CN116300420A - Servo control method, system, device, terminal equipment and storage medium - Google Patents
Servo control method, system, device, terminal equipment and storage medium Download PDFInfo
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Abstract
The invention discloses a servo control method, a servo control system, a servo control device, a servo control terminal device and a servo control storage medium, wherein error signals are obtained; inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback; and generating a target voltage signal according to the error signal and the disturbance feedback based on a preset model prediction controller, and sending the target voltage signal to a servo valve so that the servo valve can adjust the opening of a valve port according to the target voltage signal. By combining model predictive control with a finite-time disturbance observer, the controller can still ensure strong robustness and stability under the condition of input constraint and external disturbance of the servo control system, and the finite-time disturbance observer can perform online detection and real-time estimation on unknown disturbance and can quickly approximate the system and the mixed disturbance existing in the outside, so that the nonlinear control effect of the electrohydraulic servo system is improved.
Description
Technical Field
The present invention relates to the field of mechanical control technologies, and in particular, to a servo control method, a system, a device, a terminal device, and a storage medium.
Background
In the field of electrohydraulic servo control, an electrohydraulic servo system is a typical nonlinear system, and model uncertainty in the electrohydraulic servo system is mainly divided into two types, namely parameter uncertainty and uncertainty nonlinearity, wherein the parameter uncertainty comprises load mass change, hydraulic elastic modulus, viscosity friction coefficient and the like which change along with environmental temperature. Other uncertainties, such as external disturbances, leaks, friction, etc., cannot be modeled accurately, and such nonlinearities are referred to as uncertainty nonlinearities because their nonlinear functions are unknown to be accurately described.
In recent years, for nonlinear control of an electrohydraulic servo system, a plurality of nonlinear control methods are proposed, and the methods can obtain steady-state performance of gradual tracking through self-adaptive control, so that the problem of uncertainty of parameters in the electrohydraulic servo system is solved, but the problem of uncertainty of nonlinearity is solved, and the problem of limited control input in a physical system is solved, so that the control effect of the method is poor.
Therefore, there is a need to propose a solution that improves the nonlinear control effect of electro-hydraulic servo systems.
The foregoing is provided merely for the purpose of facilitating understanding of the technical solutions of the present invention and is not intended to represent an admission that the foregoing is prior art.
Disclosure of Invention
The invention mainly aims to provide a servo control method, a servo control system, a servo control device, a terminal device and a storage medium, and aims to improve the nonlinear control effect of an electrohydraulic servo system.
In order to achieve the above object, the present invention provides a servo control method including:
acquiring an error signal;
inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback;
and generating a target voltage signal according to the error signal and the disturbance feedback based on a preset model prediction controller, and sending the target voltage signal to a servo valve so that the servo valve can adjust the opening of a valve port according to the target voltage signal.
Optionally, the step of acquiring an error signal includes:
acquiring an expected displacement signal and an actual displacement signal;
and calculating the error signal according to the expected displacement signal and the actual displacement signal.
Optionally, the step of generating the target voltage signal according to the error signal and the disturbance feedback by the predictive controller based on the preset model further includes:
establishing a dynamic model of a double-rod hydraulic cylinder servo system;
Performing approximate linearization and first-order differential discretization on the dynamic model to obtain a discretized mathematical model;
model predictive controllers with state constraints are designed based on the discretized mathematical model.
Optionally, before the step of inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback, the method further includes:
based on the finite-time disturbance observer theory, a finite-time disturbance observer is designed for each state and disturbance in the dynamics model for subsequent disturbance compensation.
Optionally, the step of designing the finite time disturbance observer for each state and disturbance in the model based on the finite time disturbance observer theory further comprises:
the limited-time perturbation observer is proved to converge in a limited time by means of the lyapunov function.
Optionally, the step of establishing a dynamics model of the dual-rod hydraulic cylinder servo system includes:
and establishing a dynamic model of the double-rod hydraulic servo system according to the Newton's second law, the hydraulic cylinder inertial load dynamic equation and the hydraulic cylinder flow continuity equation.
In addition, in order to achieve the above objective, the present invention further provides a servo control system, where the servo control system includes a finite time disturbance observer, a model predictive controller, and a servo valve, where the finite time disturbance observer is configured to calculate a mismatch disturbance of the electrohydraulic servo system, and input calculated disturbance feedback to the model predictive controller, so that the model predictive controller generates a target voltage signal according to the obtained error signal and the disturbance feedback, and sends the target voltage signal to the servo valve, so that the servo valve adjusts a valve port opening according to the target voltage signal.
In addition, in order to achieve the above object, the present invention also provides a servo control device including:
the acquisition module is used for acquiring an error signal;
the feedback module is used for inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback;
the control module is used for predicting the controller based on a preset model, generating a target voltage signal according to the error signal and the disturbance feedback, and sending the target voltage signal to the servo valve so that the servo valve can adjust the opening of the valve port according to the target voltage signal.
In addition, in order to achieve the above object, the present invention also provides a terminal device including a memory, a processor, and a servo control program stored on the memory and executable on the processor, the servo control program implementing the steps of the servo control method as described above when executed by the processor.
In addition, in order to achieve the above object, the present invention also provides a computer-readable storage medium having a servo control program stored thereon, which when executed by a processor, implements the steps of the servo control method as described above.
The embodiment of the invention provides a servo control method, a servo control system, a servo control device, a servo control terminal device and a servo control storage medium, wherein error signals are acquired; inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback; and generating a target voltage signal according to the error signal and the disturbance feedback based on a preset model prediction controller, and sending the target voltage signal to a servo valve so that the servo valve can adjust the opening of a valve port according to the target voltage signal. By combining model predictive control with a finite-time disturbance observer, the controller can still ensure strong robustness and stability under the condition of input constraint and external disturbance of the servo control system, and the finite-time disturbance observer can perform online detection and real-time estimation on unknown disturbance and can quickly approximate the system and the mixed disturbance existing in the outside, so that the nonlinear control effect of the electrohydraulic servo system is improved.
Drawings
FIG. 1 is a schematic diagram of functional modules of a terminal device to which a servo control device of the present invention belongs;
FIG. 2 is a flowchart of an exemplary embodiment of a servo control method according to the present invention;
FIG. 3 is a schematic diagram of an electro-hydraulic servo system according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of an electro-hydraulic servo system model predictive control method based on a finite time disturbance observer in an embodiment of the invention;
FIG. 5 is a flowchart of another exemplary embodiment of a servo control method of the present invention;
FIG. 6 is a flowchart of a servo control method according to another exemplary embodiment of the present invention;
FIG. 7 is a schematic diagram showing the effect of control law in an embodiment of the present invention;
FIG. 8 is a schematic diagram of a second control law effect in an embodiment of the present invention;
FIG. 9 is a third schematic diagram of the control law effect in an embodiment of the present invention;
FIG. 10 is a schematic diagram showing the effect of control law in an embodiment of the present invention;
FIG. 11 is a schematic diagram showing the effect of control law in the embodiment of the present invention;
fig. 12 is a schematic diagram showing the effect of control law in the embodiment of the present invention.
The achievement of the objects, functional features and advantages of the present invention will be further described with reference to the accompanying drawings, in conjunction with the embodiments.
Detailed Description
It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The main solutions of the embodiments of the present invention are: by acquiring an error signal; inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback; and generating a target voltage signal according to the error signal and the disturbance feedback based on a preset model prediction controller, and sending the target voltage signal to a servo valve so that the servo valve can adjust the opening of a valve port according to the target voltage signal. By combining model predictive control with a finite-time disturbance observer, the controller can still ensure strong robustness and stability under the condition of input constraint and external disturbance of the servo control system, and the finite-time disturbance observer can perform online detection and real-time estimation on unknown disturbance and can quickly approximate the system and the mixed disturbance existing in the outside, so that the nonlinear control effect of the electrohydraulic servo system is improved.
Technical terms related to the embodiment of the invention:
a Finite time disturbance observer (finish-time Disturbance Observer, FTDO);
proportional integral derivative controller (PID):
model Predictive Control (MPC);
extended State Observer (ESO);
electrohydraulic servo system model predictive control (ESOMPC) based on proportional-integral-derivative controller control and extended state observer;
electrohydraulic servo system model predictive control of finite time observers (ftdomc).
The electrohydraulic servo system is a typical nonlinear system, and model uncertainty in the electrohydraulic servo system is mainly divided into two types, namely parameter uncertainty and uncertainty nonlinearity, wherein the parameter uncertainty comprises load mass change, hydraulic elastic modulus, viscous friction coefficient and the like which change along with the environmental temperature. Other uncertainties, such as external disturbances, leaks, friction, etc., cannot be modeled accurately, and such nonlinearities are referred to as uncertainty nonlinearities because their nonlinear functions are unknown to be accurately described. In recent years, for nonlinear control of electro-hydraulic servo systems, many advanced nonlinear control methods have been proposed successively. Including Adaptive Control (AC), adaptive Robust Control (ARC), sliding Mode Control (SMC), adaptive integral robust control (air), and the like. For dealing with the problem of parameter uncertainty in an electrohydraulic servo system, the adaptive control can obtain the steady-state performance of progressive tracking, but the control effect is somewhat bad for dealing with the problem of uncertainty nonlinearity and the problem of limited control input in a physical system. Therefore, researchers have constraint problems aiming at state variables, and a method based on the barrier Lyapunov function combined with backstepping self-adaption is provided to solve the problems of state constraint and model uncertainty. But this method places high demands on the initial values of the system. The sliding mode control has good anti-interference performance and strong robustness aiming at uncertain nonlinearity in a servo system. When the Control system has certain parameter perturbation, the Robust Control (robustcontrol) can still maintain the performance characteristics of the original system. Therefore, the proposal of the self-adaptive robust sliding mode controller plays a vital role in solving the problem of model uncertainty in an electrohydraulic servo system. However, because the sliding mode controller has discontinuous sliding mode approach law items in the design process, the problem of buffeting of the sliding mode control is inevitably caused, and the control performance is deteriorated. Model Predictive Control (MPC) is the most widely used control algorithm in industrial fields, except for PID algorithms, which early comes into play in the field of process control, and with the development of computer hardware, MPC is increasingly being applied to related fields such as automatic driving, unmanned aerial vehicles and robots. Model prediction has a fast transient response and flexibility to accommodate different constraints compared to PID. Model Predictive Control (MPC) may leverage the system model under certain constraints to obtain control signals or instructions by minimizing predefined cost functions or targets. The general control structure consists of three key parts of a prediction model, a cost function and a solving algorithm. In recent years, a Finite time disturbance observer (finish-time Disturbance Observer, FTDO) gradually becomes a research hotspot, and compared with an Extended State Observer (ESO), the Finite time disturbance observer can perform online detection and real-time estimation on unknown disturbance, and can quickly approximate a system and mixed disturbance existing in the outside.
The invention provides a prediction control method of an electrohydraulic servo system model based on a finite time disturbance observer. And then a first-order differential discretization method is used for obtaining a discretized kinetic equation. Model predictive controllers with input constraints are designed based on discretized dynamics models. The optimization objective function and the constraint solving problem in the linear time-varying model predictive control are converted into a quadratic programming solving problem. And a finite time disturbance observer is fused on the basis of model predictive control to accurately estimate the uncertain disturbance of the system on line. The stability of the finite time disturbance observer is demonstrated by the lyapunov function. And finally, verifying the overall performance of the electrohydraulic servo system model predictive control algorithm based on the limited time disturbance observer through numerical simulation. The invention combines a limited-time disturbance observer to enhance the inhibition effect of model predictive control on external disturbance, estimates disturbance in limited time, and can simultaneously solve the problems of input constraint, external disturbance and the like in an electrohydraulic servo system.
Specifically, referring to fig. 1, fig. 1 is a schematic diagram of functional modules of a terminal device to which a servo control device of the present invention belongs. The servo control device may be a device independent of the terminal device, capable of servo control, which may be carried on the terminal device in the form of hardware or software. The terminal equipment can be an intelligent mobile terminal with a data processing function such as a mobile phone and a tablet personal computer, and can also be a fixed terminal equipment or a server with a data processing function.
In this embodiment, the terminal device to which the servo control device belongs at least includes an output module 110, a processor 120, a memory 130, and a communication module 140.
The memory 130 stores an operating system and a servo control program, and the servo control device may store information such as an error signal and disturbance feedback in the memory 130; the output module 110 may be a display screen or the like. The communication module 140 may include a WIFI module, a mobile communication module, a bluetooth module, and the like, and communicates with an external device or a server through the communication module 140.
Wherein the servo control program in the memory 130 when executed by the processor performs the steps of:
acquiring an error signal;
Inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback;
and generating a target voltage signal according to the error signal and the disturbance feedback based on a preset model prediction controller, and sending the target voltage signal to a servo valve so that the servo valve can adjust the opening of a valve port according to the target voltage signal.
Further, the servo control program in the memory 130, when executed by the processor, further performs the steps of:
acquiring an expected displacement signal and an actual displacement signal;
and calculating the error signal according to the expected displacement signal and the actual displacement signal.
Further, the servo control program in the memory 130, when executed by the processor, further performs the steps of:
establishing a dynamic model of a double-rod hydraulic cylinder servo system;
performing approximate linearization and first-order differential discretization on the dynamic model to obtain a discretized mathematical model;
model predictive controllers with state constraints are designed based on the discretized mathematical model.
Further, the servo control program in the memory 130, when executed by the processor, further performs the steps of:
based on the finite-time disturbance observer theory, a finite-time disturbance observer is designed for each state and disturbance in the dynamics model for subsequent disturbance compensation.
Further, the servo control program in the memory 130, when executed by the processor, further performs the steps of:
the limited-time perturbation observer is proved to converge in a limited time by means of the lyapunov function.
Further, the servo control program in the memory 130, when executed by the processor, further performs the steps of:
and establishing a dynamic model of the double-rod hydraulic servo system according to the Newton's second law, the hydraulic cylinder inertial load dynamic equation and the hydraulic cylinder flow continuity equation.
The embodiment adopts the scheme, and particularly obtains an error signal; inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback; and generating a target voltage signal according to the error signal and the disturbance feedback based on a preset model prediction controller, and sending the target voltage signal to a servo valve so that the servo valve can adjust the opening of a valve port according to the target voltage signal. By combining model predictive control with a finite-time disturbance observer, the controller can still ensure strong robustness and stability under the condition of input constraint and external disturbance of the servo control system, and the finite-time disturbance observer can perform online detection and real-time estimation on unknown disturbance and can quickly approximate the system and the mixed disturbance existing in the outside, so that the nonlinear control effect of the electrohydraulic servo system is improved.
The method embodiment of the invention is proposed based on the above-mentioned terminal equipment architecture but not limited to the above-mentioned architecture.
The main execution body of the method of the present embodiment may be a servo control device or a terminal device, and the present embodiment uses the servo control device as an example.
Referring to fig. 2, fig. 2 is a flowchart illustrating an exemplary embodiment of a servo control method according to the present invention. The servo control method includes:
step S10, an error signal is obtained;
specifically, the servo control method in the embodiment of the invention is applied to an electrohydraulic servo system, the electrohydraulic servo system is a typical nonlinear system, and model uncertainty in the electrohydraulic servo system is mainly divided into two types, namely parameter uncertainty and uncertainty nonlinearity, wherein the parameter uncertainty comprises load mass change, hydraulic elastic modulus, viscosity friction coefficient and the like which change along with the environmental temperature. Other uncertainties, such as external disturbances, leaks, friction, etc., cannot be modeled accurately, and such nonlinearities are referred to as uncertainty nonlinearities because their nonlinear functions are unknown to be accurately described.
Optionally, the step of obtaining the error signal comprises:
acquiring an expected displacement signal and an actual displacement signal;
And calculating the error signal according to the expected displacement signal and the actual displacement signal.
Specifically, referring to fig. 3, fig. 3 is a schematic diagram of an electro-hydraulic servo system in an embodiment of the present invention, and as shown in fig. 3, an error signal may be calculated by using an obtained expected displacement signal and an actual displacement signal, and then the error signal is input into a finite time disturbance observer to obtain disturbance feedback.
Step S20, inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback;
further, the calculated error signal is input into a preset finite time disturbance observer to obtain disturbance feedback, the finite time disturbance observer is needed to be designed before the disturbance feedback, the finite time disturbance observer is used for accurately estimating the mismatching disturbance of the system based on the finite time disturbance observer theory, and the estimated disturbance is fed back into the model predictive controller to perform disturbance compensation.
Step S30, based on a preset model predictive controller, generating a target voltage signal according to the error signal and the disturbance feedback, and sending the target voltage signal to a servo valve so that the servo valve can adjust the opening of a valve port according to the target voltage signal.
Referring to fig. 4, fig. 4 is a schematic diagram of a model predictive control method of an electrohydraulic servo system based on a finite time disturbance observer in an embodiment of the present invention, as shown in fig. 4, a target voltage signal may be generated according to an error signal and disturbance feedback by a model predictive controller, and the obtained target voltage signal is input to a servo valve in fig. 3, so that the servo valve may adjust the opening of a valve port according to the target voltage signal, thereby controlling the amount of oil delivered.
Optionally, before generating the target voltage signal according to the error signal and the disturbance feedback based on the preset model predictive controller, a dynamic model of the double-rod hydraulic cylinder servo system is established according to the characteristics of the symmetrical double-rod valve control servo system, and the discretized state space expression of the hydraulic servo system is obtained by adopting approximate linearization and first-order difference discretization processing methods. And designing a model prediction controller with input constraint based on a discretized mathematical model, and converting a linear time-varying model prediction control optimization objective function solving problem with constraint into a Quadratic Programming (QP) solving problem.
In this embodiment, the error signal is obtained; inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback; and generating a target voltage signal according to the error signal and the disturbance feedback based on a preset model prediction controller, and sending the target voltage signal to a servo valve so that the servo valve can adjust the opening of a valve port according to the target voltage signal. By combining model predictive control with a finite-time disturbance observer, the controller can still ensure strong robustness and stability under the condition of input constraint and external disturbance of the servo control system, and the finite-time disturbance observer can perform online detection and real-time estimation on unknown disturbance and can quickly approximate the system and the mixed disturbance existing in the outside, so that the nonlinear control effect of the electrohydraulic servo system is improved.
Referring to fig. 5, fig. 5 is a flowchart illustrating a servo control method according to another exemplary embodiment of the present invention. Based on the embodiment shown in fig. 2, in this embodiment, before the step of generating the target voltage signal based on the error signal and the disturbance feedback by the predictive controller based on the preset model, the servo control method further includes:
step S01, establishing a dynamic model of a double-rod hydraulic cylinder servo system;
optionally, the step of establishing a dynamic model of the dual-rod hydraulic cylinder servo system includes:
and establishing a dynamic model of the double-rod hydraulic servo system according to the Newton's second law, the hydraulic cylinder inertial load dynamic equation and the hydraulic cylinder flow continuity equation.
Specifically, for the characteristics of the double-rod-outlet hydraulic servo system, according to Newton's second law, a hydraulic cylinder inertial load dynamics equation and a hydraulic cylinder flow continuity equation, a dynamic model of the double-rod-outlet hydraulic servo system is established:
wherein the method comprises the steps of
The simplified flow formula is:
the sign function sign (·) is defined as:
suppose 1 that the servo valve is symmetrical and matched, so k q1 ＝k q2 ＝k q The method comprises the steps of carrying out a first treatment on the surface of the The elastic modulus of hydraulic oil in two cavities of the actuator is the same, namely beta e1 ＝β e2 ＝β e The method comprises the steps of carrying out a first treatment on the surface of the The servo valve bandwidth is far higher than the system bandwidth, and the control input is assumed to be in proportional relation with the valve core displacement of the servo valve, so that the dynamic servo valve can be simplified to be a proportional link, x v ＝k i u, at this time s (x v ) =s (u). The electrohydraulic servo system works under the normal working condition, and the pressure at the two ends of the actuator meets 0<P r <P 1 <P s ，
0<P r <P 2 <P s 。
Simplifying equations (2) - (4) using hypothesis 1
In the middle of
Wherein: y is the displacement of the load, m is the mass of the load, P 1 And P 2 Respectively the pressure of two cavities of the hydraulic cylinder, A 1 ,A 2 For the effective working area of the piston rod, B represents the viscosity friction coefficient of the external load, A f Is the magnitude of the hydraulic cylinder coulomb friction,
S f representing a nonlinear coulomb friction shape function. A is that f S f Representing the approximated nonlinear coulomb friction inside the hydraulic cylinder, f representing the unmodeled dynamics and external disturbances. C (C) t Is the leakage coefficient of the hydraulic cylinder, Q 1 Oil supply flow for oil inlet cavity of hydraulic cylinder, Q 2 And oil return flow is conducted to an oil return cavity of the hydraulic cylinder. g is the total flow gain, +.>
The flow gains of the left end and the right end of the valve core displacement of the servo valve are respectively obtained. P (P) s Is the pressure of oil flowing into the servo valve, P 1 Is the oil pressure of an oil inlet of an oil cylinder, P 2 Is the oil pressure of the oil outlet of the oil cylinder. P (P) r Is the return oil pressure of the system, P r ≈0。w 1 ,w 2 The area gradients of the left end and the right end of the throttle hole of the valve core of the servo valve are respectively x v Is the servo spool displacement. ρ is the density of the hydraulic oil. u is the voltage value at two ends of the servo valve.
Defining state variables in connection with equations (1) - (6) 
The nonlinear dynamics equation of the electrohydraulic servo position system can be obtained as follows:
wherein:
the above kinetic equation is considered as a general nonlinear state space expression:
expanding the vicinity of the real-time state track of the nonlinear function f (x, u, t) into a Taylor series, and obtaining the method by only retaining a first-order term and ignoring a high-order term:
J f (x),J f (u) is the Jacobian matrix of f with respect to x and u, respectively. By subtracting the term from equation (10)
The state and control increment equation (11) is replaced by the state and control quantity to obtain:
and then, replacing the equation (12) with:
step S02, performing approximate linearization and first-order difference discretization on the dynamic model to obtain a discretized mathematical model;
further, a first order differential discrete process is used
A discrete state space expression is obtained:
in the middle of
T is sampling time, I 4×4 Is a unit vector of a fourth order; after the linearization and discretization treatment, A is obtained k ,B k The specific expression is:
wherein: x (k+1) represents the state value at time k+ 1, and is predicted from the current state and input by the nonlinear model.
Through the equations (7) to (14), the discrete linearization result of the prediction equation of the electrohydraulic servo system can be obtained as follows:
x(k+1)＝A k,t ·x(k)+B k,t u(k)+d k,t (15)
wherein a (k) =a k,t ,B(k)＝B k,t
Step S03, designing a model prediction controller with state constraint based on the discretized mathematical model.
Because the control quantity of the system is unknown, a control sequence in a control time domain is obtained by setting a proper optimization target and solving the optimization target. And designing a model prediction controller with input constraint based on the discretization linearization model, and converting the linear time-varying model prediction control optimization objective function solving problem with the constraint into a Quadratic Programming (QP) solving problem.
Setting up
A new state space expression can be obtained:
defining each matrix as:
further simplify
Wherein N is x N is the dimension of the state variable u To control variable dimension, N y Is the output variable dimension.
The prediction time domain of the system is N p Control the time domain to be N c The state quantity in the prediction time domain and the output quantity of the system can be calculated, and the output of the future time of the system is expressed in a matrix form:
Y(t)＝Ψ t ξ(t|t)+Θ t ΔU(t)+Γ t Φ t (17)
as can be seen from the above expression (17), both the state quantity and the output quantity in the prediction time domain can be calculated from the state quantity ζ (t|t) at the time of the system and the control increment Δu (t) in the control time domain. The prediction function in the model predictive control algorithm is implemented by equation (17).
In order to track the desired trajectory, the tracking performance of the controlled system is reflected by designing an objective function.
y ref (k+i|t),i＝1…N p Is the desired output quantity and,
ρ is a weight matrix. Wherein the first term is used for punishing the system in the prediction time domain N p In, predicting the deviation between the output quantity and the expected output quantity, and reflecting the rapid tracking capability of the system on the expected track; the second term is used for punishing the system in the control time domain N c The internal control increment size reflects the requirement of the system on the stable change of the control quantity; the third term is used for punishing the system in the control time domain N c The control quantity in the system reflects the requirement of the system on the control extremum.
The objective function (18) satisfies the following kinetic constraints:
x(k+1)＝A k，t ·(k)+B k，t ·u(k)+d k，t
y(k)＝C k x(k) (19)
the objective function (18) satisfies the time domain constraint condition under the control input limitation as follows:
converting the control input increment constraint into a form of lb < X < ub >:
wherein:
converting the control quantity constraint into the AX.ltoreq.b form since Δu (k+i) =u (k+i) -u (k+i-1), when i=0, there is
The control quantity constraint is thus written in matrix form: />
Wherein the method comprises the steps of
The expansion is carried out to obtain the following components:
in order to convert the optimization objective function solution problem with constraints into a quadratic programming solution problem, the following assumptions are made:
Order the
In->
Representing the kronetime sign.
Q e ＝diag([Q,…,Q]) NyNp×NyNp
R e ＝diag([R,…,R]) NuNc×NuNc
S e ＝diag([S,…,S]) NuNc×NuNc
Setting up
E(t)＝ψξ(k)+Γ t Φ t -Y ref (t)
Q(t)＝MΔ(t(t)+U(t-1)
Substitution of equations (19) - (24) into the optimization objective function (18) can result in:
setting up
Thus, the standard quadric form can be obtained as:
the above objective function is converted to a standard Quadratic Programming (QP) problem due to constraints. Solving a quadratic programming problem with inequality constraint conditions by adopting a numerical solution method:
wherein:
Feedback mechanism:
if the system state x (k) at the k moment and the control quantity u (k-1) at the previous moment are known, the control time domain N can be obtained by optimizing and solving in the control period c Within an optimal control delta sequence deltau * (t) then applying the first quantity of the sequence as the actual control quantity to the system:
the system executes the control quantity until the next moment, and at the new moment, the system predicts the output of the next time domain again according to the state information, and a new control increment sequence is obtained through an optimization process. And the method is repeated in a circulating way until the system finishes the control process.
According to the scheme, the dynamic model of the double-rod hydraulic cylinder servo system is built; performing approximate linearization and first-order differential discretization on the dynamic model to obtain a discretized mathematical model; model predictive controllers with state constraints are designed based on the discretized mathematical model. Aiming at the characteristics of the double-rod hydraulic servo system, a dynamic model of the double-rod hydraulic servo system is built according to Newton's second law, a hydraulic cylinder inertial load dynamic equation and a hydraulic cylinder flow continuity equation. And designing a model prediction controller with input constraint based on a discretized mathematical model, and converting a linear time-varying model prediction control optimization objective function solving problem with constraint into a Quadratic Programming (QP) solving problem.
Referring to fig. 6, fig. 6 is a flowchart illustrating a servo control method according to another exemplary embodiment of the present invention. Based on the embodiment shown in fig. 2, in this embodiment, before the step of inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback, the servo control method further includes:
step S04, designing a finite-time disturbance observer for each state and disturbance in the dynamics model based on the finite-time disturbance observer theory, wherein the finite-time disturbance observer is used for subsequent disturbance compensation.
Specifically, a finite-time disturbance observer is designed to estimate the disturbance forces existing in the external environment. Firstly, a mathematical model obtained by expanding a nominal system model by states is as follows:
definition of variables
The state estimates for the observers are respectively, so the finite time state observer is designed as follows: />
Discretizing the equation to obtain the following components:
wherein beta is i >0,(i＝0,...,5),α 1 ∈(0.5,1),α 2 ＝2α 1 -1,[x] α ＝sign(x)|x| α ,[z] α ＝sign(z)|z| α ，V t1 ＝V 01 +A 1 x 1 ,V t2 ＝V 02 -A 2 x 1 ，
Further, the step of designing the finite time disturbance observer for each state and disturbance in the model based on the finite time disturbance observer theory further comprises:
step S05, proving that the finite time disturbance observer converges in finite time through a Lyapunov function.
Specifically, the finite time disturbance observer is demonstrated to converge in a finite time:
combining equations (30) and (29) to subtract
The method can obtain:
wherein:
order the
Wherein->
For any given symmetric positive definite matrix Q, there is always a symmetric positive definite matrix p=p T The following equation N is satisfied T P+PN+Q＝0。
Lemma 1: assuming the presence of the Lyapunov function V (x), V (x 0 ) Is the initial value of V (x) for any real number lambda 1 >0,λ 2 >0,0<θ 1 <1,0<θ 2 <1,θ 1 <θ 2 The system will quickly converge to the near-origin field in a limited time
The finite time of convergence is
Further, finite time disturbance observer stability analysis:
selecting a positive Lyapunov function V 0 ＝ε T p epsilon, pair V 0 And (3) conducting derivation to obtain:
because of
Then->
The upper bound of (2) is:
wherein the method comprises the steps of
，
Suppose 2: assuming that all state vectors are bounded, systematic errors due to observers
Is also bounded. />
Based on hypothesis 1, and λ min (P)||ε||≤V 0 ≤λ max (P) |ε| the following inequality can be obtained
Adding the inequality equation sets to obtain:
wherein lambda is min (. Cndot.) and lambda max (. Cndot.) represents the maximum and minimum eigenvalues of the matrix (. Cndot.) and can be found in combination with inequality (32):
wherein:
λ 2 ＝(2F d2 +2F d3 +2F d4 +2M d )||P||λ min (P) -1/2 。
from the quotation 1, V can be derived 0 T in a finite time t Inner convergence to near origin neighborhood D t . The finite time disturbance observer therefore tends to stabilize.
According to the scheme, the finite-time disturbance observer is designed for each state and disturbance in the dynamic model based on the finite-time disturbance observer theory, is used for subsequent disturbance compensation, and is proved to converge in finite time through the Lyapunov function. The model predictive control algorithm with strong robustness and high tracking performance based on the electrohydraulic servo system of the limited-time disturbance observer is provided to solve the problems of uncertain nonlinear disturbance, constrained input and the like in the hydraulic servo system.
In addition, the embodiment of the invention also provides a servo control system, which comprises a finite time disturbance observer, a model predictive controller and a servo valve, wherein the finite time disturbance observer is used for calculating mismatching disturbance of the electrohydraulic servo system, and inputting calculated disturbance feedback to the model predictive controller so that the model predictive controller can generate a target voltage signal according to the acquired error signal and the disturbance feedback, and the target voltage signal is sent to the servo valve so that the servo valve can adjust the valve port opening according to the target voltage signal.
Specifically, an electrohydraulic servo system model predictive controller (FTDOMPC) based on limited time disturbance observation is provided in the embodiment of the invention, and the performance of the designed controller is verified through MATLAB simulation.
Inertial load parameter m=40 kg; viscous friction coefficient b=80n·s/m effective cross-sectional area of piston a=a 1 ＝A 2 ＝2×10 -4 m 2 The method comprises the steps of carrying out a first treatment on the surface of the Sum of two cavity volumes V t ＝2×10 -4 m 3 The method comprises the steps of carrying out a first treatment on the surface of the Oil supply pressure P s =7 Mpa; oil return pressure P r =0mpa; elastic modulus beta of oil e ＝2×10 8 Mpa; leakage coefficient C t ＝9×10 -11 m 3 s/Pa; the expected instruction for a given system is x 1d ＝0.2sin(2t)*(1-exp(-0.01t 3 ) Mm), the external disturbance force is d (t) =1220 sin (4pi t) (N). To testThe performance of the proposed controller was demonstrated, and a comparative experiment was performed with three controllers.
PID controller: proportional-integral-derivative controllers have been widely used in industry, and parameters obtained by parameter tuning are: k (K) p ＝20,K I ＝5,K D ＝3。
ESOMPC controller: the parameters of the predictive control algorithm based on the extended state observer model are as follows: predicting time domain N p Control time domain N =10 c =5, weight coefficient q=diag (2×10) 3 ,…2×10 3 ) 10×10 ，R＝[5×10 -4 ,…5×10 -4 ] 1×5 . Extended state observer parameters are
q 1 ＝1,q 2 ＝3200,q 3 ＝0.8,q 4 ＝0.8,q 5 ＝3.2×10 5 。
FTOMPC controller: the parameters of the predictive control algorithm based on the finite time disturbance observer model are as follows: predicting time domain N p Control time domain N =10 c =5, weight coefficient q=diag (2×10) 3 ,…2×10 3 ) 10×10 ，R＝[5×10 -4 ,…5×10 -4 ] 1×5 。
The finite time disturbance observer parameters are:
β 1 ＝0.1,β 2 ＝7.5,β 3 ＝800,β 4 ＝800,β 1 ＝8.3×10 4 ,α 1 ＝0.815,α 2 ＝0.63。
compared with the prior art, the invention provides the electrohydraulic servo system model predictive control method (FTDOMPC) based on the finite time observer, and the method of combining the Model Predictive Control (MPC) with the finite time disturbance observer ensures that the controller can still ensure strong robustness and stability under the condition of input constraint and external disturbance. Compared with an Extended State Observer (ESO), the Finite Time Disturbance Observer (FTDO) can perform online detection and real-time estimation on unknown disturbance, and can quickly approximate the mixed disturbance existing in a system and the outside.
Reference is made to the drawings7-12, fig. 7-12 are respectively a schematic diagram of a control law action effect first to a schematic diagram of a control law action effect sixth in the embodiment of the present invention, specifically, fig. 7 is a schematic diagram of a tracking process of a system output to an expected displacement instruction under the effect of an FTDOMPC controller designed by the present invention when an external interference force of the system is d (t) =1220 sin (4pi t) (N); FIG. 8 is a graph comparing displacement tracking errors of the system with time for the FTDOMPC controller, ESOMPC controller and PID controller designed in the present invention when the disturbance force outside the system is d (t) =1220 sin (4pi t) (N); FIG. 9 is a graph comparing displacement tracking error of the system with time for the FTDOMPC controller and ESOMPC designed in the present invention when the disturbance force outside the system is d (t) =1220 sin (4pi t) (N); FIG. 10 is a graph comparing the estimated time-varying external disturbance force with the FTDOMPC controller and ESOMPC controller designed by the present invention when the external disturbance force is d (t) =1220 sin (4pi t) (N); FIG. 11 shows the pressure p at the inlet of the system under the action of the FTDOMPC controller designed by the present invention when the disturbance force outside the system is d (t) =1220 sin (4pi t) (N) 1 And outlet pressure p 2 An estimated plot of time variation; FIG. 12 is a graph showing the change of input voltage at two ends of a servo valve with time under the action of an FTDOMPC controller designed by the present invention when the disturbance force outside the system is d (t) =1220 sin (4pi t) (N), and as shown in FIGS. 7-12, the electro-hydraulic servo model predictive control method (FTDOMPC) of the finite time observer has a better tracking effect on the expected displacement command and more accurate estimation of each state compared with the PID control and the electro-hydraulic servo model predictive control (ESOMPC) based on the extended state observer. The controller designed by the invention can obtain good control precision and can ensure the control precision requirement of the system.
Specifically, FIG. 7 illustrates the tracking effect of the FTDOMPC. Displacement error comparison diagrams under the action of three different controllers are shown in fig. 8 and 9, fig. 8 is a displacement error comparison diagram under the action of an ftdomc controller, an ESOMPC controller and a PID controller respectively, and as can be seen from fig. 8, the maximum displacement error under the action of the PID controller can reach 0.13mm, which is far greater than that of other two controllers. It can be seen from FIG. 9 that the maximum displacement of the ESOMPC controller is 4.1X10 -7 mm，Maximum displacement error of FTDOMPC controller is 8×10 -8 mm. Thus ftdomc controllers may perform better than ESOMPC controllers and PID controllers. FIG. 10 reflects an estimate of external interference by both the ESOMPC controller and the FTDOMPC controller, and from a comparison of both, it can be seen that the estimate of external interference by the FTDOMPC controller is more closely to the actual external interference force. FIG. 11 shows the oil pressure p of the FTDOMPC controller for the left and right chambers 1 And p 2 It can be seen that the complete oil pressure of the left and right chambers can be estimated by the ftdomc controller. FIG. 12 shows control inputs across an electro-hydraulic servo valve, and it can be seen that the FTDOMPC controller always limits the control input voltage delta across the servo valve to between 15V.
In addition, an embodiment of the present invention further provides a servo control device, where the servo control device includes:
the acquisition module is used for acquiring an error signal;
the feedback module is used for inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback;
the control module is used for predicting the controller based on a preset model, generating a target voltage signal according to the error signal and the disturbance feedback, and sending the target voltage signal to the servo valve so that the servo valve can adjust the opening of the valve port according to the target voltage signal.
The principle and implementation process of the servo control in this embodiment are referred to the above embodiments, and are not described herein.
In addition, the embodiment of the invention also provides a terminal device, which comprises a memory, a processor and a servo control program stored on the memory and capable of running on the processor, wherein the servo control program realizes the steps of the servo control method when being executed by the processor.
Because the servo control program is executed by the processor and adopts all the technical schemes of all the embodiments, the servo control program has at least all the beneficial effects brought by all the technical schemes of all the embodiments and is not described in detail herein.
In addition, the embodiment of the invention also provides a computer readable storage medium, wherein a servo control program is stored on the computer readable storage medium, and the servo control program realizes the steps of the servo control method when being executed by a processor.
Because the servo control program is executed by the processor and adopts all the technical schemes of all the embodiments, the servo control program has at least all the beneficial effects brought by all the technical schemes of all the embodiments and is not described in detail herein.
Compared with the prior art, the servo control method, the servo control system, the servo control device, the terminal equipment and the storage medium provided by the embodiment of the invention acquire error signals; inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback; and generating a target voltage signal according to the error signal and the disturbance feedback based on a preset model prediction controller, and sending the target voltage signal to a servo valve so that the servo valve can adjust the opening of a valve port according to the target voltage signal. By combining model predictive control with a finite-time disturbance observer, the controller can still ensure strong robustness and stability under the condition of input constraint and external disturbance of the servo control system, and the finite-time disturbance observer can perform online detection and real-time estimation on unknown disturbance and can quickly approximate the system and the mixed disturbance existing in the outside, so that the nonlinear control effect of the electrohydraulic servo system is improved.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or system. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or system that comprises the element.
The foregoing embodiment numbers of the present application are merely for describing, and do not represent advantages or disadvantages of the embodiments.
From the above description of the embodiments, it will be clear to those skilled in the art that the above-described embodiment method may be implemented by means of software plus a necessary general hardware platform, but of course may also be implemented by means of hardware, but in many cases the former is a preferred embodiment. Based on such understanding, the technical solution of the present application may be embodied essentially or in a part contributing to the prior art in the form of a software product stored in a storage medium (e.g. ROM/RAM, magnetic disk, optical disk) as above, including several instructions for causing a terminal device (which may be a mobile phone, a computer, a server, a controlled terminal, or a network device, etc.) to perform the method of each embodiment of the present application.
The foregoing description is only of the preferred embodiments of the present invention, and is not intended to limit the scope of the invention, but rather is intended to cover any equivalents of the structures or equivalent processes disclosed herein or in the alternative, which may be employed directly or indirectly in other related arts.
Claims (10)
1. A servo control method, characterized in that the servo control method comprises the steps of:
acquiring an error signal;
inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback;
and generating a target voltage signal according to the error signal and the disturbance feedback based on a preset model prediction controller, and sending the target voltage signal to a servo valve so that the servo valve can adjust the opening of a valve port according to the target voltage signal.
2. The servo control method of claim 1 wherein the step of acquiring an error signal comprises:
acquiring an expected displacement signal and an actual displacement signal;
and calculating the error signal according to the expected displacement signal and the actual displacement signal.
3. The servo control method of claim 1 wherein the step of generating a target voltage signal from the error signal and the disturbance feedback based on a preset model predictive controller further comprises:
establishing a dynamic model of a double-rod hydraulic cylinder servo system;
performing approximate linearization and first-order differential discretization on the dynamic model to obtain a discretized mathematical model;
Model predictive controllers with state constraints are designed based on the discretized mathematical model.
4. The servo control method of claim 2 wherein said step of inputting said error signal to a predetermined finite time disturbance observer to obtain a disturbance feedback further comprises, prior to said step of:
based on the finite-time disturbance observer theory, a finite-time disturbance observer is designed for each state and disturbance in the dynamics model for subsequent disturbance compensation.
5. The servo control method of claim 1 wherein the step of designing a finite time disturbance observer for each state and disturbance in the model based on finite time disturbance observer theory further comprises:
the limited-time perturbation observer is proved to converge in a limited time by means of the lyapunov function.
6. A servo control method as recited in claim 3 wherein said step of modeling the dynamics of a dual rod hydraulic cylinder servo comprises:
and establishing a dynamic model of the double-rod hydraulic servo system according to the Newton's second law, the hydraulic cylinder inertial load dynamic equation and the hydraulic cylinder flow continuity equation.
7. The electrohydraulic servo system is characterized by comprising a finite time disturbance observer, a model predictive controller and a servo valve, wherein the finite time disturbance observer is used for calculating unmatched disturbance of the electrohydraulic servo system, and inputting calculated disturbance feedback to the model predictive controller so that the model predictive controller can generate a target voltage signal according to an acquired error signal and the disturbance feedback, and the target voltage signal is sent to the servo valve so that the servo valve can adjust the valve port opening according to the target voltage signal.
8. A servo control apparatus, characterized in that the servo control apparatus comprises:
the acquisition module is used for acquiring an error signal;
the feedback module is used for inputting the error signal into a preset finite-time disturbance observer to obtain disturbance feedback;
the control module is used for predicting the controller based on a preset model, generating a target voltage signal according to the error signal and the disturbance feedback, and sending the target voltage signal to the servo valve so that the servo valve can adjust the opening of the valve port according to the target voltage signal.
9. A terminal device, characterized in that it comprises a memory, a processor and a servo control program stored on the memory and executable on the processor, which servo control program, when executed by the processor, implements the steps of the servo control method according to any of claims 1-6.
10. A computer readable storage medium, characterized in that the computer readable storage medium has stored thereon a servo control program, which when executed by a processor, implements the steps of the servo control method according to any of claims 1-6.
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