Project - Position control of mass spring damper system

Solution of Question-

We have to design a PID controller using simulink which control the mass spring damper system in any direction.

Simulink model-

Simulink model blocks-

Pulse Genrator- This block is used for generating a pulse of magnitude 1 with the time period of 10

Transfer Function- This block is used for define the mass, stiffness constant and damping constant

Kp(Proportional gain),Kd(Derivative gain) & Ki(Integral gain) are simply gain block.

For Controlling the PID-

Command Windows Command-

matlab Program-

Nominal parameters of the Spring-mass system

m = 3.6; % mass of the spring-mass system in Kg

k = 400; % Stiffness constant of spring mass system in N/m

c = 100; % Damping constant of spring mass system in Ns/m

Equivalent Wn

fn = 1.0; % Wn/(2*pi) Hz

Wn = 2*pi*fn; % Natural frequency

Design parameters-

zeta = 0.5; % Underdamed system design

Desired poles

P1 = -zeta*Wn+Wn*sqrt(zeta^2-1);

P2 = -zeta*Wn-Wn*sqrt(zeta^2-1);

P =[P1,P2];

A & B matrices

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

B = [0;1/m];

Pole Placement design

K= place(A,B,P);

Kp and Kd gains are obtained from an earlier design using the place command

• Add Ki manually with gain and integrator block and tune different values of Ki and check the impact of it on results.

Kp = 15391; Kd = 138; Ki =0;

Kp = 15391; Kd = 138; Ki = 10000;

Kp = 15391; Kd = 138; Ki = 1000;

As when the Ki is zero the output has a lag. As the Ki is 1000 the output will track the input.

A PID controller is designed through simulink to adjust the force on mass so that its position follows a reference signal to using matlab and simulink wave from plot.