CN103149843A - Ultrasonic motor model reference self-adaptation control system based on MIT (Massachu-setts Institute of Technology) - Google Patents

Abstract

The invention relates to an ultrasonic motor model reference self-adaptation control system based on MIT (Massachu-setts Institute of Technology), and belongs to the technical field of the ultrasonic motor control. According to the ultrasonic motor model self-adaptation control system, a secondary controller is additionally arranged between a closed loop proportional controller and the ultrasonic motor model; the secondary controller and the ultrasonic motor model are connected in series to form a generalized controlled object; the dynamic part of the reference model only needs to be same with the dynamic part of the generalized controlled object; the reference model does not have intimate connection with the controlled object (ultrasonic motor) model; the gain and the dynamic part of the reference model both can be different from those of the controlled object model; therefore, the expected characteristics can be accurately reflected by the reference model; the MIT control method can be applied to the ultrasonic motor control system; meanwhile, the self-adaption law based on the gradient optimization is adopted; and the calculation amount of the on-line self-adaption adjustment on the adjustable gain of the closed loop proportional controller is small so as to bring convenience for improving the operation efficiency of the system and lowering the system cost.

Description

A kind of supersonic motor Model Reference Adaptive Control System based on MIT

Technical field

The present invention relates to a kind of supersonic motor 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 the 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.With the development of digital control technology, synchronize, the control strategy of supersonic motor adopts the numerically controlled technology that realizes more and more, is presented as the control program of carrying out in real time in the embedded microprocessor chip on hardware configuration.The microprocessor chip such as single-chip microcomputer, DSP and driving circuit combine, and become Drive and Control Circuit, have formed the supersonic motor motion control device together with supersonic motor.

For the control of supersonic motor, the same with the control of other any object, we always wish to realize by relatively simple control method the control performance of expectation.Like this, not only system cost can be reduced, also the system reliability of operation can be improved because having reduced system complexity.But, due to supersonic motor have the time become nonlinear characteristic, control performance is difficult for adopting simple method to improve, and is all generally to adopt the 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 a kind of relatively simple method.As a kind of Model Reference Adaptive Control Method, the MIT control method is according to suitable adaptive law, the online controller parameter of adjusting, make the Expected Response process of the actual speed response tracking of supersonic motor revolution speed control system by the reference model expression, thereby realize the self-adapting following to the 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 has provided the basic structure of supersonic motor MIT self-adaptation revolution speed control system.Wherein, k _cfor the closed loop proportional controller, gain k _cby adaptive law, according to the generalized error of rotating speed outgoing side, adjusted online.The frequency that the output controlled quentity controlled variable of controller is the supersonic motor driving voltage.The dynamic part N (s) of reference model and supersonic motor model/D (s) is identical, 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 _vwhile being, become, during with the motor self-characteristic, the appearance of change and various disturbances changes.Adjustable gain k _ceffect, just be to compensate k _vvariation, make adjustable gain k _cwith supersonic motor time-varying gain k _vproduct equal the gain k of (being actually convergence) reference model, thereby make great efforts to make the motor speed response process consistent with the reference model characteristic of expectation.

Reference model is the important component part of this system, has embodied the requirement to system control performance, should carry out the design reference model according to the control performance of expectation.Ideally, the control performance of system is the same with the performance of reference model, has also just reached the control performance of expectation.But, in the MIT Model Reference Adaptive Control Method, require reference model and controlled device (supersonic motor) model only have the gain different, Dynamic mode is identical.For meeting this precondition, the design of the reference model of this control method is not just arbitrarily, and this just may with " expectation of reference model characterization control ", this requires inconsistent.While controlling for the supersonic motor rotating speed, this conflict just occurred, reference model can't be designed, the MIT control method also just can't be applied to the supersonic motor control system.According to supersonic motor second order mathematical model, in the situation that rotary speed setting value is 20.3r/min, after normalized, the unit transport function that obtains second order underdamping model canonical 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 of expectation is that, under the Step reference signal function, output response non-overshoot, adjusting time are in 0.3s.The given supersonic motor model for formula (1), this is a underdamped transport function of second order.If carry out the design reference model according to the requirement of MIT control method, no matter how to change gain and also can not make the reference model non-overshoot.If set up a reference model that meets performance requirement, its transport function is compared with the transport function of motor model, differ with regard to a more than proportional gain k _c.Like this, between " reference model should reflect the control performance of expectation " and " MIT control method require the dynamic part of reference model and object model identical " these two must simultaneously satisfied requirement, conflict has just appearred.So, although the MIT control method is simple, can't be for the control system of supersonic motor.

Summary of the invention

The purpose of this invention is to provide a kind of supersonic motor Model Reference Adaptive Control System based on MIT, to solve at present, the MIT control method can't be applied to the problem in the supersonic motor control system.

The present invention provides a kind of supersonic motor Model Reference Adaptive Control System based on MIT for solving the problems of the technologies described above, this adaptive control system comprises closed loop proportional controller, reference model, supersonic motor model, adaptive law module and subcontrol, described subcontrol is arranged between closed loop proportional controller and supersonic 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 supersonic motor model

Described reference model is

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

Described supersonic motor model is

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

The adjustable gain of described closed loop proportional controller is k _c, k _cvariation by the adaptive law module controls;

Described subcontrol model is

it is input as k _cn _ref;

What described adaptive law module adopted is the adaptive law of gradient optimal method, and adaptive law is k _c=μ en _m, wherein e is the error between the output of the output of reference model and supersonic 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) with supersonic motor model G _p(s) be composed in series the generalized controlled object G (s),

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

The invention has the beneficial effects as follows: the present invention by setting up a subcontrol between closed loop proportional controller and supersonic motor model, this subcontrol and supersonic motor model are composed in series the generalized controlled object, the dynamic part of reference model only need identically with the dynamic part of the generalized controlled object get final product, make reference model no longer with controlled device (supersonic motor) model, substantial connection be arranged, the gain of reference model all can be different from plant model with dynamic part, thereby make the reference model can the accurate response desired characteristic, adopt again the adaptive law based on gradient optimizing simultaneously, make adjustable gain kc to the closed loop proportional controller carry out the calculated amount of online adaptive adjustment little, thereby contribute to improve the operational efficiency of this system.

The 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 is actual measurement 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 that produces aforementioned conflict is that the MIT control method has provided strict restriction to reference model, cause reference model meeting under the prerequisite of this restriction, the control characteristic that reflection is expected simultaneously again, for eliminating this conflict, the present invention has provided a kind of supersonic motor Model Reference Adaptive Control System, as shown in Figure 2, this supersonic motor MIT Model Reference Adaptive Control System comprises the closed loop proportional controller, reference model, the supersonic motor model, adaptive law module and subcontrol, described subcontrol is arranged between closed loop proportional controller and supersonic 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 supersonic motor model, native system is compared and has been increased a subcontrol with the MIT Model Reference Adaptive Control System shown in Fig. 1, make reference model no longer with controlled device (supersonic motor) model, substantial connection be arranged, the gain of reference model all can be different from plant model with dynamic part, therefore the present invention has eliminated the restriction of control method to Reference Model Design itself, make the design of reference model only need to consider how accurately to reflect this requirement of expected performance.

Wherein reference model is

the set-point N that is input as the supersonic motor rotating speed of this reference model _ref, be output as n _m;

The supersonic motor model is

the output that is input as auxiliary control controller of this supersonic motor model, the supersonic motor model is output as n;

The adjustable gain of closed loop proportional controller is k _c, k _cvariation by the adaptive law module controls;

The subcontrol model is

it is input as k _cn _ref;

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

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, increased 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 the dotted line frame _a(s) with motor model G _p(s) be composed in series the generalized controlled object G (s)

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

Definition generalized error e is

E=n _min-n (6) formula, n _moutput for reference model; The actual output speed that n is the controlled device supersonic motor; Generalized error e is defined as, and rotary speed setting value is N _refthe time, the error between reference model output and controlled device output.

Choosing the 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.Adjust adjustable gain k if can design an adaptive law _c, make performance index J reach minimum value, also just reached the control target.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 k by gradient optimal method _cvalue should change along the direction (being negative sense) of Gradient Descent shown in formula (8), so that J convergence minimum value gradually.Thus, desirable k _cvariation delta k _cfor

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

In formula, λ is step pitch, and λ is arranged > 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 ₀value constantly, i.e. initial value, and Δ k is arranged _c=k _c-k _c0.If can access gain k _cderivative k _cexpression formula, also just obtained changing online k _cadaptive law.For this reason, formula (10) both sides, to time t differentiate, are obtained

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

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）

Formula (13) is done to the Laplace inverse transformation, obtain 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, between the input of reference model, output, following time domain relation is arranged

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

K _c=μ en _m(17) 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}, the k that the current time controller is adjusted in calculating _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 the time interval that front and back are adjusted between the kc value for twice.Because to k _cthe adjustment of value was carried out before each controller calculates, thereby dt=T is arranged _c.

In formula (18), μ and T _cbe all the prior fixed value of design, but the product that calculated off-line goes out both is in line computation.So employing formula (18) is to k _cvalue is carried out an online adaptive adjustment, only needs 2 multiplication, 1 sub-addition, and calculated amount is minimum.

Above-mentioned control system is controlled in the rotating speed of supersonic motor, and the control performance of setting expectation is that, under the Step reference signal function, output response non-overshoot, adjusting time are in 0.3s.Accordingly, the design reference model is

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

Subcontrol G _a(s) be

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

According to said system, the supersonic motor rotating speed is controlled to experiment, obtain rotating speed step response as shown in Figure 3, overshoot does not appear in the step response of actual measurement rotating speed, and the adjusting time in 0.3s, meet the desired control performance set.Therefore when supersonic motor Model Reference Adaptive Control System of the present invention had both met reference model and controlled device (supersonic motor) model and only has different, the Dynamic mode of gaining identical, can make again the expectation of reference model characterization control, the MIT control method can be applied in the control system of supersonic motor, adopt again the adaptive law based on gradient optimizing, make the adjustable gain k to the closed loop proportional controller simultaneously _cthe calculated amount of carrying out the online adaptive adjustment is little, thereby contributes to improve the operational efficiency of this system, and reduces system cost.

Claims (2)

1. the supersonic motor Model Reference Adaptive Control System based on MIT, it is characterized in that: this adaptive control system comprises closed loop proportional controller, reference model, supersonic motor model, adaptive law module and subcontrol, described subcontrol is arranged between closed loop proportional controller and supersonic 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 supersonic motor model

Described reference model is

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

Described supersonic motor model is

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

The adjustable gain of described closed loop proportional controller is k _c, k _cvariation by the adaptive law module controls;

Described subcontrol model is

it is input as k _cn _ref;

What described adaptive law module adopted is the adaptive law of gradient optimal method, and adaptive law is k _c=μ en _m, wherein e is the error between the output of the output of reference model and supersonic motor model, e=n _m-n, adaptation coefficient

λ is the step pitch in gradient optimal method, and λ>0.

2. the supersonic motor Model Reference Adaptive Control System based on MIT according to claim 1, is characterized in that: described subcontrol model G _a(s) with supersonic motor model G _p(s) be composed in series the generalized controlled object G (s),

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