东北大学自动化控制系统计算机辅助设计实验模板
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y3 0 0 0
d =
u1
y1 0
y2 0
y3 0
Continuous-time model.
>> G=tf(G)
Transfer function from input to output...
2
#1: ----------------------
s^3 + 13 s^2 + 4 s + 5
#2: 0
6
functionH=feedback(G1,G2,key)
ifnargin==2;key=-1;end,H=G1/(sym(1)-key*G1*G2);H=simple(H);
>> syms J Kp Ki s;
>> gc=(Kp*s+Ki)/s;
>> g=(s+1)/(J*s^2+2*s+5);
>> H=(z^2+0.568)/(z-1)/(z^2-0.2*z+0.99)
Transfer function:
z^2 + 0.568
-----------------------------
z^3 - 1.2 z^2 + 1.19 z - 0.99
Sampling time: 0.1
4
>> A=[0 1 0;0 0 1;-5 -4 -13];
>> plot(t,y)
>> figure;plot3(y(:,1),y(:,2),y(:,3)),grid,
2
function[y,yeq]=f2a(x)
yeq=[];
y=4*x(1)^2+x(2)^2-4;
>> Aeq=[];Beq=[];A=[];B=[];
>> xm=[0;0]; xM=[];x0=[0;0];
(s^2 + 3.667s + 3.501) (s^2 + 11.73s + 339.1) (s^2 + 203.1s + 1.07e004)
( b)
>> z=tf('z');
>> G=(35786.7*z^-1+108444)/[(z^-1+4)*(z^-1+20)*(z^-1+74.04)];
(s+12.72) (s^2 + 0.2836s + 0.3932)
5
>> num=[1,2];
>> den=[1,1,0.16];
>> H=tf(num,den,'Ts',1);
>> H
Transfer function:
z + 2
--------------
z^2 + z + 0.16
Sampling time: 1
>> gg=feedback(g*gc,1)
>> gg=feedback(g*gc,1)
gg =
((Ki + Kp*s)*(s + 1))/(J*s^3 + (Kp + 2)*s^2 + (Ki + Kp + 5)*s + Ki)
7
( a)
>> s=tf('s');
>> G=(211.87*s+317.64)/(s+20)/(s+94.34)/(s+0.1684);
东北大学自动化控制系统计算机辅助设计实验
控制系统计算机辅助设计
第
1
functiondx=lorenzeq(t,x)
dx=[-x(2)-x(3);
x(1)+0.2*x(2);
0.2+(x(1)-5.7)*x(3);]
>> x0=[0;0;0];
>> [t,y]=ode45('lorenzeq',[0,100],x0);
>> Gc=(169.6*s+400)/s/(s+4);
>> Hs=1/(0.01*s+1);
>> GG=feedback(G*Gc,Hs)
Transfer function:
359.3 s^3 + 3.732e004 s^2 + 1.399e005 s + 127056
-----------------------------------------------------------------
0.01 s^6 + 2.185 s^5 + 142.1 s^4 + 2444 s^3 + 4.389e004 s^2
+ 1.399e005 s + 127056
>> zpk(GG)
Zero/pole/gain:
35933.152 (s+100) (s+2.358) (s+1.499)
--------------------------------------------------------------------------
>> B=[0;0;2];
>> C=[1 0 0;0 0 0;0 0 0];
>> D=[0];
>> G=ss(A,B,C,D);
>> G
a =
x1 x2 x3
x1 0 1 0
x2 0 0 1
x3 -5 -4 -13
b =
u1
x1 0
x2 0
x3 2
c =ห้องสมุดไป่ตู้
x1 x2 x3
y1 1 0 0
y2 0 0 0
>> num=[2];
>> den=[1,13,4,5];
>> G=tf(num,den);
>> G
Transfer function:
2
----------------------
s^3 + 13 s^2 + 4 s + 5
>> GG=zpk(G)
Zero/pole/gain:
2
----------------------------------
>> f1=inline('x(1)^2-2*x(1)+x(2)');
>> [x,f]=fmincon(f1,x0,A,B,Aeq,Beq,xm,xM,'f2a');x',f
ans =
1.0000 0
f =
-1
3
( a)
>>s=tf('s');G=(s^3+4*s+2)/s^3/(s^2+2)/[(s^2+1)^3+2*s+5]
#3: 0
>> GG=zpk(G)
Zero/pole/gain from input to output...
2
#1: ----------------------------------
(s+12.72) (s^2 + 0.2836s + 0.3932)
#2: 0
#3: 0
根据微分方程也能够直接写出传递函数模型:
Transfer function:
s^3 + 4 s + 2
------------------------------------------------------
s^11 + 5 s^9 + 9 s^7 + 2 s^6 + 12 s^5 + 4 s^4 + 12 s^3
( b)
>> z=tf('z',0.1);
d =
u1
y1 0
y2 0
y3 0
Continuous-time model.
>> G=tf(G)
Transfer function from input to output...
2
#1: ----------------------
s^3 + 13 s^2 + 4 s + 5
#2: 0
6
functionH=feedback(G1,G2,key)
ifnargin==2;key=-1;end,H=G1/(sym(1)-key*G1*G2);H=simple(H);
>> syms J Kp Ki s;
>> gc=(Kp*s+Ki)/s;
>> g=(s+1)/(J*s^2+2*s+5);
>> H=(z^2+0.568)/(z-1)/(z^2-0.2*z+0.99)
Transfer function:
z^2 + 0.568
-----------------------------
z^3 - 1.2 z^2 + 1.19 z - 0.99
Sampling time: 0.1
4
>> A=[0 1 0;0 0 1;-5 -4 -13];
>> plot(t,y)
>> figure;plot3(y(:,1),y(:,2),y(:,3)),grid,
2
function[y,yeq]=f2a(x)
yeq=[];
y=4*x(1)^2+x(2)^2-4;
>> Aeq=[];Beq=[];A=[];B=[];
>> xm=[0;0]; xM=[];x0=[0;0];
(s^2 + 3.667s + 3.501) (s^2 + 11.73s + 339.1) (s^2 + 203.1s + 1.07e004)
( b)
>> z=tf('z');
>> G=(35786.7*z^-1+108444)/[(z^-1+4)*(z^-1+20)*(z^-1+74.04)];
(s+12.72) (s^2 + 0.2836s + 0.3932)
5
>> num=[1,2];
>> den=[1,1,0.16];
>> H=tf(num,den,'Ts',1);
>> H
Transfer function:
z + 2
--------------
z^2 + z + 0.16
Sampling time: 1
>> gg=feedback(g*gc,1)
>> gg=feedback(g*gc,1)
gg =
((Ki + Kp*s)*(s + 1))/(J*s^3 + (Kp + 2)*s^2 + (Ki + Kp + 5)*s + Ki)
7
( a)
>> s=tf('s');
>> G=(211.87*s+317.64)/(s+20)/(s+94.34)/(s+0.1684);
东北大学自动化控制系统计算机辅助设计实验
控制系统计算机辅助设计
第
1
functiondx=lorenzeq(t,x)
dx=[-x(2)-x(3);
x(1)+0.2*x(2);
0.2+(x(1)-5.7)*x(3);]
>> x0=[0;0;0];
>> [t,y]=ode45('lorenzeq',[0,100],x0);
>> Gc=(169.6*s+400)/s/(s+4);
>> Hs=1/(0.01*s+1);
>> GG=feedback(G*Gc,Hs)
Transfer function:
359.3 s^3 + 3.732e004 s^2 + 1.399e005 s + 127056
-----------------------------------------------------------------
0.01 s^6 + 2.185 s^5 + 142.1 s^4 + 2444 s^3 + 4.389e004 s^2
+ 1.399e005 s + 127056
>> zpk(GG)
Zero/pole/gain:
35933.152 (s+100) (s+2.358) (s+1.499)
--------------------------------------------------------------------------
>> B=[0;0;2];
>> C=[1 0 0;0 0 0;0 0 0];
>> D=[0];
>> G=ss(A,B,C,D);
>> G
a =
x1 x2 x3
x1 0 1 0
x2 0 0 1
x3 -5 -4 -13
b =
u1
x1 0
x2 0
x3 2
c =ห้องสมุดไป่ตู้
x1 x2 x3
y1 1 0 0
y2 0 0 0
>> num=[2];
>> den=[1,13,4,5];
>> G=tf(num,den);
>> G
Transfer function:
2
----------------------
s^3 + 13 s^2 + 4 s + 5
>> GG=zpk(G)
Zero/pole/gain:
2
----------------------------------
>> f1=inline('x(1)^2-2*x(1)+x(2)');
>> [x,f]=fmincon(f1,x0,A,B,Aeq,Beq,xm,xM,'f2a');x',f
ans =
1.0000 0
f =
-1
3
( a)
>>s=tf('s');G=(s^3+4*s+2)/s^3/(s^2+2)/[(s^2+1)^3+2*s+5]
#3: 0
>> GG=zpk(G)
Zero/pole/gain from input to output...
2
#1: ----------------------------------
(s+12.72) (s^2 + 0.2836s + 0.3932)
#2: 0
#3: 0
根据微分方程也能够直接写出传递函数模型:
Transfer function:
s^3 + 4 s + 2
------------------------------------------------------
s^11 + 5 s^9 + 9 s^7 + 2 s^6 + 12 s^5 + 4 s^4 + 12 s^3
( b)
>> z=tf('z',0.1);
