D Control Design using Matlab.                                                                                          

D1. The open loop-transfer function, G_p(s), of the process of a control system with unity feedback is described by                                                          

The required performance specifications of the system are given as:

Maximum overshoot ≤ 4%

Steady-state error to a ramp input ≤ 0.01

Rise time ≤ 0.8 s

Settling time ≤ 0.8 s

D1a)  Use symbolic maths in Matlab, plot the step and ramp response of the closed-loop system when K=1. With this gain are the specifications satisfied? Determine the value of K to satisfy the steady-state requirement. With this gain is the system stable?

b) Use root-locus to design a cascaded PD controller of the form (K_p +K_d s) to satisfy the transient response of the system whilst maintaining the steady-state error. (use K as determined in (D1a) and let Kp = K in your design). Does the PD controller satisfy all the requirements?

D2 a) Implement a PI and a PID controller using the continuous cycling method of the Ziegler-Nichols rules. Manually fine tune the PID controller to achieve the desired specifications. Explain your methodology.

1). Please try and explain the characteristic of all the plots and graphs.

2). Import all the required data in word of simply write in the script itself.

3). Use the provided data in each example and do not hesitate to email me if you need any more information.