CN103149843B - A kind of ultrasonic motor model Model Reference Adaptive Control system based on MIT - Google Patents

Abstract

The present invention relates to a kind of ultrasonic motor model Model Reference Adaptive Control system based on MIT, belong to supersonic motor control technology field.The present invention by setting up a subcontrol between closed loop proportional controller and ultrasonic motor model, this subcontrol and ultrasonic motor model are composed in series the generalized controlled object, the dynamic part of reference model only need be identical with the dynamic part of the generalized controlled object, reference model is made no longer to have substantial connection with controlled device (supersonic motor) model, the gain of reference model all can be different from plant model with dynamic part, thus make reference model can accurate response desired characteristic, MIT control method is enable to be applied in the control system of supersonic motor, adopt again the adaptive law based on gradient optimizing simultaneously, make the adjustable gain k to closed loop proportional controller _cthe calculated amount of carrying out online adaptive adjustment is little, thus contributes to the operational efficiency improving this system, reduces system cost.

Description

A kind of ultrasonic motor model Model Reference Adaptive Control system based on MIT

Technical field

The present invention relates to a kind of supersonic motor MIT Model Reference Adaptive Control System based on MIT, belong to supersonic motor control technology field.

Background technology

Supersonic motor is a kind of novel motion control executive component, has the principle of work and structure that are different from conventional motors.Due to the singularity of operation mechanism, the operation of supersonic motor be unable to do without suitable driving circuit and control strategy.Synchronous with the development of digital control technology, the control strategy of supersonic motor adopts numerically controlled actualizing technology more and more, and hardware configuration is presented as the control program performed in real time in embedded microprocessor chip.The microprocessor chip such as single-chip microcomputer, DSP and driving circuit combine, and become Drive and Control Circuit, together form supersonic motor motion control device with supersonic motor.

For the control of supersonic motor, the same with the control of other any object, we always wish the control performance realizing expectation by relatively simple control method.Like this, not only can reducing system cost, also improve the reliability of system cloud gray model because reducing system complexity.But due to the time-variant nonlinear feature that supersonic motor has, control performance not easily adopts simple method to improve, be all generally adopt self-adaptation self-adaptation control method.In numerous self-adaptation control methods, the MIT Model Reference Adaptive Control Method based on gradient optimizing method is the relatively simple method of one.As a kind of Model Reference Adaptive Control Method, MIT control method is according to suitable adaptive law, on-line tuning controller parameter, make the Expected Response process that the actual speed response tracking of supersonic motor revolution speed control system is expressed by reference model, thus the self-adapting following realized supersonic motor time-varying characteristics, improve control performance.The controller of MIT method is a simple proportional controller, so control algolithm is succinct, on-line calculation is little.Fig. 1 gives the basic structure of supersonic motor MIT self-adaptation revolution speed control system.Wherein, k _cfor closed loop proportional controller, gain k _con-line tuning is carried out according to the generalized error of rotating speed outgoing side by adaptive law.The output controlled quentity controlled variable of controller is the frequency of supersonic motor driving voltage.Reference model is identical with dynamic part N (the s)/D (s) of ultrasonic motor model, and only gain is different, is respectively k and k _v.The gain k of reference model is constant, the gain k of supersonic motor _vbecome when being then, change with the appearance of change and various disturbance during motor self-characteristic.Adjustable gain k _ceffect, be just compensate k _vchange, make adjustable gain k _cwith supersonic motor time-varying gain k _vproduct equal the gain k of (being actually convergence) reference model, thus make great efforts to make motor speed response process consistent with the reference model characteristic of expectation.

Reference model is the important component part of this system, embodies the requirement to system control performance, should carry out design reference model by control performance desirably.Ideally, the control performance of system is the same with the performance of reference model, also just reaches the control performance of expectation.But in MIT Model Reference Adaptive Control Method, gain is different, Dynamic mode is identical to require reference model and controlled device (supersonic motor) model only to have.For meeting this precondition, the design of the reference model of this control method is not just arbitrary, and this just may this requires inconsistent with " reference model characterization control is expected ".When controlling for supersonic motor rotating speed, just occurred this conflict, reference model cannot be designed, and MIT control method also just cannot be applied to supersonic motor control system.According to supersonic motor second mathematical model, when rotary speed setting value is 20.3r/min, after normalized, the unity transfer function obtaining second order underdamping model criteria form is

$G_p\left(s\right)=\frac{k_v}{D\left(s\right)}=\frac{710509.0689}{s^2+632.6935002s+710509.0689}---\left(1\right)$

The control performance expected is, under Step reference signal function, output response non-overshoot, regulating time are within 0.3s.For the ultrasonic motor model given by formula (1), this is a underdamped transport function of second order.If design reference model will be carried out according to the requirement of MIT control method, no matter how to change gain and also can not make reference model non-overshoot.If set up the reference model that meets performance requirement, its transport function compared with the transport function of motor model, just more than proportional gain k of difference _c.Like this, between " reference model should reflect the control performance of expectation " and " MIT control method requires that reference model is identical with the dynamic part of object model " these two requirements that must simultaneously meet, just there is conflict.So, although MIT control method is simple, the control system of supersonic motor cannot be used for.

Summary of the invention

The object of this invention is to provide a kind of ultrasonic motor model Model Reference Adaptive Control system based on MIT, to solve the problem that MIT control method cannot be applied at present in supersonic motor control system.

The present invention is for solving the problems of the technologies described above and providing a kind of ultrasonic motor model Model Reference Adaptive Control system based on MIT, this adaptive control system comprises closed loop proportional controller, reference model, ultrasonic motor model, adaptive law module and subcontrol, described subcontrol is arranged between closed loop proportional controller and ultrasonic motor model, the input end of subcontrol is connected with the output terminal of closed loop proportional controller, the output terminal of subcontrol is connected with the input end of ultrasonic motor model

Described reference model is k is the gain section of model, the dynamic part that A (s)/B (s) is model, the set-point N being input as supersonic motor rotating speed of this reference model _ref, export as N _m;

Described ultrasonic motor model is k _vfor the gain section of model, the dynamic part that N (s)/D (s) is model, the output being input as auxiliary control controller of this ultrasonic motor model, the output of ultrasonic motor model is n;

The adjustable gain of described closed loop proportional controller is k _c, k _cchange controlled by adaptive law module;

Described subcontrol model is it is input as k _cn _ref;

The adaptive law of what described adaptive law module adopted is gradient optimal method, adaptive law is wherein e is the error between the output of reference model and the output of ultrasonic motor model, e=n _m-n, adaptation coefficient λ is the step pitch in gradient optimal method, and λ >0.

Described subcontrol model G _a(s) and ultrasonic motor model G _ps () is composed in series the generalized controlled object G (s),

$G\left(s\right)=G_a\left(s\right)\·G_p\left(s\right)=\frac{A\left(s\right)D\left(s\right)}{B\left(s\right)N\left(s\right)}\·\frac{k_{v}N\left(s\right)}{D\left(s\right)}=\frac{k_{v}A\left(s\right)}{B\left(s\right)}.$

The invention has the beneficial effects as follows: the present invention by setting up a subcontrol between closed loop proportional controller and ultrasonic motor model, this subcontrol and ultrasonic motor model are composed in series the generalized controlled object, the dynamic part of reference model only need be identical with the dynamic part of the generalized controlled object, reference model is made no longer to have substantial connection with controlled device (supersonic motor) model, the gain of reference model all can be different from plant model with dynamic part, thus make reference model can accurate response desired characteristic, adopt again the adaptive law based on gradient optimizing simultaneously, make the adjustable gain k to closed loop proportional controller _cthe calculated amount of carrying out online adaptive adjustment is little, thus contributes to the operational efficiency improving this system.

Accompanying drawing explanation

Fig. 1 is MIT Model Reference Adaptive Control System structural drawing;

Fig. 2 is supersonic motor MIT Model Reference Adaptive Control System block diagram of the present invention;

Fig. 3 surveys rotating speed step response schematic diagram in the embodiment of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is further described.

The reason producing aforementioned conflict is that MIT control method gives strict restriction to reference model, cause reference model cannot under the prerequisite meeting this restriction, reflect the control characteristic of expectation more simultaneously, for eliminating this conflict, The present invention gives a kind of ultrasonic motor model Model Reference Adaptive Control system, as shown in Figure 2, this supersonic motor MIT Model Reference Adaptive Control System comprises closed loop proportional controller, reference model, ultrasonic motor model, adaptive law module and subcontrol, described subcontrol is arranged between closed loop proportional controller and ultrasonic motor model, the input end of subcontrol is connected with the output terminal of closed loop proportional controller, the output terminal of subcontrol is connected with the input end of ultrasonic motor model, a subcontrol is added compared with MIT Model Reference Adaptive Control System shown in native system with Fig. 1, reference model is made no longer to have substantial connection with controlled device (supersonic motor) model, the gain of reference model all can be different from plant model with dynamic part, therefore this invention removes the restriction of control method to Reference Model Design itself, the design of reference model is made only to need to consider how accurately to reflect this requirement of expected performance.

Wherein reference model is the set-point N being input as supersonic motor rotating speed of this reference model _ref, export as n _m;

Ultrasonic motor model is the output being input as auxiliary control controller of this ultrasonic motor model, the output of ultrasonic motor model is n;

The adjustable gain of closed loop proportional controller is k _c, k _cchange controlled by adaptive law module;

Subcontrol model is it is input as k _cn _ref;

What adaptive law module adopted is gradient optimal method, and its input is the error e between the output of reference model and the output of ultrasonic motor model, wherein e=N _m-n, adaptive law module references adaptive control system realizes adaptive key link.To derive below its adaptive law.

In system shown in Figure 2, the general type of reference model and motor model is respectively

$G_m\left(s\right)=\frac{\mathrm{kA}\left(s\right)}{B\left(s\right)}---\left(2\right)$

$G_p\left(s\right)=\frac{k_{v}N\left(s\right)}{D\left(s\right)}---\left(3\right)$

At adaptive controller k _coutput terminal and the input end of motor model between, add a subcontrol G _a(s)

$G_a\left(s\right)=\frac{A\left(s\right)D\left(s\right)}{B\left(s\right)N\left(s\right)}---\left(4\right)$

As shown in Figure 2, the G in dotted line frame _a(s) and motor model G _ps () is composed in series the generalized controlled object G (s)

$G\left(s\right)=G_a\left(s\right)\·G_p\left(s\right)=\frac{A\left(s\right)D\left(s\right)}{B\left(s\right)N\left(s\right)}\·\frac{k_{v}N\left(s\right)}{D\left(s\right)}=\frac{k_{v}A\left(s\right)}{B\left(s\right)}---\left(5\right)$

Definition generalized error e is

e＝n _m-n (6)

In formula, n _mfor the output of reference model; N is the actual output speed of controlled device supersonic motor; Generalized error e is defined as, and rotary speed setting value is N _reftime, the error between reference model output and controlled device export.

Choosing performance index functional is

$J=\frac{1}{2}{\∫}_{t_0}^t{e}^2\left(\mathrm{\τ}\right)\mathrm{d\τ}---\left(7\right)$

In formula, t ₀for the initial time of control procedure, t is current time.If an adaptive law can be designed to adjust adjustable gain k _c, make performance index J reach minimum value, also just reach control objectives.For this reason, ask J to adjustable parameter k _cgradient

$\frac{\∂J}{\∂k_c}={\∫}_{t_0}^{t}e\left(\mathrm{\τ}\right)\frac{\∂e\left(\mathrm{\τ}\right)}{\∂k_c}\mathrm{d\τ}---\left(8\right)$

Known by gradient optimal method, k _cvalue should change along the direction (i.e. negative sense) of Gradient Descent formula (8) Suo Shi, to make J convergence minimum value gradually.Thus, desirable k _cvariation delta k _cfor

$\mathrm{\Δ}{k}_c=-\mathrm{\λ}\frac{\∂J}{\∂k_c}=-\mathrm{\λ}{\∫}_{t_0}^{t}e\left(\mathrm{\τ}\right)\frac{\∂e\left(\mathrm{\τ}\right)}{\∂k_c}\mathrm{d\τ}---\left(9\right)$

In formula, λ is step pitch, and has λ >0.So, the k after adjustment _cvalue is

$k_c=-\mathrm{\λ}{\∫}_{t_0}^{t}e\left(\mathrm{\τ}\right)\frac{\∂e\left(\mathrm{\τ}\right)}{\∂k_c}\mathrm{d\τ}+k_{c0}---\left(10\right)$

In formula, k _c0for adjustable gain k _cat t ₀the value in moment, i.e. initial value, and have Δ k _c=k _c-k _c0.If gain k can be obtained _cderivative expression formula, also just obtain and can change k online _cadaptive law.For this reason, by formula (10) both sides to time t differentiate,

$\stackrel{\·}{k_c}=-\mathrm{\λe}\left(\mathrm{\τ}\right)\frac{\∂e\left(\mathrm{\τ}\right)}{\∂k_c}---\left(11\right)$

Formula (11) right side unknown.The open-loop transfer function of the adaptive control system of supersonic motor shown in Fig. 2 is

$\frac{e\left(s\right)}{N_{\mathrm{ref}}\left(s\right)}=\frac{(k-k_c{k}_v)A\left(s\right)}{B\left(s\right)}---\left(12\right)$

In formula, N _reffor rotary speed setting value.Can be obtained fom the above equation

B(s)E(s)＝(k-k _ck _v)A(s)N _ref(s) (13)

Laplace inverse transformation is done to formula (13), obtains time-domain expression

B(p)e(t)＝(k-k _ck _v)A(p)N _ref(t) (14)

In formula, p is differentiating operator both sides are simultaneously to k _cdifferentiate,

$B\left(p\right)\frac{\∂e\left(t\right)}{\∂k_c}=-k_{v}A\left(p\right)N_{\mathrm{ref}}\left(t\right)---\left(15\right)$

By Fig. 2, the input of reference model, export between have following temporal relationship

B(p)n _m(t)＝kA(p)N _ref(t) (16)

Can be obtained by formula (15) and formula (16), and n _m(t) proportional relation

$\stackrel{\·}{k_c}=\mathrm{\μ}\·e\·n_m---\left(17\right)$

In formula, adaptation coefficient above formula is adaptive law.

Utilize formula (17), can realize k _con-line control, as shown in Figure 2.Specifically, if establish the k of previous moment _cvalue is k _{c_last}, then the k of adjustment in the calculating of current time controller _cvalue is

k _c＝k _{c_last}+μen _m·dt＝k _{c_last}+μT _Cen _m(18)

In formula, T _cfor control cycle, dt is that front and back adjust k twice _cthe time interval between value.Because to k _cthe adjustment of value was carried out before each controller calculates, and thus had dt=T _c.

In formula (18), μ and T _call the fixed value of in advance design, can the calculated off-line product that goes out both in line computation.So, adopt formula (18) to k _cvalue carries out an online adaptive adjustment, and only need 2 multiplication, 1 sub-additions, calculated amount is minimum.

Controlled by the rotating speed of above-mentioned control system in supersonic motor, the control performance that setting is expected is, under Step reference signal function, output response non-overshoot, regulating time are within 0.3s.Accordingly, design reference model is

$G_m\left(s\right)=\frac{2427}{s^2+96s+2427}---\left(19\right)$

Subcontrol G _a(s) be

$G_a\left(s\right)=\frac{A\left(s\right)D\left(s\right)}{B\left(s\right)N\left(s\right)}=\frac{s^2+632.6935002s+710509.0689}{s^2+96s+2427}---\left(20\right)$

Carry out Control release according to said system to supersonic motor rotating speed, obtain rotating speed step response as shown in Figure 3, not there is overshoot in the step response of actual measurement rotating speed, and regulating time is within 0.3s, meets set desired control performance.Therefore ultrasonic motor model Model Reference Adaptive Control system of the present invention had both met reference model and controlled device (supersonic motor) model only that gain is different, Dynamic mode identical while, reference model characterization control can be made again to expect, MIT control method is enable to be applied in the control system of supersonic motor, adopt again the adaptive law based on gradient optimizing simultaneously, make the adjustable gain k to closed loop proportional controller _cthe calculated amount of carrying out online adaptive adjustment is little, thus contributes to the operational efficiency improving this system, and reduces system cost.

Claims (2)

1. the ultrasonic motor model Model Reference Adaptive Control system based on MIT, it is characterized in that: this adaptive control system comprises closed loop proportional controller, reference model, ultrasonic motor model, adaptive law module and subcontrol, described subcontrol is arranged between closed loop proportional controller and ultrasonic motor model, the input end of subcontrol is connected with the output terminal of closed loop proportional controller, the output terminal of subcontrol is connected with the input end of ultrasonic motor model

Described reference model is k is the gain section of model, the dynamic part that A (s)/B (s) is model, the set-point N being input as supersonic motor rotating speed of this reference model _ref, export as n _m;

Described ultrasonic motor model is k _vfor the gain section of model, the dynamic part that N (s)/D (s) is model, the output being input as auxiliary control controller of this ultrasonic motor model, the output of ultrasonic motor model is n;

The adjustable gain of described closed loop proportional controller is k _c, k _cchange controlled by adaptive law module;

Described subcontrol model is it is input as k _cn _ref;

The adaptive law of what described adaptive law module adopted is gradient optimal method, adaptive law is k _c=μ en _m, wherein e is the error between the output of reference model and the output of ultrasonic motor model, e=n _m-n, adaptation coefficient λ is the step pitch in gradient optimal method, and λ >0.

2. the ultrasonic motor model Model Reference Adaptive Control system based on MIT according to claim 1, is characterized in that: described subcontrol model G _a(s) and ultrasonic motor model G _ps () is composed in series the generalized controlled object G (s),

$G\left(s\right)=D_a\left(s\right)\·G_p\left(s\right)=\frac{A\left(s\right)D\left(s\right)}{B\left(s\right)N\left(s\right)}\·\frac{k_{v}N\left(s\right)}{D\left(s\right)}=\frac{k_{v}A\left(s\right)}{B\left(s\right)}.$