CN108107728B - Electro-hydraulic position servo system control method based on interference compensation - Google Patents

Electro-hydraulic position servo system control method based on interference compensation Download PDF

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CN108107728B
CN108107728B CN201711349283.0A CN201711349283A CN108107728B CN 108107728 B CN108107728 B CN 108107728B CN 201711349283 A CN201711349283 A CN 201711349283A CN 108107728 B CN108107728 B CN 108107728B
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李旭东
陈雄
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Nanjing University of Science and Technology
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Abstract

The invention discloses an electro-hydraulic position servo system control method based on interference compensation, which belongs to the field of electro-hydraulic position servo control and comprises the following steps: establishing a mathematical model of the electro-hydraulic position servo system; establishing a mathematical model of the disturbance term observer; designing an electro-hydraulic position servo system controller based on interference compensation; the stability is proved by applying the Lyapunov stability theory. The method estimates and compensates the matching and non-matching disturbance in the electro-hydraulic servo system by a model compensation method, and can effectively improve the system performance; the interference estimation method is convenient and easy to implement, is beneficial to actual production implementation, and verifies the effectiveness of the controller by comparing simulation results.

Description

Electro-hydraulic position servo system control method based on interference compensation
Technical Field
The invention relates to the field of electro-hydraulic position servo systems, in particular to an electro-hydraulic position servo system control method based on interference compensation.
Background
The electro-hydraulic servo system has the outstanding advantages of large transmission torque, high transmission efficiency and the like, and is widely applied to various important industrial fields, such as engineering machinery, machine tools, aerospace and the like. With the rapid development of these fields, the position tracking performance of the electro-hydraulic system is more and more required, and the performance of the system is closely related to the design of the controller. The electrohydraulic servo system is a typical nonlinear system, and many modeling uncertainties including parameter uncertainties and unmodeled disturbances are encountered in the process of designing a controller, wherein the disturbance entering the system through the same channel as the control input of the controller is called matched disturbance, and the disturbance entering the system through different channels as unmatched disturbance. These modeling uncertainties can severely degrade the desired control performance, resulting in less than ideal control accuracy, making the design of the controller difficult.
In the face of these model uncertainties in electro-hydraulic servo systems, numerous scholars have proposed corresponding controller design methods. The problem of parameter uncertainty in the design process of the controller is solved by introducing a parameter adaptive method. Other unmodeled interference problems in the controller design process are overcome by a robust control method. However, in the robust control method, the interference of the interference on the control performance is mainly suppressed by designing the gain of the controller, and when the system is faced with a large disturbance, the gain of the controller must be increased to ensure the stability of the system, which may deteriorate the tracking performance of the system.
The unmodeled interference is observed by a disturbance observer, and then the interference is compensated by utilizing the interference estimation value in the design process of the controller, so that a good effect can be achieved. The stability of the system is ensured, and the position tracking performance of the system is improved. Most of the existing interference observers can only observe matched disturbance, but cannot observe the matched disturbance. Some observers can observe two kinds of disturbances at the same time, but the design process is very complicated, and engineering practice is not facilitated. Therefore, a simple and feasible interference observation compensation control method for the electro-hydraulic position servo system, which can observe matched and unmatched disturbance simultaneously, is urgently needed.
Disclosure of Invention
The invention aims to provide an electro-hydraulic position servo system control method based on interference compensation, so that matching and non-matching interference can be compensated, and the control precision of the electro-hydraulic servo system is improved.
The technical solution for realizing the purpose of the invention is as follows: an electro-hydraulic position servo system control method based on interference compensation comprises the following steps:
step 1, establishing a mathematical model of an electro-hydraulic position servo system;
step 2, establishing a mathematical model of the disturbance term observer;
step 3, designing an electro-hydraulic position servo system controller based on interference compensation;
and 4, carrying out stability verification by using the Lyapunov stability theory.
Compared with the prior art, the invention has the following remarkable advantages: (1) estimating and compensating matching and non-matching disturbance existing in the electro-hydraulic servo system by a model compensation method; (2) the interference estimation method is very convenient and easy to implement, and is beneficial to actual production implementation.
Drawings
FIG. 1 is a diagram of an electro-hydraulic position servo system model.
Fig. 2 is a diagram of position command signals.
Fig. 3 is a graph of tracking error over time for two controllers.
FIG. 4 shows disturbance d under the action of the controller designed by the present invention1And estimating an error map.
FIG. 5 shows disturbance d under the action of the controller designed by the present invention2And estimating an error map.
FIG. 6 is a graph of the control input of a controller designed according to the present invention as a function of time.
Detailed Description
The invention provides a simple and easy-to-implement method for designing the interference observer of the electro-hydraulic servo system, so that matching and non-matching interference can be compensated, and the control precision of the electro-hydraulic servo system is improved.
An electro-hydraulic position servo system control method based on interference compensation comprises the following steps:
step 1, establishing a mathematical model of the electro-hydraulic position servo system, wherein according to Newton's second law, a motion equation of the electro-hydraulic position servo system is as follows:
Figure BDA0001509924790000021
in the formula (1), m is an inertial load parameter, y is inertial load displacement,
Figure BDA0001509924790000022
and
Figure BDA0001509924790000023
respectively inertial load velocity and acceleration, PLTo load pressure, DmIs the displacement of the hydraulic motor, B is the coefficient of viscous friction, FeThe uncertainty items of external interference and unmodeled friction and the like.
Wherein the load pressure PLCan be expressed as
Figure BDA0001509924790000024
V in formula (2)tIs the total volume of the hydraulic cylinder; beta is aeThe effective elastic modulus of the hydraulic oil; ctIs the internal leakage coefficient;
Figure BDA0001509924790000025
representing the total uncertainty present in equation (2). QLFor load flow, the expression is:
Figure BDA0001509924790000031
k in formula (3)tIs the total flow gain, PsIs the oil supply pressure; sign (#) is a sign function, and a specific expression is
Figure BDA0001509924790000032
Defining the state variables of the system as
Figure BDA0001509924790000033
The state equation of the system is:
Figure BDA0001509924790000034
wherein
Figure BDA0001509924790000035
In the formula (6), δ1And delta2Is a known constant.
And 2, establishing a mathematical model of the disturbance term observer.
Figure BDA0001509924790000036
In the formula (7), the first and second groups,
Figure BDA0001509924790000037
as interference term d1Is determined by the estimated value of (c),
Figure BDA0001509924790000038
as interference term d2Estimate of (a) ("lambda1And λ2Is the gain of the observer. p is a radical of1And p2Variables were designed for the observer's assistance.
Figure BDA0001509924790000039
And
Figure BDA00015099247900000310
are each p1And p2A derivative value with respect to time;
from the equations (5) and (7), it can be found
Figure BDA00015099247900000311
In the formula (8), e1As interference term d1Observation error of (e)2As interference term d2The observation error of (2).
And 3, designing the controller of the electro-hydraulic position servo system based on interference compensation.
The goal of the controller design is to make the position output x of the motor position servo system1Tracking as accurately as possible the position instruction x desired to be tracked1d。
The variables are defined as follows
Figure BDA0001509924790000041
Wherein alpha is2And alpha3Is a virtual control quantity;
defining a semi-positive definite function V1As follows
Figure BDA0001509924790000042
Derivation of V1Is expressed as
Figure BDA0001509924790000043
Wherein
Figure BDA0001509924790000044
The command is tracked for the desired speed, so that the virtual control quantity alpha can be designed2Is composed of
Figure BDA0001509924790000045
In the formula (12), k1The gain is designed for the controller.
According to the formulae (11) and (12), it is possible to obtain
Figure BDA0001509924790000046
Defining a semi-positive definite function V2As follows
Figure BDA0001509924790000047
Derivation of V2Is expressed as
Figure BDA0001509924790000048
Thereby, the virtual control quantity alpha can be designed3Is composed of
Figure BDA0001509924790000049
In the formula (16), k2The gain is designed for the controller.
From the equations (15) and (16), it is found that
Figure BDA0001509924790000051
Defining a semi-positive definite function V3As follows
Figure BDA0001509924790000052
Derivation of V3Is expressed as
Figure BDA0001509924790000053
So that the controller output u can be designed to be
Figure BDA0001509924790000054
Wherein
Figure BDA0001509924790000055
From the equations (19), (20) and (21), it is found that
Figure BDA0001509924790000056
And 4, analyzing the stability of the electro-hydraulic position servo system:
according to the stability analysis of the system in the control theory:
Figure BDA0001509924790000057
wherein λ is the minimum feature root of matrix Λ
Figure BDA0001509924790000061
The stability is proved by applying the Lyapunov stability theory, and the stability can be obtained according to a formula (24):
Figure BDA0001509924790000062
so that the system can be made to be bounded stable.
The present invention will be described in detail with reference to the following examples and drawings.
Examples
The values of the parameters of the motor servo system are as follows:
m＝30kg，B＝10N·m·rad-1·s-1，Vt＝7.962e-5m3，βe＝700e6pa，Dm＝9e-4m2，Ct＝3e-12m3/s/pa，kt＝1.18e-8m3/s/V/pa-1/2，Ps＝10e6pa。
to verify the control performance of the controller, the controller proposed by the present invention is named NRDC controller, and the controller used for comparison is named FLC controller, and the two controllers have the same expression but different parameters. The FLC controller does not have an interference compensation item for interference.
NRDC controller parameter k1＝1000，k2＝2000，k3＝1000，λ1＝100，λ2＝2000。
FLC controller parameter k1＝1000，k2＝2000，k3＝1000，λ1＝0，λ2＝0。
Position command signal x1d(t)＝0.04sin(t)·[1-exp(-0.01t3)]
FIG. 2 is a graph of a position command signal and FIG. 3 is a graph of tracking error versus time for two controllers, and it can be seen that the controller designed by the present invention is significantly superior to the FLC controller. FIG. 4 shows disturbance d under the action of the controller designed by the present invention1Fig. 5 shows the interference d under the action of the controller designed according to the present invention2And estimating an error map. According to the figure4 and 5, it can be seen that the estimation performance of the disturbance observer is excellent. The superior performance of a controller designed according to the present invention in the face of interference is fully illustrated with respect to fig. 3, 4 and 5. Fig. 6 is a time-varying control input curve of the controller designed by the present invention, and it can be seen from the graph that the control input signal obtained by the present invention is continuous, which is beneficial to the application in engineering practice.

Claims (1)

1. An electro-hydraulic position servo system control method based on interference compensation is characterized by comprising the following steps:
step 1, establishing a mathematical model of the electro-hydraulic position servo system, wherein according to Newton's second law, a motion equation of the electro-hydraulic position servo system is as follows:
Figure FDA0002799559940000011
in the formula (1), m is an inertial load parameter, y is inertial load displacement,
Figure FDA0002799559940000012
and
Figure FDA0002799559940000013
respectively inertial load velocity and acceleration, PLTo load pressure, DmIs the displacement of the hydraulic motor, B is the coefficient of viscous friction, FeFriction uncertainty terms for external disturbances and unmodeled;
wherein the load pressure PLIs expressed as
Figure FDA0002799559940000014
V in formula (2)tIs the total volume of the cylinder, betaeIs the effective elastic modulus of hydraulic oil, CtIn order to be the internal leakage coefficient,
Figure FDA0002799559940000015
representing the total uncertainty, Q, present in equation (2)LFor load flow, the expression is:
Figure FDA0002799559940000016
k in formula (3)tIs the total flow gain, PsFor supply pressure, u represents the output signal of the controller, sign (#) is a sign function, and the specific expression is
Figure FDA0002799559940000017
Defining the state variables of the system as
Figure FDA0002799559940000018
The state equation of the system is:
Figure FDA0002799559940000019
wherein
Figure FDA0002799559940000021
In the formula (6), δ1And delta2Is a known constant;
step 2, establishing a mathematical model of the disturbance term observer; the method specifically comprises the following steps:
mathematical model for establishing disturbance term observer
Figure FDA0002799559940000022
In the formula (7), the first and second groups,
Figure FDA0002799559940000023
as interference term d1Is determined by the estimated value of (c),
Figure FDA0002799559940000024
as interference term d2Estimate of (a) ("lambda1And λ2For the gain of the observer, p1And p2For the auxiliary design variables of the observer,
Figure FDA0002799559940000025
and
Figure FDA0002799559940000026
are each p1And p2A derivative value with respect to time;
from the equations (5) and (7), it can be found
Figure FDA0002799559940000027
In the formula (8), e1As interference term d1Observation error of (e)2As interference term d2The observation error of (2);
step 3, designing an electro-hydraulic position servo system controller based on interference compensation; the method specifically comprises the following steps:
the variables are defined as follows
Figure FDA0002799559940000028
Wherein alpha is2And alpha3As a virtual control quantity, x1dA position instruction for a desired tracking;
defining a semi-positive definite function V1As follows
Figure FDA0002799559940000029
Derived from the aboveV1Is expressed as
Figure FDA0002799559940000031
Wherein
Figure FDA0002799559940000032
The command is tracked for the desired speed, and a virtual control quantity alpha is designed accordingly2Is composed of
Figure FDA0002799559940000033
In the formula (12), k1Designing a gain for the controller;
according to the formulae (11) and (12), it is possible to obtain
Figure FDA0002799559940000034
Defining a semi-positive definite function V2As follows
Figure FDA0002799559940000035
Derivation of V2Is expressed as
Figure FDA0002799559940000036
Thereby designing a virtual control quantity alpha3Is composed of
Figure FDA0002799559940000037
In the formula (16), k2Designing a gain for the controller;
from the equations (15) and (16), it is found that
Figure FDA0002799559940000038
Defining a semi-positive definite function V3As follows
Figure FDA0002799559940000039
Derivation of V3Is expressed as
Figure FDA00027995599400000310
So that the controller output u can be designed to be
Figure FDA00027995599400000311
Wherein
Figure FDA00027995599400000312
From the equations (19), (20) and (21), it is found that
Figure FDA0002799559940000041
Wherein k is3Is a controller parameter;
step 4, carrying out stability verification by using the Lyapunov stability theory; the method specifically comprises the following steps:
according to the stability analysis of the system in the control theory:
Figure FDA0002799559940000042
wherein λ is the minimum feature root of matrix Λ
Figure FDA0002799559940000043
The stability is proved by applying the Lyapunov stability theory, and the stability can be obtained according to a formula (24):
Figure FDA0002799559940000044
so that the system can be made to be bounded stable.
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