Use MATLAB for the questions. Please show the MATLAB code. Given is the transfer
ID: 2249753 • Letter: U
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
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