bo dkhien pid-23

8/2/2019 Bo Dkhien Pid-23

1/23

Ph n I : Yu c u thi t k . 1. Thi t k h th ng i u khi n t ng c:

B i u khi n PID c hm truy n:

WPID(s)=KP(1+ sTi.

1

+Tds)

V i cc tham s Kp,Ti,Td ch nh nh c. i t ng l khu tr v khu qun tnh b c nh t c hm truy n:

WT(s)=1+

Ts

eLs

V i tham s L,T cho tr c: L/T=0.1; T=20.

H th ng c s nh hnh v :

2. Tnh ton cc tham s Kp,Ti,Td m b o tnh n nh v ch t l ng c a h th ng ( theo Ziegler-Nichols ).3. Xt tnh n nh c a h th ng. Tm cc i m c c v i m khng. 4. Kh o st ch t l ng, v ch n cc tham s v i cc quy lu t P, PI, PID m b o cho h th ng c ch t l ng t t nh t ( ch nh nh b ng tay ). 5. Tnh tham s t i u c a b i u khi n PID dng hm least-squares ( sai s bnh ph ng nh nh t ) v i cc tham s L v T cho.


2/23

Ph n II : Tnh ton v i MATLAB.1. Tnh ton cc tham s Kp, Ti, Td m b o tnh n nh v ch t l ng c a h

th ng:

T cng th c th c nghi m c a Ziegler-Nichols:

Lu t i u khi n Kp Ti TdP T/L 0PI 0.9T/L 10L/3 0PID 1.2T/L 2L 0.5L

V i cc tham s : L/T=0.1T=20

Ta c:L=2T=20

Khi ta c cc tham s i u khi n nh sau:

Lu t i u khi n Kp Ti TdP 10 0PI 9 6.667 0

PID 12 4 1

2. Xt h th ng v i cc lu t i u khi n P, PI, PID :

T hm truy n c a i t ng:

WT(s)=1+

Ts

eLs

Khai tri n Taylor ta c hm truy n c a khu tr g n ng ( l y n b c 3 ) nh sau:

>> T=20;L=0.1*T;

>> [num,den]=pade(L,3);>> Wtre=tf(num,den)Transfer function:-s^3 + 6 s^2 - 15 s + 15-------------------------------s^3 + 6 s^2 + 15 s + 15


3/23

>> Wdt=tf(1,[T 1])*WtreTransfer function:

-s^3 + 6 s^2 - 15 s + 15

------------------------------------------------------20 s^4 + 121 s^3 + 306 s^2 + 315 s + 15

V i cc lu t P, PI, PID ta c cc thng s Kp, Ti, Td khc nhau. Ta kh o st h th ng v i cc lu t i u khi n khc nhau:

a)Lu t P:B i u khi n chnh l khu khuy ch i v i h s khuy ch i:

Kp=10S kh i c a h th ng:

Ch ng trnh Matlab nh sau:

>> Kp=T/L;>> Wpid=Kp;>> Who=Wpid*Wdt;>> Wkin=feedback(Who,1)Transfer function:

-10 s^3 + 60 s^2 - 150 s + 150-------------------------------------------------------20 s^4 + 111 s^3 + 366 s^2 + 165 s + 165

>> pzmap(Wkin)>> step(Wkin)>> [p,z]=pzmap(Wkin)

T ta c th cc i m c c v i m khng:


4/23

th hm qu :


5/23

T a cc i m c c v i m khng:

p =

-2.6008 + 3.0343i-2.6008 - 3.0343i-0.1742 + 0.6973i-0.1742 - 0.6973i

z =

1.8389 + 1.7544i1.8389 - 1.7544i2.3222

Nh n xt:- ng c tnh t n c a h th ng h khng bao l y i m Nyquist nn h th ng n nh:


6/23

- Cc i m c c v i m khng u n m bn tri c a tr c o ( t c l cc i m c c c ph n th c nh h n 0 ). Qu trnh qu t t d n theo th i gian.

- Tuy v y ch t l ng h th ng ch a cao: + Th i gian qu c a h th ng: t qd=23.9s.+ qu i u ch nh l: max= 48.4%.+ Th i gian tng t c: t tt= 1.59s.

Nh v y th i gian qu c a h th ng l n, qu i u ch nh cao, v t qu yu c u cho php.

Ch nh nh cc tham s h th ng c ch t l ng t t nh t:

>> Kp=4.13;>> Wpid=Kp;>> Who=Wpid*Wdt;>> Wkin=feedback(Who,1)

Transfer function:

-4.13 s^3 + 24.78 s^2 - 61.95 s + 61.95-----------------------------------------------------------------20 s^4 + 116.9 s^3 + 330.8 s^2 + 253.1 s + 76.95

>> step(Wkin)


7/23

>> pzmap(Wkin)

>> [p,z]=pzmap(Wkin)p =

-2.4440 + 2.3583i-2.4440 - 2.3583i-0.4778 + 0.3245i-0.4778 - 0.3245i

z =

1.8389 + 1.7544i1.8389 - 1.7544i2.3222

Sau khi hi u ch nh ta thu c cc c tnh sau: - Th i gian qu : t qd= 8.23s.

- qu i u ch nh: max= 1.02 %.


8/23

Nh v y so v i ban u, h th ng t cht l ng cao, i m c c cch xa tr c o h n.

b) Lu t PI:B i u khi n bao g m khu khuy ch i h s K p v khu tch phn c hm

truy n:

Wtp =s

iK

S kh i c a h th ng:

Ta c ch ng trnh Matlab nh sau:

>> T=20;L=0.1*T;>> [num,den]=pade(L,3);>> Wtre=tf(num,den)Transfer function:-s^3 + 6 s^2 - 15 s + 15--------------------------------s^3 + 6 s^2 + 15 s + 15>> Wdt=tf(1,[T 1])*Wtre

Transfer function:-s^3 + 6 s^2 - 15 s + 15

------------------------------------------------------20 s^4 + 121 s^3 + 306 s^2 + 315 s + 15

>> Kp=0.9*T/L;>> Ti=10*L/3;>> Ki=Kp/Ti;


9/23

>> Wpid=Kp+tf(Ki,[1 0])Transfer function:9 s + 1.35-------------

s

>> Who=Wpid*Wdt;>> Wkin=feedback(Who,1)Transfer function:

-9 s^4 + 52.65 s^3 - 126.9 s^2 + 114.8 s + 20.25------------------------------------------------------------------------------20 s^5 + 112 s^4 + 358.6 s^3 + 188.1 s^2 + 129.8 s + 20.25

>> pzmap(Wkin)>> step(Wkin)

>> [p,z]=pzmap(Wkin)p =

-2.5593 + 2.9173i-2.5593 - 2.9173i-0.1453 + 0.5756i-0.1453 - 0.5756i-0.1907

z =

1.8389 + 1.7544i1.8389 - 1.7544i2.3222-0.1500

Qu trnh qu c a h th ng:


10/23

Cc i m c c v i m khng:


11/23

Nh n xt:V i cc thng s ban u c a b i u khi n PI, h th ng n nh nh ng ch t

l ng ch a cao: - Th i gian qu l n: t qd= 29.7s.- qu i u ch nh cao: max= 71.2%.

- Th i gian tng t c: t tt= 1.66s.

Ch nh nh cc tham s h th ng c ch t l ng t t h n:

>> Kp=0.213;>> Ti=10*L/3;>> Ki=Kp/Ti;>> Wpid=Kp+tf(Ki,[1 0])

Transfer function:0.213 s + 0.03195------------------------

s>> Who=Wpid*Wdt;>> Wkin=feedback(Who,1)

Transfer function:-0.213 s^4 + 1.246 s^3 - 3.003 s^2 + 2.716 s + 0.4793

---------------------------------------------------------------------------------20 s^5 + 120.8 s^4 + 307.2 s^3 + 312 s^2 + 17.72 s + 0.4793

Ta nh n c qu trnh qu :


12/23

th cc i m c c v i m khng:

Ta th y r ng: - Th i gian qu : t qd= 141s.- qu i u ch nh: max= 3.82%.

- Cc i m c c v i m khng: p =

-1.8924 + 1.7658i-1.8924 - 1.7658i-2.1960-0.0293 + 0.0278i-0.0293 - 0.0278i

z =

1.8389 + 1.7544i1.8389 - 1.7544i2.3222-0.1500

c) Lu t PID:


13/23

Hm truy n c a b i u khi n PID:

WPID(s)=s

KsKsK ipd ++2

S kh i c a h th ng:

Ch ng trnh Matlab nh sau:

>> T=20;L=T*0.1;>> [num,den]=pade(L,3);>> Wtre=tf(num,den)Transfer function:

-s^3 + 6 s^2 - 15 s + 15------------------------s^3 + 6 s^2 + 15 s + 15>> Wdt=tf(1,[L 1])*WtreTransfer function:

-s^3 + 6 s^2 - 15 s + 15-----------------------------------2 s^4 + 13 s^3 + 36 s^2 + 45 s + 15

>> Kp=1.2*T/L;>> Ti=2*L;>> Td=0.5*L;>> Kd=Kp*Td;>> Ki=Kp/Ti;>> Wpid=tf([Kd Kp Ki],[1 0]);>> Who=Wpid*Wdt;


14/23

>> Wkin=feedback(Who,1)Transfer function:12 s^5 - 60 s^4 + 111 s^3 - 18 s^2 - 135 s - 45-----------------------------------------------

10 s^5 - 73 s^4 + 75 s^3 - 63 s^2 - 150 s - 45>> pzmap(Wkin)>> step(Wkin)>> nyquist(Who)>> [p,z]=pzmap(Wkin)

p =

6.33490.9673 + 1.4460i0.9673 - 1.4460i-0.5000-0.4694

z =

1.8389 + 1.7544i1.8389 - 1.7544i2.3222

-0.5000-0.5000

Sau khi ch y ch ng trnh Matlab ta thu c cc k t qu sau:

- Qu trnh qu c a h th ng:


15/23

- th cc i m c c v i m khng:


16/23

- ng c tnh t n:

Nh n xt:V i cc thng s ban u c a b i u khi n PID tnh theo cng th c th c

nghi m c a Ziegler-Nichols th h th ng khng n nh. T n t i i m c c n m bn ph i tr c o, qu trnh qu khng t t d n theo th i gian.

Ch nh nh h th ng n nh v i ch t l ng t t nh t:

>> Kp=0.16;Kd=0.16;Ki=0.13;>> Wpid=tf([Kd Kp Ki],[1 0]);>> Who=Wpid*Wdt;>> Wkin=feedback(Who,1)

Transfer function:-0.16 s^5 + 0.8 s^4 - 1.57 s^3 + 0.78 s^2 + 0.45 s + 1.95

------------------------------------------------------------1.84 s^5 + 13.8 s^4 + 34.43 s^3 + 45.78 s^2 + 15.45 s + 1.95>> step(Wkin)


17/23

>> pzmap(Wkin)>> nyquist(Who)>> [p,z]=pzmap(Wkin)

p =

-4.4659-1.3086 + 1.5164i-1.3086 - 1.5164i-0.2084 + 0.1254i-0.2084 - 0.1254i

z =

1.8389 + 1.7544i1.8389 - 1.7544i2.3222-0.5000 + 0.7500i-0.5000 - 0.7500i

K t qu :- th qu trnh qu :


18/23

- th cc i m c c v i m khng:

- c tnh t n:


19/23

Ta th y r ng: - Th i gian qu : t qd= 18.1s.- qu i u ch nh: max= 0.516%.- ng c tnh t n bao l y i m Nyquist. H th ng l m t h n nh.


20/23

Ph n III:M hnh ha h th ng b ng Simulink - M c ch: Tnh cc tham s t i u c a b i u khi n PID, dng hm least-

squares (sai s bnh ph ng b nh t) v i cc tham s L v T cho.

H th ng t ch t l ng t t nh t khi hm J= dtteo

)(2

t gi tr nh nh t

v i cc gi tr t i u K p, Ki, Kd.

M hnh ha h th ng b ng Simulink:

Cc thng s trong s kh i: - Cc tham s K p, Ki, Kd c a b i u khi n PID:

Kp= 1.45; Ki= 0.23 ; Kd= 0.23 ;- Cc thng s c a khu bo ha:

Upper limit: 1.5Lower limit:-1.5

- Khu Rate Limiter:Rising slew rate: 1Falling slew rate: -1

- Khu c tr : time delay: 1

Sau khi cho ch y , kick chu t vo Scope ta c hnh v :


21/23

Ta th y:- Th i gian qu t q= 59.7s.- qu i u ch nh: max=15%.

By gi ta thay cc bi n K p, Ki, Kd vo b i u khi n PID . tnh ton cc tham s t i u ta t o cc file sau:

e.m:function e=yout_1(pid,model,tspan)opt=simset(solver,ode5);assignpid(pid);

[t,x,y]=sim(model,tspan,opt);e= y-1;

assignpid(pid):function assignpid(pid)assignin(base,Kp,pid(1));assignin(base,Ki,pid(2));assignin(base,Kd,pid(3));

pid.m:function pid=lsqpid(pid0,model,tspan)options=foptions;options=[1 0.01 0.01];pid= leastsq(yout_1,pid0,options,[],model,tspan);

Copy 3 file trn vo th m c C:\MATLAB\WORK


22/23

Tr l i c a s Command ta th c hi n nh sau:

>> pid0=[Kp Ki Kd];>> pid=lsqpid(pid0,baitap,[0 500])

Ta c cc tham s t i u c a b i u khi n:

f-COUNT RESID STEP-SIZE GRAD/SD LAMBDA4 2.13046 1 -0.14710 2.12166 0.265 -0.0341 1.3445316 2.02559 1 -0.125 0.44816222 2.00171 1 2.58e-005 0.22413929 2.00144 2.21 -2.61e-008 0.069918236 2.00111 2.66 -3.92e-008 0.0191028

43 2.00098 1.32 -1.76e-009 0.0082276449 2.00096 1.22 -8.86e-011 0.00822764Optimization Terminated Successfully

pid =

1.0935 0.0731 0.3411

Ki m tra


23/23

Tr l i s Simulink , kick chu t vo Scope ta nh n c hnh v sau: Ta th y :

- Th i gian qu : t q=39s- qu i u ch nh: max=2.5%

K T LU N:Cc tham s t i u c a b i u khi n PID ng v i i t ng bi t hm

truy n:Kp =1.0935Ki = 0.0731Kd =-0.3411

V i cc tham s t i u ny h th ng t ch t l ng t t nh t.

bo dkhien pid-23

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