Challenge

Project - Position control of mass spring damper system

SSiva Datta Venkata Swamy Domada1 Mar 2023

DESIGN

Q.1

Ans:-

Transfer function of a mass spring damper system:-

Given:-

m=3.6kg;

c=100 ns/m;

k=400 n/m;

*The differential equation representing the spring mass damper system are:

f(t)= mx_dot_dot+cx_dot+kx

where:-

'm' = mass

'c' = damping coefficient

'k' =stiffness (or) spring constant

'x' = displacement

'x_dot' = velocity

'x_dot_dot' = acceleration

* If we apply laplace transform to the abovedifferential equation we get,

f(s) = ms^2*x(s) + c(s)*x(s) + k*x(s)

f(s) = (ms^2 + cs +k) * x(s)

[x(s) / f(s)]= 1/ (ms^2 + cs +k) .......eq(1).

by these eq(1) we obtained a design of spring mass damper system.

SCRIPT:-

%system parameters

m=3.6; %mass in kg

k=400; %stiffness (or) spring constant in N/m

c=100; %damping coefficient in Ns/m

%Design for PID controller

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

B=[0 ; 1/m];

%pole placement design

fn=1.0;

wn=2*pi*fn;

zeta=0.5;

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=-257.8777;

Kd=-77.3805;

Ki=0.0;

%initial conditions

x10=0.01;

x20=0.0;

A =

0 1.0000
-111.1111 -27.7778

B =

0
0.2778

PID DESIGN FOR SPRING MASS DAMPER SYSTEM:-

XY PLOT:-

OUTPUT:-

OUTPUTS FOR DIFFERENT ZETA VALUES:-

PID DESIGN FOR SPRING MASS DAMPER SYSTEM:-

XY PLOT:-

OUTPUTS FOR DIFFERENT ZETA VALUES:-

CONCLUSION:-

* Transfer function of a mass spring damper system was obtained and using of these transfer function model for mass spring damper system was designed.

* The designed model was performed different outputs using different zeta values followed by the given reference signal.

Project - Position control of mass spring damper system

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