CN101488010A - Essentially nonlinear compensation controller of servo system - Google Patents

Abstract

The invention relates to a non-linear compensating controller in essence of a servo system, belonging to the field of industrial control. The compensating controller of the invention comprises a variable structure neural network feedback compensation part, forward adaptive compensation part and a robust compensation part; therefore, the controller can simultaneously compensate friction non-linearity and driver dead area non-linearity existing in the compensating system. The variable structure neural network compensates for the friction non-linearity in the system while the adaptive robust control carries out compensation control on the dead area non-linearity and external perturbation in a system driver; the variable structure neural network technology reduces network size and calculation amount and strengthens practicality of the controller; the adaptive robust control ensures static precision, transient performance and robustness of the system; applied to location tracking control of the electric motor, as indicated by actual operation results, the compensating controller of the invention can endow the system with excellent static tracking precision and robustness.

Description

A kind of essentially nonlinear compensation controller of servo system

Technical field

The present invention relates to a kind of essentially nonlinear compensation controller of servo system, it belongs to industrial control field.

Background technology

Servo-drive system is widely used in fields such as industry manufacturing, national defence.Along with The development in society and economy, the working condition of production system is complicated day by day, to the control performance requirement of servo-drive system also more and more higher (comprising high-precision requirement and response fast).And the friction in the system is non-linear, the dead band is non-linear etc. all is one of principal element of infringement system performance.To rub non-linear is example, if well do not compensated, can influence the stable state accuracy of system, also can cause so-called " creeping " phenomenon when low speed, even may cause system limit cycle or instability to occur; Also extensively exist in servo-drive system and the dead band is non-linear, show as insensitive to small-signal,, can have a strong impact on the performance of servo-drive system equally if do not handled.

For the compensation of nonlinearity that rubs in the servo-drive system, many ready-made achievements have been arranged, roughly can be divided into two big classes: based on model friciton compensation and model-free friciton compensation.There is the model friciton compensation all to be based on the model of experimental result, can not summarizes all friction phenomenons fully; And the model-free friciton compensation generally all adopts the method for Based Intelligent Control, utilizes omnipotent approximation of function devices such as neural network, fuzzy system, and is online to rubbing the non-linear identification of carrying out, then the design compensation controller.Yet this quasi-controller generally all needs huge basis function or fuzzy rule, and the controller calculated amount is excessive, is unfavorable for practical application.

For dead band compensation of nonlinearity in the servo-drive system, generally all be the self-adaptation Inverse Model Control thoughts of people in " Adaptive Control of Systems with Actuator andSensor Nonlinearities " this this book of publishing in 1996 such as employing Gang Tao; People such as RastkoR.Selmic have adopted the adaptive neural network Inverse Model Control in article " Deadzone Compensationin Motion ControlSystems Using Neural Networks ", loaded down with trivial details but these class methods are complicated, be difficult to be applied in the engineering reality.

In the past in the control method of servo-drive system, major part only all is at wherein a kind of non-linear the compensating in friction, dead band or gap, and the neural net method that is mostly fixed sturcture that adopts, just adopt the fixed sturcture neural network only system input gap to be compensated as people such as Rastko R.Selmic in patent " Backlash compensation usingnetwork " (US Patent 6611823).In order to satisfy the requirement of modern industry and national defence better, strengthen the practicality and the robustness of control method, the present invention adopts the adaptive robust control technology in conjunction with becoming the artificial neural compensation technique, and the dead band in the non-linear and driver is non-linear to the friction that exists in the servo-drive system simultaneously compensates control.It is non-linear that adaptive robust control not only can compensate the dead band, can also suppress the external disturbance and the neural net model establishing error of system.Adopt the present invention to improve stable state accuracy, response speed and the antijamming capability of system greatly.

Summary of the invention

The objective of the invention is that non-linear non-linear and external disturbance carries out online compensation control problem with the dead band in order to solve friction in the servo-drive system, propose a kind of essentially nonlinear compensation controller of servo system, be used to improve response speed, stable state accuracy and the disturbance rejection ability of servo-drive system; Reduce the design complexities and the computation burden of controller, make things convenient for the practical application of controller, reduce the design of Controller cost.

A kind of essentially nonlinear compensation controller of servo system that the present invention proposes in order more clearly to describe the design process of this controller, is divided into following step:

Step 1: set up to contain and rub and the dead band nonlinear system model

To the direct current generator servo-drive system, it is dynamic to ignore its electric current, can be described system with a second order SISO model

$\left\{\begin{array}{c}\frac{\mathrm{d\θ}}{\mathrm{dt}}=\mathrm{\ω}\left(t\right)\\ \frac{\mathrm{d\ω}}{\mathrm{dt}}={\mathrm{\τ}}_f\left(\mathrm{\ω}\right)+\mathrm{bw}+{\mathrm{\τ}}_d\left(t\right)\\ w=D\left(u\left(t\right)\right)\\ y=\mathrm{\θ}\end{array}\right.---\left(1.1\right)$

Wherein θ is the position output of motor, and ω is a motor speed; τ _fBe that system friction is non-linear (ω), w is the motor input voltage, and D (w) is that the driver dead band is non-linear, τ _d(t) be external disturbance.

Step 2: to the non-linear modeling analysis that carries out in the dead band in the model (1.1)

Dead zone nonlinearity model such as Fig. 3 describe, and for simplifying the design of controller, are convenient to the engineering practical application, and the present invention carries out following modification to the dead band model

w(t)＝D(u(t))＝mu(t)+d(u(t)) (1.2)

Wherein m is the nonlinear slope in dead band, and d (u (t)) can be expressed as

$d\left(u\left(t\right)\right)=\left\{\begin{array}{cc}-{\mathrm{mb}}_r& u\left(t\right)\&GreaterEqual;b_r,\\ -\mathrm{mu}\left(t\right)& b_l<u\left(t\right)<b_r,\\ {-\mathrm{mb}}_l& u\left(t\right)\&le;b_l.\end{array}\right.\&CenterDot;\&CenterDot;\&CenterDot;\left(1.3\right)$

D in real system (u (t)) is a bounded, supposes | d (u (t)) | and≤d ₀, during CONTROLLER DESIGN d (u (t)) is considered as disturbance.With (1.2) formula substitution model (1.1), the dynamic equation that can get system is

$\left\{\begin{array}{c}\frac{\mathrm{d\&theta;}}{\mathrm{dt}}=\mathrm{\&omega;}\left(t\right)\\ \frac{\mathrm{d\&omega;}}{\mathrm{dt}}={\mathrm{\&tau;}}_f\left(\mathrm{\&omega;}\right)+\mathrm{mbu}\left(t\right)+\mathrm{bd}\left(u\left(t\right)\right)+{\mathrm{\&tau;}}_d\left(t\right)\end{array}\right.---\left(1.4\right)$

Step 3: to the non-linear τ that rubs _f(ω) set up change structure Gauss RBF network model

The friction model of servo-drive system generally all is and the function of velocity correlation that the present invention adopts the Gauss RBF neural network that becomes structure that friction model is carried out on-line identification.When reducing network size, accurately catch friction nonlinearity.Utilize and become the unknown friction model τ of artificial neural on-line identification _f(

).By shown in Figure 2, the speed of the system that is input as of network

, be output as the value of approaching of friction

(

), in actual applications, suppose that network weight W is a bounded.The approximate error of model

(

) compensate by the robust item of controller, the weights of change artificial neural are then restrained by adaptive learning and are guaranteed.

The structural drawing that becomes artificial neural as shown in Figure 2, its principle is the position according to the current state vector, utilizes network node to activate and the hypnosis technology, realizes having only the node of activation to participate in approximation of function, also has only the corresponding weights of these nodes to obtain renewal.Activating a node, just to increase an initial weight in network be 0 node, wake a node up and then be in network, add weights inherited before the node of learning outcome.Node of hypnosis is just temporarily left out a node through study from network.Along with the transfer of state, active node constantly changes like this, makes number of network node be in smaller state always.Activate with the judgment criterion of hypnosis and determine according to the value of basis function output under the current state.Such as for network node

, when the output of basis function during, just can ignore its effect to whole network less than given positive number ρ, that is to say and can from network, remove this node.Therefore, only be positioned at current state

Be the centre of sphere, radius $r=\sqrt{-{2\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A200910008737E00112.png,A200910008737E00113.png"\; state="\{\{state\}\}">i</figure-callout>}}^2\ln \left(\mathrm{\&rho;}\right)}$ Interior node just belongs to the node of current activation.Promptly work as ${\left|\right|\mathrm{\&omega;}-c_i\left|\right|}^2\&le;{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A200910008737E00112.png,A200910008737E00113.png"\; state="\{\{state\}\}">r</figure-callout>}}^2=-{2\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A200910008737E00112.png,A200910008737E00113.png"\; state="\{\{state\}\}">i</figure-callout>}}^2\ln \left(\mathrm{\&rho;}\right)$ The time, this node activates or wakes up, otherwise to its hypnosis.

By the neural network approximation theory as can be known, non-linear can being expressed as of friction by neural network

Wherein N is the node number that network uses, but dynamic change; W is the network weight vector, and Ψ is a basis function vector.The approximate model that uses during CONTROLLER DESIGN is

${\widehat{\mathrm{\&tau;}}}_f\left(\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\right)={\hat{W}}^T\mathrm{\&Psi;}\left(\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\right)---\left(1.6\right)$

Then Model Distinguish error

${\widetilde{\mathrm{\&tau;}}}_f={\mathrm{\&tau;}}_f-{\widehat{\mathrm{\&tau;}}}_f={\tilde{W}}^T\mathrm{\&Psi;}\left(\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\right)+\mathrm{\&xi;}\left(\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\right)---\left(1.7\right)$

Can be used as one of reference quantity of robust control item design.Wherein $\tilde{W}=W-\hat{W}.$

Step 4: design of Controller

After finishing first three step, just can design structure-changeable self-adaptive robust controller of the present invention, its structure is as shown in Figure 1.Adaptive technique has realized the online adjustment of neural network weight and other unknown parameters, and robust control technique has suppressed external disturbance, model approximate error etc., has guaranteed the strong robustness energy of system.The form of parameter adaptive rule draws by the Lyapunov of system stability analysis method, has guaranteed the stability of system.The tracking error e=θ of supposing the system _d-θ, wherein θ _dFor with reference to input, make B=mb, CONTROLLER DESIGN u _cFor

u _c＝u _a+u _s

$u_a=\frac{1}{\hat{B}}(-{\widehat{\mathrm{\&tau;}}}_f\left(\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\right)+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_d)$ (1.8)

$u_s=\frac{1}{\hat{B}}({\mathrm{<figure-callout\; id="1"\; label="u\; s"\; filenames="A200910008737E00101.png"\; state="\{\{state\}\}">u</figure-callout>}}_s+u_{s2}),u_{s1}=k_{d}s+{\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A200910008737E00112.png,A200910008737E00113.png"\; state="\{\{state\}\}">e</figure-callout>}}_2$

s＝λ ₁e ₁+e ₂

U wherein _S2To determine subsequently.By (1.1) formula and (1.8), we can obtain error state equation

$\stackrel{\&CenterDot;\&CenterDot;}{e}=-k_{d}s-{\mathrm{\&lambda;}}_1{e}_2-{\tilde{W}}^T\mathrm{\&psi;}-\tilde{B}{u}_c-\mathrm{\&xi;}\left(\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\right)-d_r\left(t\right)-u_{s2}---\left(1.9\right)$

D wherein _r(t)=bd (u (t))+τ _d(t) for dividing value is arranged.Utilize the projection operator technology, regulate the parameter adaptive rule, avoid the control coefrficient that occurs being prone in the adaptive control unusual problem, therefore, choose the parameter adaptive rule $\stackrel{\&CenterDot;}{\hat{W}}={\mathrm{Proj}}_{\hat{W}}(\mathrm{\&eta;s\&psi;}/k_d),$ $\stackrel{\&CenterDot;}{\hat{B}}={\mathrm{Proj}}_{\hat{B}}(\mathrm{\&gamma;}{\mathrm{su}}_c/k_d).$ Robust control item u _S2Satisfy following two conditions

$p1:s(-\tilde{B}{u}_c-d_r\left(t\right)-u_{s2})\&le;\mathrm{\&epsiv;},\mathrm{\&epsiv;}>0;$ (1.10)

p2：-su _s2≤0.

So far, design of Controller of the present invention finishes.

Adopt controller of the present invention, can guarantee in t → 0 o'clock, tracking error converges in the minimum neighborhood of initial point, speed of convergence and k _dChoose relevant, k _dBig more, speed of convergence is fast more.

Beneficial effect

The present invention combines adaptive robust control technology and neural network control technique.Adopt to become artificial neural, realized the friciton compensation of small scale network, avoided numerous and diverse huge network structure, strengthened the practicality of nerual network technique; The introducing of robust control item has overcome the influence to system stability of network approximate error, external disturbance, weights saltus step, makes the system have very strong robustness, has widened range of application of the present invention; Adopt adaptive control, realized the online adjustment of unknown parameter, simplified the adjustment process of practical application, reduced human and material resources and the financial resources of debug phase; Change for the wearing and tearing of system, the parameter that environmental change causes, the present invention can revise any parameter, realizes self-adaptation adjusting and robust stabilizing, prolongs the length of service of system, reduces maintenance cost.

Description of drawings

Fig. 1 is a motor servo system nonlinear compensation control system block diagram;

Fig. 2 becomes structure Gauss RBF network structure;

Fig. 3 is the dead band nonlinear model;

Fig. 4 is a DC moment electric motor location tracker hardware block diagram;

Fig. 5 is that the neural network node is counted dynamic change figure;

Fig. 6 is the Position Tracking curve map;

Fig. 7 is the Position Tracking error curve diagram;

Among the figure: 1-host computer (desired locations), 2-DSP2812,3-Copley412 type driver, 4-direct current torque motor, 5-round induction synchrometer, 6-DSP serial ports, 7-I/O port, 8-D/A, 9-DSP central processor CPU.

Embodiment

Core concept of the present invention is to adopt the change artificial neural to approach unknown nonlinear function in the servo-drive system (it is non-linear to rub), has very little network size when realizing friciton compensation; Utilize adaptive robust control technology on-line study network weight and other unknown parameters, suppress system's external disturbance and modeling error etc., improve response speed, stable state accuracy and the robust performance of servo-drive system.

Adopt the TMS320DSP2812 processor as the hardware platform that control algolithm realizes, this invention is applied in the DC moment electric motor location servo-drive system, verify the superiority of this invention.

The performing step of controller is as follows:

1. by the reference input

Arrive system state amount with sensor acquisition

Calculate error vector ${\left[\begin{array}{cc}e& \stackrel{\&CenterDot;}{e}\end{array}\right]}^T={\left[\begin{array}{cc}{e}_1& e_2\end{array}\right]}^T;$

2. with the Position Tracking error through a wave filter

S → 0 obtains similar sliding formwork variable s, as long as just can guarantee error e → 0;

3. design change artificial neural obtains the adaptive equalization item $u_a=\frac{1}{\hat{B}}(-{\widehat{\mathrm{\&tau;}}}_f\left(\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\right)+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_d);$

4. calculate the u of first of robust compensation item _S1=k _dS+ λ ₁e ₂

5. calculate robust compensation item second portion u _S2=k _vS satisfies formula (1.10), is used for existing in the inhibition system that the driver dead band is non-linear, external disturbance and modeling error etc.

The hardware block diagram of servo-control system such as Fig. 4 adopt DSP2812 (2) to realize carrier for controller hardware, 412 type DC motor drivers of U.S. Copley company, and sensor employing precision is 0.0001 ° a round induction synchrometer (5).During experiment, send the desired locations instruction from host computer (1) by serial ports, the serial ports (6) of DSP2812 (2) receives instruction, by round induction synchrometer (5) acquisition system outgoing position, become the calculating of artificial neural adaptive robust control algorithm by the central processor CPU (9) of DSP, comprise neural network, the on-line study of parameter, at last the controlled quentity controlled variable that draws D/A (8) module by DSP is outputed to Copley412 type driver (3), via driver control signal is amplified, drive direct current torque motor (4), realize Position Tracking Control direct current torque motor (4).

Choose with reference to input θ _d=10sin (t), the expression amplitude is 10 ° a sinusoidal signal, external disturbance τ _d(t)=rand (1).Variable $s=\stackrel{\&CenterDot;}{e}+e,$ Other parameters are elected k respectively as _d=1, h=4, ε=0.001, the scope of W is [2020].Initial value $w_i=0,\hat{B}=0.1;$ All node Gaussian function width are assumed to be normal value σ=0.3, and central point is distributed in zone [1.51.5] * [33].Activate radius $r=\sqrt{-{2\mathrm{\&sigma;}}^2\ln \mathrm{\&rho;}},$ When ρ=0.1, r=0.6438.Fig. 5 shows that adopted after the change artificial neural technology, the scale of whole network reduces greatly, and the node number remains on below 16.Fig. 6,7 shows that even have external disturbance, system modelling error, the Position Tracking error also can converge in the minimum neighborhood of initial point apace.

Above-described only is preferred embodiment of the present invention, and the present invention not only is confined to the foregoing description, all any changes of being done within the spirit and principles in the present invention, is equal to replacement, improvement etc. and all should be included within protection scope of the present invention.

Claims (3)

1. an essentially nonlinear compensation controller of servo system is characterized in that: comprise becoming artificial neural feedback compensation part, forward direction adaptive equalization part and robust compensation part; Method for designing is at first carried out modeling to control system, analyze dead band nonlinear model wherein then and provide the nonlinear change structure Gauss RBF neural network model of friction, provide controller mathematical form of the present invention at last, nerual network technique and ADAPTIVE ROBUST technology are organically combined non-linear and the non-linear and external disturbance in driver dead band of friction that exists in the bucking-out system simultaneously; Become artificial neural and compensate, and adaptive robust control compensates control to the dead band of system drive existence is non-linear with external disturbance the friction that exists in the system is non-linear.

2. a kind of essentially nonlinear compensation controller of servo system according to claim 1 is characterized in that: it is non-linear that foundation becomes structure Gauss RBF network model on-line identification friction, and number of network node dynamically changes with state.

3. a kind of essentially nonlinear compensation controller of servo system according to claim 1, it is characterized in that: design ADAPTIVE ROBUST compensator, ADAPTIVE ROBUST is organically combined with becoming artificial neural, form a kind of new change artificial neural self-adaptive robust controller.

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