Project - Position control of mass spring damper system

Ans:

Consider m is mass , K is spring constant and C is damping coefficient of spring.

the transfer functionis derived as below

Z(s)/F(s)=1/(m*s^2+c*s+k)

Find the poles to be stable.

Obtain the A and B matrices to pace ploes.

A=[0 1;

-k/m -c/m]

B=[0 1/m]

Obtain reference signal by setting pulse genarator paramters as below

Amplitude=1, No of samples =10 and pulse widt 5.

Define spring mass system paramters in script as below

% Take paramters for spring mass damper sytem as given

m=3.6; %kg

k=400; %N/m

c=100; %Ns/m

% assume

fn=1; %1hz

wn=6.2832;

zeta=0.5; %underdamped system

x10=0.01; x20=0; %initial conditions assumed

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

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

P=[p1;p2];

A=[0 1;... %x1_dot=x2

-k/m -c/m]; %x2_dot=-k/m*x1-c/m*x2+1/m*u

B=[0; 1/m];

K=place(A ,B, P);

ki=2000;

K(1)=900;

the simulink model is as below

The output position is following the ref input signal as below

Matlab codes file and Simulink files and Scope output file attached .

Run the files and adjusted ki and Kp to get the desired output.

end.