Excercise 4: PI control for a first-order plant. Suppose you are to design a feedback controller for a first-order plant depicted in the figure below: Controller Plant К y и Кр TS1 ki This configuration is referred to as a proportional-integral (PI) controller. You are to design the controller to satisfy some given time-domain specifications. (a) Find the (closed-loop) transfer function Gyr from r to y (see hw02) (b) Determine the steady-state error for a unit step input (Hint: e r - y). (c) Find the transfer function Gum from n to u (d) Determine kp and ki such that the feedback controlled system has damping ratio Ç = 0.5 and fre- quency wo. (Hint: the desired denominator polynomial for a closed-loop transfer function is of the form: d(s) s22wos +w2.)

Question
Excercise 4: PI control for a first-order plant. Suppose you are to design a feedback controller for a
first-order plant depicted in the figure below:
Controller
Plant
К
y
и
Кр
TS1
ki
This configuration is referred to as a proportional-integral (PI) controller. You are to design the controller
to satisfy some given time-domain specifications.
(a) Find the (closed-loop) transfer function Gyr from r to y (see hw02)
(b) Determine the steady-state error for a unit step input (Hint: e r - y).
(c) Find the transfer function Gum from n to u
(d) Determine kp and ki such that the feedback controlled system has damping ratio Ç = 0.5 and fre-
quency wo. (Hint: the desired denominator polynomial for a closed-loop transfer function is of the
form: d(s) s22wos +w2.)

Image Transcription

Excercise 4: PI control for a first-order plant. Suppose you are to design a feedback controller for a first-order plant depicted in the figure below: Controller Plant К y и Кр TS1 ki This configuration is referred to as a proportional-integral (PI) controller. You are to design the controller to satisfy some given time-domain specifications. (a) Find the (closed-loop) transfer function Gyr from r to y (see hw02) (b) Determine the steady-state error for a unit step input (Hint: e r - y). (c) Find the transfer function Gum from n to u (d) Determine kp and ki such that the feedback controlled system has damping ratio Ç = 0.5 and fre- quency wo. (Hint: the desired denominator polynomial for a closed-loop transfer function is of the form: d(s) s22wos +w2.)

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