Laboratory in Automatic Control Lab4

8/2/2019 Laboratory in Automatic Control Lab4

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Laboratory in Automatic Control

Lab 4

Control System Characteristics


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Max and Min Function

SyntaxC=max(A)

D=min(A)

MATLAB code

a=magic(3)b=max(a)

c=min(a)

d=max(b)

e=min(c)


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Residue Function

Syntax

[r,p,k]=residue(num,den)

MATLAB code

1 2

1 2

n

n

N s rr rF s k sD s s p s p s p

...

num=3

den=[1 6 5]

[r,p,k]=residue(num,den)

23 0 75 0 75

6 5 5 1F s

s s s s

. .


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Flow Control

Syntaxfor variable=expression

statements

end

MATLAB code% create a 3*4 zero matrix

% method 1

for i=1:3

for j=1:4

a(i,j)=0;end

end

b=a

% method 2

c=zeros(3,4)


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Flow Control

% a(i,j) & a(i)

a=[6 5 4;3 2 1]

b=a;

size(a)

s1=min(size(a));

s2=max(size(a));

d=s1*s2;

for i=1:d

b(i)=i;end

c=b

d=[a(1,1) a(1,2) a(1,3);a(2,1) a(2,2) a(2,3)]

MATLAB code

size(a)


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Flow Control

Syntaxifexpression

statements

end

MATLAB codet=0:10;

for i=1:length(t)

if(t(1,i)>5)&(t(1,i)


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Flow Control

Syntax

ifexpression 1

statements 1

elseifexpression 2

statements 2

elseifexpression N-1

statements N-1

elsestatements N

end


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Flow Control

MATLAB code

a=[2 0 0 7;1 0 1 6]

for i=1:2

for j=1:4

ifmod(a(i,j),2)==0

even(i,j)=a(i,j);else

odd(i,j)=a(i,j);

end

end

endodd,even


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Flow Control

Syntax

switch switch_expr

case case_expr

statement, ..., statement

case {case_expr1, case_expr2, case_expr3, ...}statement, ..., statement

otherwise

statement, ..., statement

end


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Flow Control

MATLAB code

a=[2 0 0 7;1 0 1 6]

for i=1:2

for j=1:4

switch mod(a(i,j),2)

case 1

odd(i,j)=a(i,j);

otherwise

even(i,j)=a(i,j);

endend

end

odd,even


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Flow Control

Example MATLAB code

for k=0:0.1:5

sys_cl=feedback(tf([10],[1 k 0]),[1]);

t=0:0.1:5;

[y,t]=step(sys_cl,t);

ymax=max(y);

if(ymax>1.01)&(ymax


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Flow Control


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Flow Control

MATLAB code

for k=0:0.1:5

sys_cl=feedback(tf([10],[1 k 0]),[1]);

t=0:0.1:5;

[y,t]=step(sys_cl,t);

ymax=max(y);

if(ymax>1.01)&(ymax


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Flow Control


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Lab 4 Homework

P1. Consider the transfer function (without feedback)

when the input is a unit step, the desired steady-state value

of the output is one. Using the MATLAB step function,show that the steady-state error to a unit step input is 0.8.

( )

25

2 25G s

s s

0 0 1 10t : . :


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Lab 4 Homework

P2. Consider the closed-loop control system shown in

Figure 1. Develop a MATLAB script to assist in the search

for a value ofkso that the percent over-shoot to a unit step

input is greater than 1 %, but less than 10%. The script

should compute the closed-loop transfer

function, , and generate the step response.

Verify graphically that the steady-state error to a unit step

input is zero. (Hint: search kwithin [1, 5], )

T s Y s R s

0 0 1 5t : . :

10

s

Controller

1

s k

Plant

R s Y s

Figure 1

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Laboratory in Automatic Control Lab4