Project - Position control of mass spring damper system

AIM;

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.

given data;

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

solution;

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. the matlab model of the pid control and transfer function pulse wavefrome generator.

PID controller;

Deriving the Mass Spring Damper System based on Newton’s second law F = m*a

where

F = Resultant of all the forces

m = Mass

a = Acceleration

x(s)/F(s) = 1/(m*s^2 + d*s + k)......transfer function.

The above equation is the transfer function

Input signal setting:

Pole design:

m = 3.6; % kg

k = 400; % N/m

c = 100; % Ns/m

% Pole placement design

fn = 1.0;

wn = 2*pi*fn;

% A & B matrix value

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

B = [0; 1/m]; % Design values

zeta = 0.5; % for an under-damped behavior

% Desied poles value

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

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

p= [p1;p2];

K = place(A,B,p);

Kp = K(1);

Kd = K(2);

% End

Design:

Output: