Project - Position control of mass spring damper system

Given :

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.

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

Step 1:

The transfers function of a mass spring damper is,1/(ms^2+cs+k).

here m,k and c value were given above.

To find poles assume wn(wn=sqrt(k/m) formula were used and consider zeta as 0.9 and following data were given below.

k is find by using above parameters resullt as shown below and named as kp and kd and ki should need to be asumed.

P =

-9.4868 + 4.5947i
-9.4868 - 4.5947i

K =

-0.0000 -31.6948....

Step 2:

After finding the kp and kd next step the model should need to built..

import the blocks from the library such as (pulse generator, clock,simout,scope, gain,sum and tansferfunction )

first import the transfer function block and enter the input as given below.

Step 3:

And inter linked with the PID controller given below.

where PID controller were interlinked with refernce signal pulse generator

enter the input as given below in pulse generator.

Step 4:

after the obtaining the model enter the model setting as given below start time and end time.

save and start run the model and the will be shown..

RESULT:

Hence by adjusting the force on mass so that its position follows a reference signal.