CN102420553B - Based on the adjacent cross-linked many motor proportional synchronization control algorithms of modified model - Google Patents

Abstract

The present invention proposes a kind of based on the adjacent cross-linked many motor proportional synchronization control algorithms of modified model.This algorithm improves adjacent cross-coupling control structure, makes the rotating speed synchronous operation in proportion in multi-drive synchronization system between each motor.Meanwhile, for motor time become, the characteristic such as non-linear, devise fuzzy controller, propose the many motor proportional synchronization control algorithms of the adjacent cross-couplings of a kind of follow-on fuzzy.This algorithm and traditional pid algorithm have carried out simulation comparison, and demonstrate this control algolithm fast convergence rate, stability is high, can realize the synchronous operation in proportion of many motors well, specifically good dynamic property and practical value.

Description

Based on the adjacent cross-linked many motor proportional synchronization control algorithms of modified model

Technical field

The invention belongs to multi-motor synchronous control technology, particularly a kind of Synchronization Control of many motor proportionals based on intelligent control algorithm.

Background technology

In the systems such as weaving, papermaking, film take-up, the problem of multi-motor synchronous control extensively exists.It is ω 1=ω 2=that common multi-drive synchronization closes ...=ω n, namely the speed sync proportionality coefficient of each motor is all 1, and it is the simplest synchronized relation.But when actual production is as film stretching rolling, for ensureing that film runs with certain tension force, the speed between motor needs to increase progressively by a certain percentage, i.e. ω 1: ω 2: ...: ω n=μ 1: μ 2: ...: μ n.The reliability of the direct influential system of quality of multi-motor synchronous control and control precision.

Traditional synchronous control structure mainly comprises parallel control, master & slave control, Virtual-shaft control etc., and control accuracy is not high.For improving control precision, Koren proposes cross coupling structure in parallel, as motor number n>2, because Compensation Rule is difficult to determine and inapplicable (1.Yoram Koren.Cross-coupled biaxialcomputer controls for manufacturing systems [J] .Journal of Dynamic Systems, Measurement and Control, 1980,102 (4), 265-272).Perez-Pinal proposes the inclined cross-coupling control being applicable to motor number n>2, it can realize net synchronization capability well, but when motor number is too much, control structure very complicated (2.Perez-Pinal, F.J., Calderon, G., Araujo-Vargas, I.RelativeCoupling Strategy [C] //IEEE International Electric Machines and Drives Conference, 2003:1162-1166).The people such as Shih in 2002 propose adjacent cross-coupling control structure on this basis, for every platform motor, only consider the impact of adjacent two motor speeds, relatively partially cross-couplings, and control structure simplifies widely.But due to the dynamic characteristic of Alternating Current Governor System, become when there is inner parameter, the factor such as non-linear and load variations, people are difficult to set up controlled process Mathematical Modeling accurately, the application of this strategy is made to be restricted (3.Yi-Ti Shih, Chin-Sheng Chen, An-Chen Lee.A novel cross-coupling controldesign for Bi-axis motion [J] .International Journal of Machine Tool and Manufacture, 2002,42 (14): 1539-1548).The people such as Cao Ling sesames in 2008 add sliding mode controller on adjacent cross-linked basis, it can reduce external disturbance and inner parameter changes the impact brought, obtain very high synchronous control accuracy (4.CAO L Z, LI C W, NIU C, et al.Synchronized sliding-mode control formulti-induction motors based on adjacent cross-coupling [J] .Electric machines andcontrol, 2008, 12 (5): 586-592.5.LI C W, ZHAO D Z, REN J.Total sliding modespeed synchronization control of multi induction motors [J] .Systems EngineeringTheory and Practice, 2009, 29 (10): 110-117).It is applicable to the multi-motor synchronous control that proportionality coefficient is 1, and when needing synchronous with certain proportion between many motors, the design of this algorithm is comparatively complicated, acquires a certain degree of difficulty in the application.

Summary of the invention

The object of the present invention is to provide a kind of synchronization control algorithm based on the adjacent cross-couplings of modified model and fuzzy controller, thus realize the arbitrary proportion Synchronization Control of many motors.

The technical solution realizing the object of the invention is: a kind of based on the adjacent cross-linked many motor proportional synchronization control algorithms of modified model, adjacent cross-coupling control structure is improved, multi-drive synchronization system is divided into n synchronization subsystem, the controling parameters of each synchronization subsystem in adjacent cross-coupling control structure is set, add proportional component, again the controling parameters of each synchronization subsystem is reset, and set up the relation equation group of the controling parameters reset, make the rotating speed synchronous operation in proportion in multi-drive synchronization system between each motor; In each synchronization subsystem, comprise 3 parameters fuzzy self-adjusted PID controllers, realize a tracking error controlling functions and two synchronous error controlling functions respectively.

The concrete steps improved adjacent cross-coupling control structure are as follows:

The first step: establish synchronous motor to have n platform, this multi-drive synchronization system is divided into n synchronization subsystem, and division methods is: (1,2,3), (2,3,4),, (i-1, i, i+1),, (n-1, n, 1), (n, 1,2), n >=3, i is any motor;

Second step: set the tracking error of i-th motor as:

e _i(t)＝ω _i(t)-ω _i*(t)

Wherein, ω _it () is the output speed of i-th motor in t, ω _i* (t) is the reference velocity of i-th motor in t, t>=0;

3rd step: the synchronous error ε establishing i-th motor and the i-th-1 motor _i1the synchronous error ε of (t) and i-th motor and the i-th+1 motor _i2t () is respectively:

ε _i1(t)＝e _i(t)-e _i-1(t)

ε _i2(t)＝e _i(t)-e _i+1(t)

4th step: the controling parameters relation equation group setting up each synchronization subsystem in adjacent cross-coupling control structure: the tracking error e making every platform motor _it (), every platform motor are adjacent the synchronous error ε of two motors _i1(t), ε _i2t () stable convergence, namely will meet following formula:

$\left\{\begin{array}{c}\underset{t\→\∞}{\lim }{e}_i\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)-{{\mathrm{\ω}}_i}^{*}\left(t\right))=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i1}\left(t\right)=\underset{t\→\∞}{\lim }(e_i\left(t\right)-e_{i-1}\left(t\right))=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i2}\left(t\right)=\underset{t\→\∞}{\lim }(e_i\left(t\right)-e_{i+1}\left(t\right))=0\end{array}\right.$

5th step: when the rotation speed relation in multi-drive synchronization system between n platform motor is ω ₁: ω ₂: ...: ω _n=μ ₁: μ ₂: ...: μ _ntime, μ _ibe the proportionality coefficient of i-th motor, μ _i> 0, i ∈ n, if the ratio synchronous error between two motors be the output speed of each motor in t divided by the difference after respective proportionality coefficient, then the ratio synchronous error ε of i-th motor and the i-th-1 motor _i1 ^*the ratio synchronous error ε of (t) and i-th motor and the i-th+1 motor _i2 ^*t () is respectively:

ε _i1 ^*(t)＝ω _i(t)/μ _i-ω _i-1(t)/μ _i-1

ε _i2 ^*(t)＝ω _i(t)/μ _i-ω _i+1(t)/μ _i+1

6th step: the relation equation group setting up parameter in the adjacent cross-coupling control structure through resetting: when controlling each subsystem, should be able to e be made _i(t), ε _i1 ^*(t), ε _i2 ^*t () converges on zero, namely will meet following formula:

$\left\{\begin{array}{c}\underset{t\→\∞}{\lim }{e}_i\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)-{{\mathrm{\ω}}_i}^{*}\left(t\right))=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i1}^{*}\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)/{\mathrm{\μ}}_i-{\mathrm{\ω}}_{i-1}\left(t\right)/{\mathrm{\μ}}_{i-1})=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i2}^{*}\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)/{\mathrm{\μ}}_i-{\mathrm{\ω}}_{i+1}\left(t\right)/{\mathrm{\μ}}_{i+1})=0\end{array}\right.$

7th step: make ω * (t)=ω _i* (t)/μ _i, it is i-th motor in the reference velocity of t divided by the proportionality coefficient of this motor; Reference speed value ω * (t) that first given one, each motor is unified, then i-th motor is at the reference velocity ω of t _i* (t) is multiplied by respective proportionality coefficient μ for this unifies reference speed value ω * (t) _i, then the reference velocity ω of each motor is controlled in real time by fuzzy controller _i* (t).

The described parameters fuzzy self-adjusted PID controller realizing tracking error controlling functions is tracking error controller, and the described parameters fuzzy self-adjusted PID controller realizing synchronous error controlling functions is synchronous error controller; If C _i0be the tracking error controller of i-th motor, C _i1, C _i2be two synchronous error controllers of i-th motor; C _i0deviation be input as e _it (), exports as u _i0(t), C _i1, C _i2deviation input be respectively ε _i1 ^*(t), ε _i2 ^*t (), exports and is respectively u _i1(t), u _i2(t), then u _i(t)=u _i0(t)+u _i1(t)+u _i2t () is the output of i-th synchronization subsystem, i.e. the rate controlling amount of i-th motor.

The present invention compared with prior art, its remarkable advantage:

(1) adjacent cross-coupling control structure is improved, increase proportional component on the original basis, controling parameters is redefined, and set up the relation equation group of the controling parameters redefined.This modified model control structure can not only realize the speed Complete Synchronization of many motors, can also realize many motors and carry out synchronously with arbitrary proportion.

(2) utilize the thought of fuzzy reasoning, fuzzy controller is combined with PID controller, devise fuzzy controller.Compared with conventional PID controllers, it can overcome parameter time varying in complication system, the problem such as non-linear better, eliminates steady-state error, has higher synchronous control accuracy and convergence rate faster.

Accompanying drawing explanation

Fig. 1 is the adjacent cross-coupling control structure of modified model.

Fig. 2 is fuzzy controller structure.

Fig. 3 a, 3b are the simulated program of this control algolithm in Matlab software.

Fig. 4 a, 4b, 4c, 4d are modified model adjacent cross-couplings Fuzzy PID Control Simulation curves.

Fig. 5 a, 5b, 5c, 5d are modified model adjacent cross-couplings PID control imitation curves.

Fig. 6 is the flow chart of the synchronization control algorithm that the present invention is based on the adjacent cross-couplings of modified model and fuzzy controller.

Embodiment

The present invention is a kind of based on the adjacent cross-linked many motor proportional synchronization control algorithms of modified model, and on the basis of improving adjacent cross-coupling control structure, add fuzzy controller, step is as follows:

The first step: define the parameter in adjacent cross-coupling control structure, the basic thought of adjacent cross-coupling control structure is, when implementing to control to each motor, only considers the state of self and adjacent two motors, and this will simple control structure greatly; On this basis, adjacent cross-coupling control structure is improved, multi-drive synchronization system is divided into n synchronization subsystem, define the controling parameters of each synchronization subsystem in adjacent cross-coupling control structure, add proportional component, again the controling parameters of each synchronization subsystem is redefined, and set up the relation equation group of the controling parameters redefined, make the rotating speed synchronous operation in proportion in multi-drive synchronization system between each motor.

Second step: because the dynamic characteristic of many motors is different, there is the phenomenons such as parameter time varying, non-linear, delay, and fuzzy control does not rely on the accurate model of object, has good self study and None-linear approximation ability during operation.Therefore, the present invention utilizes the thought of fuzzy reasoning, is combined by fuzzy controller with conventional PID controllers, in the adjacent cross-coupling control structure of modified model, designs parameters fuzzy self-adjusted PID controller.In each synchronization subsystem, comprise 3 parameters fuzzy self-adjusted PID controllers, realize a tracking error controlling functions and two synchronous error controlling functions respectively.Therefore, 3n fuzzy controller is comprised in whole control structure altogether.

Below in conjunction with accompanying drawing, the present invention is described in further detail.

The present invention is based on the adjacent cross-linked many motor proportional synchronization control algorithms of modified model, on the basis that adjacent cross-coupling control structure is improved, add fuzzy controller.Specific operation process is as follows:

The first step: composition graphs 1, if synchronous motor has n platform, this multi-drive synchronization system is divided into n synchronization subsystem, and division methods is: (1,2,3), (2,3,4) ..., (i-1, i, i+1) ..., (n-1, n, 1), (n, 1,2), n >=3, i is any motor;

Second step: the tracking error of definition i-th motor is:

e _i(t)＝ω _i(t)-ω _i*(t)

Wherein, ω _it () is the output speed of i-th motor in t, ω _i* (t) is the reference velocity of i-th motor in t, t>=0;

3rd step: the synchronous error ε of definition i-th motor and the i-th-1 motor _i1the synchronous error ε of (t) and i-th motor and the i-th+1 motor _i2t () is respectively:

ε _i1(t)＝e _i(t)-e _i-1(t)

ε _i2(t)＝e _i(t)-e _i+1(t)

4th step: the controling parameters relation equation group setting up each synchronization subsystem in adjacent cross-coupling control structure: the tracking error e making every platform motor _it (), every platform motor are adjacent the synchronous error ε of two motors _i1(t), ε _i2t () stable convergence, namely will meet following formula:

$\left\{\begin{array}{c}\underset{t\→\∞}{\lim }{e}_i\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)-{{\mathrm{\ω}}_i}^{*}\left(t\right))=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i1}\left(t\right)=\underset{t\→\∞}{\lim }(e_i\left(t\right)-e_{i-1}\left(t\right))=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i2}\left(t\right)=\underset{t\→\∞}{\lim }(e_i\left(t\right)-e_{i+1}\left(t\right))=0\end{array}\right.$

This formula is applicable to the simplest synchronous proportional coefficient μ _ithe synchronous control system of=1.

5th step: when the rotation speed relation in multi-drive synchronization system between n platform motor is ω ₁: ω ₂: ...: ω _n=μ ₁: μ ₂: ...: μ _ntime, μ _ibe the proportionality coefficient of i-th motor, μ _i> 0, i ∈ n, the ratio synchronous error defined between two motors be the output speed of each motor in t divided by the difference after respective proportionality coefficient, then the ratio synchronous error ε of i-th motor and the i-th-1 motor _i1 ^*the ratio synchronous error ε of (t) and i-th motor and the i-th+1 motor _i2 ^*t () is respectively:

ε _i1 ^*(t)＝ω _i(t)/μ _i-ω _i-1(t)/μ _i-1

ε _i2 ^*(t)＝ω _i(t)/μ _i-ω _i+1(t)/μ _i+1

6th step: the relation equation group setting up parameter in the adjacent cross-coupling control structure through redefining: when controlling each subsystem, should be able to e be made _i(t), ε _i1 ^*(t), ε _i2 ^*t () converges on zero, namely will meet following formula:

$\left\{\begin{array}{c}\underset{t\→\∞}{\lim }{e}_i\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)-{{\mathrm{\ω}}_i}^{*}\left(t\right))=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i1}^{*}\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)/{\mathrm{\μ}}_i-{\mathrm{\ω}}_{i-1}\left(t\right)/{\mathrm{\μ}}_{i-1})=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i2}^{*}\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)/{\mathrm{\μ}}_i-{\mathrm{\ω}}_{i+1}\left(t\right)/{\mathrm{\μ}}_{i+1})=0\end{array}\right.$

7th step: in Fig. 1, makes ω * (t)=ω _i* (t)/μ _i, it is i-th motor in the reference velocity of t divided by the proportionality coefficient of this motor; Reference speed value ω * (t) that first given one, each motor is unified, then i-th motor is at the reference velocity ω of t _i* (t) is multiplied by respective proportionality coefficient μ for this unifies reference speed value ω * (t) _i, then the reference velocity ω of each motor is controlled in real time by fuzzy controller _i* (t);

8th step: composition graphs 1, Fig. 2, in the adjacent cross-coupling control structure of modified model, utilizes the thought of fuzzy reasoning, is combined by fuzzy controller with PID controller, design fuzzy controller.

In each synchronization subsystem, comprise 3 parameters fuzzy self-adjusted PID controllers, realize a tracking error controlling functions and two synchronous error controlling functions respectively; What be used for realizing tracking error controlling functions is also called tracking error controller, and what be used for realizing synchronous error controlling functions is also called synchronous error controller; Definition C _i0be the tracking error controller of i-th motor, C _i1, C _i2be two synchronous error controllers of i-th motor; C _i0deviation be input as e _it (), exports as u _i0(t), C _i1, C _i2deviation input be respectively ε _i1 ^*(t), ε _i2 ^*t (), exports and is respectively u _i1(t), u _i2(t), then u _i(t)=u _i0(t)+u _i1(t)+u _i2t () is the output of i-th synchronization subsystem, i.e. the rate controlling amount of i-th motor.In the adjacent cross-coupling control structure of this modified model, comprise 3n fuzzy controller altogether.

The design procedure of fuzzy controller is as follows:

(1) composition graphs 2, fuzzy controller is divided into fuzzy controller and the whole PID controller two parts of Parameter adjustable, fuzzy controller adopts dual input three to export control structure, and the deviation e of motor speed and deviation variation rate ec is input, three parameter Δ K of the whole PID controller of Parameter adjustable _p, Δ K _i, Δ K _dfor exporting; According to the change of input e, ec, to parameter Δ K _p, Δ K _i, Δ K _dcarry out online self-tuning, obtain new PID controller parameter K _p, K _i, K _d, thus PID controller is again to the knots modification of motor output speeds;

(2) to input e, ec and output Δ K _p, Δ K _i, Δ K _dcarry out obfuscation; Set respectively 7 linguistic variables as NB, NM, NS, Z, PS, PM, PB}, implication is followed successively by negative large, in negative, negative little, zero, just little, center, honest; Their basic domain, fuzzy domain and quantizing factor are as follows respectively:

e：(-a,a)，{-6，6}，K _e＝6/a；

ec：(-b,b)，{-6，6}，K _ec＝6/b；

ΔK _P：(-c,c)，{-6，6}，K _ΔKP＝c/6；

ΔK _I：(-d,d)，{-6，6}，K _ΔKI＝d/6；

ΔK _D：(-e,e)，{-6，6}，K _ΔKD＝e/6；

Wherein, a, b, c, d, e constant all for being greater than 0, K _e, K _ec, K _{Δ KP}, K _{Δ KI}, K _{Δ KD}be respectively e, ec, Δ K _p, Δ K _i, Δ K _dquantizing factor;

(3) input e, ec and output Δ K is set up _p, Δ K _i, Δ K _dmembership function, all get trigonometric function;

(4) formulate fuzzy control rule, altogether (7 × 7) 49, formulate principle as follows: | when e| is larger, for when accelerating response speed and prevent from starting, deviation e becomes large instantaneously, get larger K _pless K _d; As | e| and | ec| is median size, for making the overshoot of system responses reduce, K _p, K _i, K _dall can not be too large, less K should be got _ivalue, K _pand K _dsize is moderate, to ensure the response speed of system; When | e| is less, for making system have good steady-state behaviour, should increase K _pand K _ivalue, simultaneously for avoiding system oscillation, and consider anti-interference, K _dbe generally median size.

Fuzzy control rule is formulated to Δ K _p, Δ K _i, Δ K _dfuzzy control rule table, as table 1.

Table 1 Δ K _p, Δ K _iwith Δ K _dfuzzy reasoning table

(5) fuzzy control rule of fuzzy reasoning table is generated following conditional statement:

If e is Ai and ec is Bi,thenΔK _Pis Ci,ΔK _Iis Di,ΔK _Dis Ei

Ai, Bi, Ci, Di and Ei in conditional statement are the fuzzy sets of input/output variable, then fuzzy reasoning table can be regarded as and export rule base constructed by rule by a series of dual input three, totally 49:

1.If e is NB and ec is NB,thenΔK _Pis PB,ΔK _Iis NB,ΔK _Dis PS

2.If e is NB and ec is NM,thenΔK _Pis PB,ΔK _Iis NB,ΔK _Dis NS

3.If e is NB and ec is NS,thenΔK _Pis PM,ΔK _Iis NM,ΔK _Dis NB

……

49.If e is PB and ec is PB,thenΔK _Pis NB,ΔK _Iis PB,ΔK _Dis PB

(6) according to fuzzy control rule, carry out fuzzy reasoning, fuzzy reasoning adopts " Mamdani " reasoning algorithm conventional in engineering, adopts " very big-minimum " composition rule to carry out fuzzy operation, obtains Δ K respectively _p, Δ K _i, Δ K _dthe degree of membership of all fuzzy value under different e and ec, follow the principles into:

μ _U(Z _U)＝(w ₁∧μ _C1(U))∨(w ₂∧μ _C2(U))

w ₁＝μ _A1(E ₀)∧μ _B1(EC ₀)

w ₂＝μ _A2(E ₀)∧μ _B2(EC ₀)

Wherein, " ∧ " is minimizing operation, and " ∨ " is maximizing operation; μ _u(Z _u) be the degree of membership of controlled quentity controlled variable U fuzzy set, controlled quentity controlled variable U comprises Δ K _p, Δ K _i, Δ K _d; E ₀for error; EC ₀for error change; μ _a1(E ₀), μ _a2(E ₀) be E ₀to fuzzy set A ₁, A ₂degree of membership; μ _b1(EC ₀), μ _b2(EC ₀) be EC ₀to fuzzy set B ₁, B ₂degree of membership; μ _c1(U), μ _c2(U) for controlled quentity controlled variable U is to fuzzy set C ₁, C ₂degree of membership.

(7) by e, ec, Δ K _p, Δ K _i, Δ K _dfuzzy subset's degree of membership, and the measured value of error e and error rate ec, uses anti fuzzy method gravity model appoach to calculate, by fuzzy quantity defuzzification, is converted into controling parameters Δ K _p, Δ K _i, Δ K _dexact value, thus obtain fuzzy control table;

(8) three the output variable Δ K obtained by fuzzy algorithmic approach _p, Δ K _i, Δ K _d, in conjunction with conventional PID controllers initial parameter K _p0, K _i0, K _d0, bring computing formula K into _p=K _p0+ Δ K _p, K _i=K _i0+ Δ K _i, K _d=K _d0+ Δ K _d, complete the on-line correction to pid parameter.

Composition graphs 3a, Fig. 3 b, in the simulink module of matlab, establishes the simulation model of this control algolithm.

Set in this system, every platform motor speed is 1.01 times of last motor, and namely the synchronous proportional of four motors closes is ω ₁: ω ₂: ω ₃: ω ₄=1:1.01:1.01 ²: 1.01 ³.Wherein the initial speed of First motor is given as 100rad/s, and when 25s, rotating speed is reduced to 60rad/s, and other three motors synchronously change according to ratio, when 40s, gives their disturbances of the amplitude such as simultaneously.Simulation result as shown in Figure 4.

Fig. 4 a is the output speed ω of each motor _i; Fig. 4 b is the tracking error e of each motor _i, e _i(t)=ω _i(t)-ω _i* (t); Fig. 4 c is the ratio synchronous error ε between motor _i1 ^*, ε _i1 ^*(t)=ω _i(t)/μ _i-ω _i-1(t)/μ _i-1, be respectively motor 1 and motor 4, motor 2 and motor 1, motor 3 and motor 2, the ratio synchronous error between motor 4 and motor 3; Fig. 4 d is synchronous proportional coefficient μ actual between each motor _i, make μ here ₁=1, then μ _i(t)=ω _i(t)/ω ₁(t).

Can find out by figure, the tracking error of 4 motors all can converge on zero in 2s, speed change or when there is disturbance, and waveform can produce beating in various degree, but can restrain rapidly and reach stable, shows that system has good convergence and adaptivity; Ratio synchronous error between motor, can converge on zero in 5s when system cloud gray model or speed change, and worst error is no more than 10%, when there is disturbance wave form varies very little and very rapid convergence to stable, show that system does not have cumulative errors, there is higher synchronization accuracy; Synchronous proportional coefficient between motor, except there is obviously fluctuation when speed change except, almost remains unchanged when stable operation or disturbance, embodies the stability of synchronization of system and good robustness.

This control algolithm and other algorithm also compare by the present invention, and when control structure is constant, realized by controller by common PID, simulated effect as shown in Figure 5.As can be seen from Figure, tracking error and the synchronous error convergence time of motor are all correspondingly elongated, and synchronous error value also increases to 25%, and synchronous proportional coefficient has obvious fluctuation, and stability reduces, and changes greatly when speed change, and synchronism is deteriorated.

Two emulation experiments indicate the control algolithm of the present invention's proposition, in system cloud gray model, speed change or when there is disturbance, can realize each motor with certain proportion synchronous operation fast and stable, and net synchronization capability is better than conventional control algolithm.

Claims (3)

1. one kind based on the adjacent cross-linked many motor proportional synchronization control algorithms of modified model, it is characterized in that: adjacent cross-coupling control structure is improved, multi-drive synchronization system is divided into n synchronization subsystem, the controling parameters of each synchronization subsystem in adjacent cross-coupling control structure is set, add proportional component, again the controling parameters of each synchronization subsystem is reset, and set up the relation equation group of the controling parameters reset, make the rotating speed synchronous operation in proportion in multi-drive synchronization system between each motor; In each synchronization subsystem, comprise 3 parameters fuzzy self-adjusted PID controllers, realize a tracking error controlling functions and two synchronous error controlling functions respectively;

The concrete steps improved adjacent cross-coupling control structure are as follows:

The first step: establish synchronous motor to have n platform, this multi-drive synchronization system is divided into n synchronization subsystem, and division methods is: (1,2,3), (2,3,4),, (i-1, i, i+1),, (n-1, n, 1), (n, 1,2), n >=3, i is any motor;

Second step: set the tracking error of i-th motor as:

e _i(t)＝ω _i(t)-ω _i*(t)

Wherein, ω _it () is the output speed of i-th motor in t, ω _i* (t) is the reference velocity of i-th motor in t, t>=0;

3rd step: the synchronous error ε establishing i-th motor and the i-th-1 motor _i1the synchronous error ε of (t) and i-th motor and the i-th+1 motor _i2t () is respectively:

ε _i1(t)＝e _i(t)-e _i-1(t)

ε _i2(t)＝e _i(t)-e _i+1(t)

4th step: the controling parameters relation equation group setting up each synchronization subsystem in adjacent cross-coupling control structure: the tracking error e making every platform motor _it (), every platform motor are adjacent the synchronous error ε of two motors _i1(t), ε _i2t () stable convergence, namely will meet following formula:

$\left\{\begin{array}{c}\underset{t\→\∞}{\lim }{e}_i\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)-{{\mathrm{\ω}}_i}^{*}\left(t\right))=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i1}\left(t\right)=\underset{t\→\∞}{\lim }(e_i\left(t\right)-e_{i-1}\left(t\right))=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i2}\left(t\right)=\underset{t\→\∞}{\lim }(e_i\left(t\right)-e_{i+1}\left(t\right))=0\end{array}\right.$

5th step: when the rotation speed relation in multi-drive synchronization system between n platform motor is ω ₁: ω ₂: ...: ω _n=μ ₁: μ ₂: ...: μ _ntime, μ _ibe the proportionality coefficient of i-th motor, μ _i> 0, i ∈ n, if the ratio synchronous error between two motors be the output speed of each motor in t divided by the difference after respective proportionality coefficient, then the ratio synchronous error ε of i-th motor and the i-th-1 motor _i1 ^*the ratio synchronous error ε of (t) and i-th motor and the i-th+1 motor _i2 ^*t () is respectively:

ε _i1 ^*(t)＝ω _i(t)/μ _i-ω _i-1(t)/μ _i-1

ε _i2 ^*(t)＝ω _i(t)/μ _i-ω _i+1(t)/μ _i+1

6th step: the relation equation group setting up parameter in the adjacent cross-coupling control structure through again establishing: when controlling each subsystem, should be able to e be made _i(t), ε _i1 ^*(t), ε _i2 ^*t () converges on zero, namely will meet following formula:

$\left\{\begin{array}{c}\underset{t\→\∞}{\lim }{e}_i\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)-{{\mathrm{\ω}}_i}^{*}\left(t\right))=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i1}^{*}\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)/{\mathrm{\μ}}_i-{\mathrm{\ω}}_{i-1}\left(t\right)/{\mathrm{\μ}}_{i-1})=0\\ \underset{t\→\∞}{\lim }{\mathrm{\ϵ}}_{i2}^{*}\left(t\right)=\underset{t\→\∞}{\lim }({\mathrm{\ω}}_i\left(t\right)/{\mathrm{\μ}}_i-{\mathrm{\ω}}_{i+1}\left(t\right)/{\mathrm{\μ}}_{i+1})=0\end{array}\right.$

7th step: make ω * (t)=ω _i* (t)/μ _i, it is i-th motor in the reference velocity of t divided by the proportionality coefficient of this motor; Reference speed value ω * (t) that first given one, each motor is unified, then i-th motor is at the reference velocity ω of t _i* (t) is multiplied by respective proportionality coefficient μ for this unifies reference speed value ω * (t) _i, then the reference velocity ω of each motor is controlled in real time by fuzzy controller _i* (t);

The described parameters fuzzy self-adjusted PID controller realizing tracking error controlling functions is tracking error controller, and the described parameters fuzzy self-adjusted PID controller realizing synchronous error controlling functions is synchronous error controller; Definition C _i0be the tracking error controller of i-th motor, C _i1, C _i2be two synchronous error controllers of i-th motor; C _i0deviation be input as e _it (), exports as u _i0(t), C _i1, C _i2deviation input be respectively ε _i1 ^*(t), ε _i2 ^*t (), exports and is respectively u _i1(t), u _i2(t), then u _i(t)=u _i0(t)+u _i1(t)+u _i2t () is the output of i-th synchronization subsystem, i.e. the rate controlling amount of i-th motor.

2. according to claim 1 based on the adjacent cross-linked many motor proportional synchronization control algorithms of modified model, it is characterized in that the realization of described parameters fuzzy self-adjusted PID controller, step is as follows:

The first step: fuzzy controller is divided into fuzzy controller and the whole PID controller two parts of Parameter adjustable, fuzzy controller adopts dual input three to export control structure, the deviation e of motor speed and deviation variation rate ec is input, three parameter Δ K of the whole PID controller of Parameter adjustable _p, Δ K _i, Δ K _dfor exporting; According to the change of input e, ec, to parameter Δ K _p, Δ K _i, Δ K _dcarry out online self-tuning, obtain new PID controller parameter K _p, K _i, K _d, thus PID controller is again to the knots modification of motor output speeds;

Second step: to input e, ec and output Δ K _p, Δ K _i, Δ K _dcarry out obfuscation; Set respectively 7 linguistic variables as NB, NM, NS, Z, PS, PM, PB}, implication is followed successively by negative large, in negative, negative little, zero, just little, center, honest; Their basic domain, fuzzy domain and quantizing factor are as follows respectively:

e：(-a,a)，{-6，6}，K _e＝6/a；

ec：(-b,b)，{-6，6}，K _ec＝6/b；

ΔK _P：(-c,c)，{-6，6}，K _ΔKP＝c/6；

ΔK _I：(-d,d)，{-6，6}，K _ΔKI＝d/6；

ΔK _D：(-e,e)，{-6，6}，K _ΔKD＝e/6；

Wherein, a, b, c, d, e constant all for being greater than 0, K _e, K _ec, K _{Δ KP}, K _{Δ KI}, K _{Δ KD}be respectively e, ec, Δ K _p, Δ K _i, Δ K _dquantizing factor;

3rd step: set up input e, ec and output Δ K _p, Δ K _i, Δ K _dmembership function, all get trigonometric function;

4th step: formulate fuzzy control rule, and make Δ K _p, Δ K _i, Δ K _dfuzzy control rule table;

5th step: the fuzzy control rule of fuzzy reasoning table is generated following conditional statement:

If e is Ai and ec is Bi,then ΔK _Pis Ci,ΔK _Iis Di,ΔK _Dis Ei

Ai, Bi, Ci, Di and Ei in conditional statement are the fuzzy sets of input/output variable, then fuzzy reasoning table is for being exported the rule base constructed by rule by a series of dual input three;

6th step: according to fuzzy control rule, carries out fuzzy reasoning; Fuzzy reasoning adopts " Mamdani " reasoning algorithm, adopts " very big-minimum " composition rule to carry out fuzzy operation, obtains Δ K respectively _p, Δ K _i, Δ K _dthe degree of membership of all fuzzy value under different e and ec, follow the principles into:

μ _U(Z _U)＝(w ₁∧μ _C1(U))∨(w ₂∧μ _C2(U))

w ₁＝μ _A1(E ₀)∧μ _B1(EC ₀)

w ₂＝μ _A2(E ₀)∧μ _B2(EC ₀)

Wherein, " ∧ " is minimizing operation, and " ∨ " is maximizing operation; μ _u(Z _u) be the degree of membership of controlled quentity controlled variable U fuzzy set, controlled quentity controlled variable U comprises Δ K _p, Δ K _i, Δ K _d; E ₀for error; EC ₀for error change; μ _a1(E ₀), μ _a2(E ₀) be E ₀to fuzzy set A ₁, A ₂degree of membership; μ _b1(EC ₀), μ _b2(EC ₀) be EC ₀to fuzzy set B ₁, B ₂degree of membership; μ _c1(U), μ _c2(U) for controlled quentity controlled variable U is to fuzzy set C ₁, C ₂degree of membership;

7th step: by e, ec, Δ K _p, Δ K _i, Δ K _dfuzzy subset's degree of membership, and the measured value of error e and error rate ec, uses anti fuzzy method gravity model appoach to calculate, by fuzzy quantity defuzzification, is converted into controling parameters Δ K _p, Δ K _i, Δ K _dexact value, thus obtain fuzzy control table;

8th step: three the output variable Δ K obtained by fuzzy algorithmic approach _p, Δ K _i, Δ K _d, in conjunction with PID controller initial parameter K _p0, K _i0, K _d0, bring computing formula K into _p=K _p0+ Δ K _p, K _i=K _i0+ Δ K _i, K _d=K _d0+ Δ K _d, complete the on-line correction to pid parameter.

3. according to claim 2 based on the adjacent cross-linked many motor proportional synchronization control algorithms of modified model, it is characterized in that described fuzzy control rule table is as follows: