Project - Position control of mass spring damper system

Obtain the transfer function of a mass spring damper system and use it in the model. Add a PID controller to adjust the force on mass so that its position follows a reference signal.

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

The reference signal is shown in the following figure.

Give data value:

m = 3.6; % value of mass.

c = 100; % Damping coefficient (ks/m).

k = 400; % stiffness constant (N/m).

fn = 1.0;% Hz in frequency.

wn = sqrt(k/m); % red/sec.

zeta = 0.9; % underdamping system.

 

To find a pole value:

 

A = [0 1; (-k/m) (-c/m)];

B = [0; (1/m)];

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

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

P = [p1,p2];

K = place(A,B,P);

kd = K(2);

kp = K(1);

ki = 500.0;

 

PID control output simulation and graph;