Question

The transfer function for a SISO system is given as follows:
G(s)= (s²+2s+10)/(s⁴+5s³+8s²+3s+12)

1 Is the open loop system stable? Draw pole zero map of the system. What is the steady
state response of this system for a unit step input?
2 When unit feedback (K_p= 1) is implemented on this system, write down the closed loop
transfer function. Draw pole-zero map. Is the system stable with this type of control law?
3 Find all possible proportional controller gains (K_p) that drive the system to stability? Use
Routh table and Root Locus methods.
4 Choose a K_p that makes the system stable from the previous question. Show the closed
loop poles. Draw the time response for a unit step input.
5 The control law is PD based, and the ratio of K_p and K_d is equal to 10 (K_p/K_d=10). Find all
possible K_p and K_d that make the system stable. Use Routh table and Root Locus
methods.
6 Choose a K_p , K_d pair that makes the system stable, from the previous question. Show the
closed loop poles. Draw the time response for a unit step input.
7 If the relation between K_p and K_d is not known, meaning they are independent of each
other, find all possible K_p and K_d that stabilizes the system. Draw a graph on K_p-K_d
plane.
8 Choose a K_p, K_d pair that makes the system stable, from the previous question. Show the
closed loop poles. Draw the time response for a unit step input.
9 Finally, when the controller is PID based, find all possible K_p, K_i and K_d that makes the
system stable. For this one you can use computational methods.
10 Choose a K_p, K_i? and K_d that makes the system stable, from the previous question. Show
the closed loop poles. Draw the time response for a unit step input.

Answer 1