1. HW-03
Problem 03-01
Kuo-95 (p. 377)
Find the steady-state errors for step, ramp and parabolic inputs. Determine the type of the system. ) s ( R
Problem 03-02
A PI controller is used for the control system shown in the figure. Determine the integral controller coefficient Ki to obtain a steady-state error of 4% to a ramp input (Assume Kp=10).
Find the roots of the closed loop control system. Is the closed loop system stable?

2. Solutions of HW-3: Problem 1:
a) There are two roots as s=0 in the transfer function of the forward path. Then the type of the system is 2.

3. Solutions of HW-3:
b) There are two roots as s=0 in the transfer function of the forward path. Then the type of the system is 2.

4. Solutions of HW-3:
Problem 02:
ess=0.04

5. Closed system is stable since real parts of all roots are negative.
Solutions of HW-3:
Roots of the closed loop control system for Ki =
DH=polyadd(conv([1],[ ]),conv([ ],[2 7.2]))
DH(s)
s1= i
s2= i
s3=
roots([ ])
Closed system is stable since real parts of all roots are negative.

6. Solutions of HW-3:
Problem 03-03: Determine the Kp and Kd values to obtain steady-state error as and damping ratio as to a ramp input.
Kuo-91 (p. 545)
Denominator of transfer function:

7. Solutions of HW-3:
Input
Output