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## Homework Statement

So I have been asked to design a PD Controller on Matlab that satisfies certain performance criteria which are as follows :

1. The 10-90% rise time is less than 0.5 s

2. The percentage overshoot is less than 5%.

3. The settling time is less than 5 s

I was given the closed loop transfer function of the system which had two parameters as Kd and Kp where

Kp lies between a range of 0<Kp<1.5

and Kd lies between a range of 0<Kd<4.4

Question is to figure out how Kd and Kp influence the performance criterias.

## Homework Equations

The closed loop transfer function = ## G_{cl}(s) \ ## = ## \frac {K_Ds + K_P} {1.1{s}^2+K_Ds+K_P} \ ##

## The Attempt at a Solution

I have acheived the performance criteria as stated on MATLAB when I put ## K_D \ ## as maximum of 4.39 and ## K_P \ ## as around the half of the range as 0.7. However, I really can't tell how exactly they affect the performance criterias because I have produced many graphs with different values of both parameters and I just can't figure out a relationship between them. Please HELP!