Hi @Mohamed
Since no performance requirements are specified, the pidtune() command can be used as the initial step in designing the PID controller. Additionally, it is possible to cancel out the undesired pole in the closed-loop transfer function, as demonstrated in this case.
%% Original system in State-space
A = [ 0 0 -2.2444 0 0.01995
0 0 0.81081 -1.3514 -0.0054054
29.508 -19.672 -0.0018769 0 0
0 222.22 0 -4444.4 0
-0.2623 0.13115 0 0 0];
B = [104.74
0
-2.56
0
0];
C = [0 0 1 0 0];
D = 0*C*B;
sys = ss(A, B, C, D);
%% Plant
P = tf(sys)
%% Controller
[C, info] = pidtune(P, 'PIDF')
%% Closed-loop system
% Gcl = minreal(feedback(C*sys, 1));
Gcl = minreal(feedback(C*P, 1));
zcl = zero(Gcl) % closed-loop zeros
pcl = pole(Gcl) % closed-loop poles
%% Plot the results
subplot(2,1,1)
step(sys), grid on, legend('Original system', 'location', 'east')
subplot(2,1,2)
step(Gcl, 6000), grid on, legend('Compensated system', 'location', 'east')
