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.

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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?

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.

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.

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

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 =1097.22 DH=polyadd(conv([1],[1 22 316]),conv([10 1097.22],[2 7.2])) DH(s) s1=-19.3929 +45.6255i s2=-19.3929 -45.6255i s3=-3.2143 roots([1 42 2582.44 7899.98]) Closed system is stable since real parts of all roots are negative.

Solutions of HW-3: Problem 03-03: Determine the Kp and Kd values to obtain steady-state error as 0.001 and damping ratio as 0.707 to a ramp input. Kuo-91 (p. 545) Denominator of transfer function:

Solutions of HW-3: Input Output