency positioning performances of the servo system;
s3.5: sampling the optimized objective function J;
s3.6: sequentially updating the ith control parameter according to the following formula;
wherein
For the high-frequency filter state to be,
for the value of the parameter by modulation and filtering, alphaicos(Ωik) Representing harmonic modulated signals, alphaiFor modulating the amplitude of the signal, omegaiFor modulating the angular frequency of the signal, h is the high-frequency filter parameter, gammaiIs the gain of the integral term;
s3.7: if k +1 is determined>kmaxOr J<JthresholdIf yes, skipping to the step 3.2 after the interval of the set time; otherwise, jump to step 3.3.
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