CN109324503B - Multilayer neural network motor system control method based on robust integration - Google Patents

Multilayer neural network motor system control method based on robust integration Download PDF

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CN109324503B
CN109324503B CN201810990916.4A CN201810990916A CN109324503B CN 109324503 B CN109324503 B CN 109324503B CN 201810990916 A CN201810990916 A CN 201810990916A CN 109324503 B CN109324503 B CN 109324503B
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姚志凯
姚建勇
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Abstract

The invention provides a multilayer neural network motor system control method based on robust integration, which comprises the following steps: step 1, establishing a mathematical model of a motor system; step 2, designing a multilayer neural network controller of robust integration; and 3, performing stability verification by using a Lyapunov stability theory, and obtaining a semi-global asymptotic stable result of the system by using a median theorem.

Description

Multilayer neural network motor system control method based on robust integration
Technical Field
The invention relates to a motor servo control technology, in particular to a multilayer neural network motor system control method based on robust integration.
Background
The motor servo system has the outstanding advantages of fast response, convenient maintenance, high transmission efficiency, convenient energy acquisition and the like, and is widely applied to various important fields, such as robots, machine tools, electric automobiles and the like. With the rapid development of the modern control engineering field, the requirement on the tracking performance of the motor servo system is higher and higher, but how to design the controller to ensure the high performance of the motor servo system is still a difficult problem. This is because the motor servo system is a typical non-linear system and is subject to many modeling uncertainties (e.g., unmodeled disturbances, non-linear friction, etc.) during the design of the controller, which may destabilize or reduce the order of the controller designed with the system nominal model.
Many efforts have been made to control the non-linearity of the servo system of the motor. For example, a feedback linearization control method can ensure the high performance of the system, but the premise is that the established mathematical model is very accurate, and all nonlinear dynamics are known; in order to solve the problem of modeling uncertainty, an adaptive robust control method is provided, which can make the tracking error of a motor servo system obtain a consistent and final bounded result under the condition of the existence of modeling uncertainty, and if high tracking performance is to be obtained, the tracking error must be reduced by improving feedback gain; also, the integral robust control method (RISE) can effectively solve the problem of modeling uncertainty, and can obtain continuous control input and performance of asymptotic tracking. However, the value of the feedback gain of the control method is closely related to the modeling uncertainty, once the modeling uncertainty is large, a high-gain feedback controller is obtained, which is not allowed in engineering practice; the sliding mode control method can also enable a motor servo system to obtain the performance of asymptotic tracking under the condition that modeling uncertainty exists, but a discontinuous controller designed by the method is easy to cause the problem of flutter of a sliding mode surface, so that the tracking performance of the system is deteriorated. In summary, the disadvantages of the existing control method of the motor servo system mainly include the following points:
one, neglecting system modeling uncertainty. Modeling uncertainty of the motor servo system includes non-linear friction and unmodeled disturbances, among others. Friction is one of the main sources of damping of a motor servo system, and adverse factors such as stick-slip motion and limit ring oscillation caused by the existence of the friction have important influence on the performance of the system. In addition, the actual motor servo system is interfered by external load, and if not considered, the tracking performance of the system is deteriorated;
and secondly, high-gain feedback. Many current control methods suffer from high gain feedback, which reduces tracking errors by increasing the feedback gain. However, problems with high frequency dynamics and measurement noise caused by high gain feedback will affect system tracking performance.
Disclosure of Invention
The invention aims to provide a multilayer neural network motor system control method based on robust integration, which comprises the following steps:
step 1, establishing a mathematical model of a motor system;
step 2, designing a multilayer neural network controller of robust integration;
and 3, performing stability verification by using a Lyapunov stability theory, and obtaining a semi-global asymptotic stable result of the system by using a median theorem.
Compared with the prior art, the invention has the following remarkable advantages: the method effectively solves the problem of high-gain feedback existing in the traditional robust integral control method, and obtains better tracking performance. The simulation result verifies the effectiveness of the test paper.
The invention is further described below with reference to the accompanying drawings.
Drawings
Fig. 1 is a schematic diagram of the motor system of the present invention.
FIG. 2 is a schematic diagram of a hydraulic system adaptive robust low-frequency learning control method.
Fig. 3 is a schematic diagram of the input u of the system under the action of an adaptive robust controller.
FIG. 4 is a schematic diagram of the position tracking of the system output to the desired command under the action of an adaptive robust controller.
Fig. 5 is a comparison of the tracking error of the method proposed by this patent with other methods.
Detailed Description
The invention relates to a robust integration-based multilayer neural network control method, which comprises the following steps of:
step 1, establishing a mathematical model of a hydraulic system;
(1.1) according to Newton's second law, the motion equation of the motor position servo system is as follows:
Figure GDA0001876846020000021
in the formula (1), m is an inertial load parameter, kiThe torque amplification factor, B the viscous friction factor,
Figure GDA0001876846020000022
the method comprises the following steps that uncertainty items of friction modeling errors and external interference are included, y is displacement of an inertial load, u is control input of a system, and t is a time variable;
(1.2) defining state variables:
Figure GDA0001876846020000023
equation of motion (1) is converted to an equation of state:
Figure GDA0001876846020000031
in the formula (2), phi is Bx2/m，f(x1,x2)@f(x1,x2,t)-d(t)，g@Ki/m，S@f-fdWherein f isdIndicating that the function is only related to the system instruction and the derivative of the instruction, d (t) @ f (t)/m is the concentrated disturbance of the system, f (x)1,x2T) is as described above
Figure GDA0001876846020000032
x1Representing the displacement, x, of the inertial load2Representing the velocity of the inertial load.
For the controller design, assume the following:
assume that 1: system interference d (t) and its derivatives are bounded
|d(t)|≤δ1,|d&(t)|≤δ2 (3)
Wherein delta1,δ2Is a known normal number.
Assume 2: desired position trajectory xd∈C3And is bounded.
Properties 1: f can be represented by three layers of neural networks according to the capability of the multilayer neural network to have any smooth function after all
Figure GDA0001876846020000033
In the formula
Figure GDA0001876846020000034
V∈R3×10Is bounded, W ∈ R11Also bounded, the activation function σ (-) can be a derivable function such as a sigmoid function, tanh function, etc., ε (-) is the reconstruction error of the function,
from (4) to obtain
Figure GDA0001876846020000035
Here, the
Figure GDA0001876846020000036
Recall that the parameter estimate to be designed, the error between the output estimate and the true parameter is defined as
Figure GDA0001876846020000037
The error between the output layers is defined as
Figure GDA0001876846020000038
Step 2, designing a self-adjusting controller, comprising the following steps:
(2.1) definition of e1＝x1-x1dAs a tracking error of the system, x1dIs a position command that the system expects to track and that is continuously differentiable in three orders, according to the first equation in equation (2)
Figure GDA0001876846020000039
Selecting x2For virtual control, let equation
Figure GDA00018768460200000310
Tends to a stable state; let α be the expected value of the virtual control, α and the real state x2Has an error of e2＝α-x2To e is aligned with1The derivation can be:
Figure GDA0001876846020000041
designing a virtual control law:
Figure GDA0001876846020000042
in the formula (5), k1If > 0 is adjustable gain, then
Figure GDA0001876846020000043
Due to e1(s)＝G(s)e2(s) wherein G(s) is 1/(s + k)1) Is a stable transfer function when e2When going to 0, e1And necessarily tends to 0. So in the next design, e will be2Tending to 0 as the primary design goal.
To e2Derivation yields (10):
Figure GDA0001876846020000044
defined in the following auxiliary functions
Figure GDA0001876846020000045
k2>0 is the adjustable feedback gain of the system
The expression of r can be found as
Figure GDA0001876846020000046
(2.2) according to equation (13), the model-based controller may be designed to:
Figure GDA0001876846020000047
k in formula (14)rFor positive feedback gain, uaFor model-based compensation terms, usIs a robust control law and in which us1For a linear robust feedback term, us2The nonlinear robust term is used for overcoming modeling uncertainty and the influence of interference on system performance. In formula (13), r is derived by substituting formula (14):
Figure GDA0001876846020000051
equation (15) can be written as
Figure GDA0001876846020000052
In the formula
Figure GDA0001876846020000053
Lemma 1. according to the median theorem
Figure GDA0001876846020000054
Wherein
z(t):＝[e1,e2,r]T (19)
ρ (| z |) is the non-attenuating function.
N:＝Nd+NB (20)
Figure GDA0001876846020000055
NB:＝NB1+NB2 (22)
Figure GDA0001876846020000056
Figure GDA0001876846020000057
Figure GDA0001876846020000058
Figure GDA0001876846020000059
Is a positive number.
(2.3) based on the Lyapunov stability proving process, the online parameter adaptive rate of the neural network parameters can be obtained:
Figure GDA00018768460200000510
Figure GDA0001876846020000061
step 3, the stability of the hydraulic system is proved by applying the Lyapunov stability theory, and the global asymptotic stability result of the system is obtained by applying the Barbalt theorem, which is concretely as follows:
introduce the following functions
Figure GDA0001876846020000062
Figure GDA0001876846020000063
Selecting
Figure GDA0001876846020000064
Figure GDA0001876846020000065
It can be demonstrated that P (t) ≧ 0.
Figure GDA0001876846020000071
Wherein
Figure GDA0001876846020000072
The obtained phi (t) is more than or equal to 0.
The lyapunov function is defined as follows:
Figure GDA0001876846020000073
defining functions
Figure GDA0001876846020000074
The lyapunov stability theory is used for stability verification, and the median theorem is used for obtaining the semi-global asymptotic stability result of the system, so that the gain k is adjusted1、k2、krAnd gamma1、Γ2The tracking error of the system tends to zero under the condition that the time tends to be infinite.
Figure GDA0001876846020000075
Figure GDA0001876846020000076
Selecting a lower positive definite matrix
Figure GDA0001876846020000077
Satisfy the requirement of
Figure GDA0001876846020000078
Therefore, the designed controller meets the condition that the tracking error of the system tends to zero under the condition that the time tends to be infinite in the following convergence domain,
Figure GDA0001876846020000079
the robust integral multilayer neural network control principle schematic diagram of the motor system is shown in FIG. 2.
Examples
The motor position servo system parameters are inertia load parameters: m is 0.02 kg; a viscous friction coefficient B of 10N · m · s/°; coefficient of moment amplification ki6N/V; time varying external interference
Figure GDA0001876846020000081
The position command that the system expects to track is a sinusoidal command as shown in fig. 4, with the time-varying curves of commanded velocity and acceleration also given.
Comparing simulation results: multi-layer neural network controller (NNRISE) parameter selection based on robust integration k1＝300；k2100; β 60; PID controller parameter selection: k is a radical ofP＝1699；kI＝13097；kD＝0。
The PID controller parameter selection steps are as follows: firstly, a set of controller parameters is obtained through a PID parameter self-tuning function in Matlab under the condition of neglecting the nonlinear dynamics of a motor servo system, and then the nonlinear dynamics of the system is adjustedAnd then, fine tuning is carried out on the obtained self-tuning parameters so that the system obtains the optimal tracking performance. k is a radical ofDThe reason for taking zero is that in the engineering practice, it is possible to avoid generating speed measurement noise, which affects the performance of the system, so that a PI controller is actually obtained.
The controller has the following effects: FIG. 4 shows the system angle tracking error under the NNRISE controller, and FIG. 5 shows the curve comparison of the system tracking error with time under the effect of the PID controller RISE and the NNRISE controller.

Claims (2)

1. A multi-layer neural network motor system control method based on robust integration is characterized by comprising the following steps:
step 1, establishing a mathematical model of a motor system;
step 2, designing a multilayer neural network controller of robust integration;
step 3, stability verification is carried out by applying the Lyapunov stability theory, and a semi-global asymptotic stability result of the system is obtained by applying the median theorem;
the motion equation of the mathematical model motor position servo system of the motor system in the step 1 is as follows:
Figure FDA0003367680720000011
in the formula (1), m is an inertial load parameter, kiThe torque amplification factor, B the viscous friction factor,
Figure FDA0003367680720000012
the method comprises the following steps that uncertainty items of friction modeling errors and external interference are included, y is displacement of an inertial load, u is control input of a system, and t is a time variable;
converting the equation of motion of equation (1) into an equation of state:
Figure FDA0003367680720000013
variable of state
Figure FDA0003367680720000018
φ＝Bx2/m，
Figure FDA0003367680720000014
Figure FDA0003367680720000015
Wherein f isdIndicating that the function is related only to the system command and the derivative of the command,
Figure FDA0003367680720000016
is the concentrated interference of the system, f (x)1,x2T) is as described above
Figure FDA0003367680720000019
x1Representing the displacement, x, of the inertial load2Representing the velocity, x, of the inertial load1dIs a position instruction that the system expects to track and the three orders of the instruction are sequentially differentiable;
for the controller design, assume the following:
assume that 1: system interference d (t) and its derivatives are bounded
Figure FDA0003367680720000017
Wherein delta1,δ2Is a known normal number;
assume 2: desired position trajectory xd∈C3And is bounded;
properties 1: f can be represented by a three-layer neural network according to the capability of the multilayer neural network to have any smooth function
Figure FDA0003367680720000021
In the formula
Figure FDA0003367680720000022
V∈R3×10Is bounded, W ∈ R11The method is bounded, R represents a constant, an activation function sigma (-) is a sigmoid function or a tanh function, and epsilon (-) is a reconstruction error of the function;
step 2, designing a robust integrated multilayer neural network controller, comprising the following steps:
step 2.1, define e1＝x1-x1dAs a tracking error of the system, x1dIs a position command that the system expects to track and that is continuously differentiable in three orders, according to the first equation in equation (2)
Figure FDA0003367680720000023
Selecting x2For virtual control, let equation
Figure FDA0003367680720000024
Tends to a stable state;
let α be the expected value of the virtual control, α and the real state x2Has an error of e2＝α-x2；
To e1The derivation can be:
Figure FDA0003367680720000025
designing a virtual control law:
Figure FDA0003367680720000026
in the formula (9), k1If > 0 is adjustable gain, then
Figure FDA0003367680720000027
Due to e1(s)＝G(s)e2(s) wherein G(s) is 1/(s + k)1) Is a stable transfer function when e2When going to 0, e1Also inevitably tends to 0;
to e2Derived by derivation
Figure FDA0003367680720000028
Defined in the following auxiliary functions
Figure FDA0003367680720000031
k2>0 is the adjustable feedback gain of the system,
the expression of r can be found as
Figure FDA0003367680720000032
Step 2.2, the model-based controller can be designed as:
Figure FDA0003367680720000033
in formula (11), krFor positive adjustable feedback gain, uaFor model-based compensation terms, usFor a robust control law, us1For a linear robust feedback term, us2For the non-linear robust term to overcome modeling uncertainty and the influence of interference on system performance, beta is the robust integrated multilayer neural network controller parameter, fdIndicating that the function is related only to the system command and the derivative of the command;
step 2.3, obtaining the online parameter self-adaptive rate of the neural network parameters based on the Lyapunov stability proving process
Figure FDA0003367680720000034
Figure FDA0003367680720000035
Wherein, gamma is1And Γ2Is a positive determined adaptive gain matrix.
2. The method according to claim 1, wherein the specific process of step 3 is as follows:
introduce the following functions
Figure FDA0003367680720000036
Figure FDA0003367680720000037
Selecting
Figure FDA0003367680720000038
It can be demonstrated that P (t) is ≧ 0;
Figure FDA0003367680720000041
obtaining phi (t) is more than or equal to 0;
the lyapunov function is defined as follows:
Figure FDA0003367680720000042
defining functions
Figure FDA0003367680720000043
The lyapunov stability theory is used for stability verification, and the median theorem is used for obtaining the semi-global asymptotic stability result of the system, so that the gain k is adjusted1、k2、krAnd gamma1、Γ2The tracking error of the system tends to zero under the condition that the time tends to be infinite.
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