This question has two parts which I\'ve submitted as two separate questions: Con
ID: 2084811 • Letter: T
Question
This question has two parts which I've submitted as two separate questions: Continuing Exercise CE7.2 part (a). Since this is a fourth-order system, we will need four desired eigenvalues for future control law design in CE2. Use a fourth-order ITAE approach with undamped natural frequency n = 3 rad/s to generate the four desired eigenvalues. Plot the desired system impulse response.
Only consider case i (input force, output pendulum angle). Perform the analysis and design only for the equilibrium condition corresponding to = 0 (rad). - Submit a MATLAB® script m-file that produces the numerical and graphical results that you integrate into your solution.
Textbook: Linear State Space Control Systems, 2007, ISBN: 978-0-471-73555-7
m2 f(a) FIGURE 1.15 Diagram for Continuing Exercise 2.Explanation / Answer
ITAE for any number of order for the given system with Mechanical translation system given in state space
********************************************
p=cell(7,1);
p1=cell(7,1);
f=zeros(7,1);
f1=zeros(7,1);
for n=2:8
[p{n-1},f(n-1),p1{n-1},f1(n-1)]=optimitaestep(n);
end
fprintf(' New ITAE coefficients: ')
for n=2:8
fprintf(' Order = %i, ITAE = %g ',n,f(n-1))
fprintf('%7.3f ',p{n-1});
end
fprintf(' Old ITAE coefficients: ')
for n=2:8
fprintf(' Order = %i, ITAE = %g ',n,f1(n-1))
fprintf('%7.3f ',p1{n-1});
end
fprintf(' ');
*************************************
// for the ramp response for the given system
dt=0.01;
tf=20;
t=(0:dt:tf)';
N=numel(t);
y=zeros(N,7);
for n=1:7
A=[zeros(n,1) eye(n);fliplr(-p{n}(2:end))];
B=[zeros(n,1);1];
A=expm([A B;zeros(1,n+2)]*dt);
x=[zeros(n+1,1);1];
for k=1:N
x=A*x;
y(k,n)=x(1);
end
end
y1=zeros(N,7);
for n=1:7
A=[zeros(n,1) eye(n);fliplr(-p1{n}(2:end))];
B=[zeros(n,1);1];
A=expm([A B;zeros(1,n+2)]*dt);
x=[zeros(n+1,1);1];
for k=1:N
x=A*x;
y1(k,n)=x(1);
end
end
subplot(211)
plot(t,y,'Linewidth',2)
grid
title('ramp Response of Systems with New Coefficients')
subplot(212)
plot(t,y1,'Linewidth',2)
grid
title('ramp Response of Systems with Old Coefficients')
*********************************************************************
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