Project - Position control of mass spring damper system

AIM: Obtain the transfer function of a mass spring damper system witha PID controller for following parameters;

mass=3.6kg; k=400N/m; c=100Ns/m

CODE:

%Parameters

k=400;%(given, in N/m)

%c=2*zeta*wn*m

c=100;%(given, in Ns/m)

m=3.6;%(Kg)

wn=10.54;

zeta=(c*0.5)/((m*k)^(1/2));

G=tf([400],[1,100,111.5]);

pzmap(G)

grid on

[p,z]=pzmap(G)

A=[0,1;111.11,27.77];

B=[0;0.278];

p1=-zeta*wn+wn*sqrt(zeta^2-1);

p2=-zeta*wn-wn*sqrt(zeta^2-1);

P=[p1;p2];

K=place(A,B,P);

POLES & K:

Zeta value:

As zeta>1 that implies it is a critically damped condition.

Model:

Input For Reference- A pulse generator withfollowing conditions:

Output w.r.t the reference signal:

As we can see it is overdamped w.r.t the reference signal position.