Project - Position control of mass spring damper system

REPORT :

we know the transfer function of mass spring damper system

f(t)-cdx/dt-kx(t)=mdx^2/dt^2

Byapplying laplace transform

F(s)-csX(s)-kX(s)=ms^2X(s)

T(s)=1/ ms^2+Cs+k

% Also we know that

wn = sqrt(k/m);

zeta =0.9;

% We know that Transfer function of spring mass damper system is

G = wn^2/s^2+2*zeta*wn+wn^2;

% Finding the poles which makes system stable

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];

% From above details we can find controller gain using place commands

% Finding the values of Kp & Kd

K = place(A,B,P);

We find the transfer function of the given sysytem and designed a PID controller for that and build a simulimk model. as shown below image

NOTE : I have attached matlab file which contains the Matlab program for finding controller gains.

The values of Kp & Kd obtained from the using a 'place' command are 0 and -31.6948 respectively so for obtaining a desired output we observe the output waveform for the diffrenat values of the integral gain i.e. Ki

1. Set Ki = 100

As we see in the above image the output waveform does not folllow the Ref. signal.

2. Set Ki = 500

As we see in the above image the output waveform tries to folllow the Ref. signal as we incresres the value of Ki

3. Set Ki = 1000

As we see in the above image the output waveform folllows the Ref. signal

CONCLUSION:

Obtained the transfer function of a mass spring damper system with m = 3.6kg k = 400 N/m c = 100 Ns/m using matlab programming and Created a transferfunction model and added PID controller and adjusted the force on mass so its position follows a reference signal when Kp=0 ; Ki=1000 and Kd= -31.6948