Project - Position control of mass spring damper system

For this project work;

1. mass and damping ratio and spring contant values were given.

2. using the above I deduced the value of wn and zeta and the system happen to be over damped.

3. Pole placement method was used to get the values of p1 and p2 and kp,kd.

4. A and B matrices were deduced by using [0 1;-k/m 0] and [0 1/m].

But for the above kp and kd and ki = 0 ; The response was erratic and did not the respond to pulse generator.

Therefore i attened a live session through which i was advised to any values for the pid's to get the expented response.

As per the samei have considered Kp as 4200 , Ki as 12000, kd = -220 . Derivative controller was taken to minus 220 because only then the overshoot and undershoot waa reduced.

As per the attached graph, We can see that along with input reference( pulse generator) the output is also aligned and there is a mild overshoot but the undershoot is nil after which it goes to equilibrium and dips along with the step response.

Therefore output signal dips and raises along wth pulse step for every 5 seconds.

Note : I feel that the mild bend in the yellow cross hair could be reduced.