Use MATLAB for the questions. Please show the MATLAB code. Given is the transfer

Question

Use MATLAB for the questions. Please show the MATLAB code.

Given is the transfer function of a linear time invariant system: G(s)-Y(s) = N(s) U(s) D(s) 5-s4+s3-s2+2s+1 1. Find a (any) state-space representation for the system and draw the corresponding block 2. Find the system's eigenvalues and eigenvectors. Is the system stable? Identify the unstable 3. Is the system diagonalizable? If yes, find the matrix T that diagonalizes the system [Note, x(t) 4. diagram. Give the dimensions of A, B, C, D, x(t), u(t) and y(t) modes, if any. = Tzit).] Is the system controllable, observable, stabilizable? Is it reachable and detectable? Find the canonical decomposition of the system, i.e.. C-O, C-nonO, nonC-O, nonC-nonO and write the state-space equations in the corresponding form. 5.

Explanation / Answer

ss = tf('s');
syss = (s + 7)/(s*(s + 5)*(s + 15)*(s + 20));
rlocuss(sys)
axiss([-22 3 -15 15])
zetaa = 0.7;
wnn = 1.8;
sgridn(zeta,wn)
K, = 350;
sys_cl. = feedback(K*sys,1)
step.(sys_cl)
ss = tf('s');
plantt = (s + 7)/(s*(s + 5)*(s + 15)*(s + 20));
wa = logspace(2,5.1,100);
H0. = feedback(frd(G,w),1);
hh = sigmaplot(H0,'b',H1,'g--',H2,'r');
legendd('Reference H0','H1=feedback(G,1)','H2=G/(1+G)','location','southwest')
setoptionss(h,'YlimMode','manual','Ylim',{[-60 0]})
clff
t. = 0:0.01:4;
u. = sin(10*t);
lsimm(sys,u,t)
A = [-0.7 3.6 -2.1;-3 -1.2 4.8;3 -4.3 -1.1];
B = [0; -1.0; -0.2];
C = [1.2 0 0.5];
D = -0.6;
G = ss(A,B,C,D,E);
x0 = [-1;0;1]; % initiall state
initiall(G,x0)
gridd

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.