Design and lead-lag controller for the system (root locus method) G(s)=\frac{1 K}{s(0.1 s+1)} ; O S<1 \% ; \begin{aligned} &t_{s 9 8 \%}<3 s \\ &t r<1 s \end{aligned} ; \text { Input

1.       Design and lead-lag controller for the system (root locus method)  :  (10 marks)

G(s) : (Equation Attached) 

In order to obtain a OS, Ts, Tr are given as Table below (unity feedback system)

2.       Check the system is stable or not with unit feedback (with all different methods: root locus, Bode plot, Nyquist ); inputs: step (10 marks)

3.       Compare uncompensated and lead compensator in continuous time  (Use root locus method) (5marks)

4.       Compare uncompensated and lead-lag compensators in continuous time (5 marks)

Discrete:

5.       Find the discrete system of the plant and redesign the lead-lag compensator (Ts=0.02 )  (5 marks)

6.       Compare uncompensated and lead compensator in the discrete domain  (Use root locus method) (5 marks)

7.       Compare uncompensated and lead-lag compensator in the discrete domain  (5 marks)

8.       Show that the steady-state controllable canonical form of the system  above (5 marks)

9.       Find the gain K in order to have a deadbeat response for the system above (10 marks)

10.   Find the gain L in order to have a deadbeat response for the observation error (10 marks)

11.   Discretizes control system in step 1 and compare with step 4 (10 marks)

12.   Discuss all results from 1 to 11 in detail with proper graphical methods (Bode plot and Nyquist)  (20marks)