Automatic Control
Problem Set #6
Due: Wednesday, Azar 1st
Problem 1.
Part I. For the system shown here:
(a) Find the static error constants.
(b) Find the steady state error for the following inputs:
x! 1(t) = 10 × 1(t), x2(t) = 20 × t.1(t), x3(t) = 30 × t 2.1(t)
Part II. For the system shown here, design a PD
controller to achieve:
e! ss = 15 % , ωn =
12, ζ = 0.6
Problem 2.
Part I. For the system shown here, find K
! to achieve
0.5
% steady-state error.
!
Part II. For the system shown here:
(a) Find the sensitivity of the steady-state error to
parameter α
! .
(b) Plot the sensitivity obtained in (a) as a function of α
!
and interpret the results.
Automatic Control
Problem Set #6
Due: Wednesday, Azar 1st
Problem 3. For the system shown here:
(a) Determine the area in the s−
! plane for
the location of closed-loop poles to
achieve maximum overshoot of 5%
and rise time less than 1.3 seconds.
(b) Design a PID controller to achieve the spec as described in (a). (Hint: Choose the desired
complex conjugate pole locations according to the spec and put the real pole anywhere to
minimize its impact on the system dynamics.)
(c) Implement the PID controller first using the configuration shown above and then by putting
the derivative term in the feedback path. Plot the step response of the closed-loop system
for each of these configurations and determine their rise time and overshoot and explain the
difference between them.
Note: You MUST implement your design in part c in Matlab/Simulink.