Excercise 1: Controller design. The block diagram for an aircraft's attitude control system is shown below Controller Plant 2s4 е C(s) s20.1s4 п We will attempt to design a controller that meets the following specifications: Rise time of less than 1.2 seconds Settling time of less than 4 seconds Steady-state error less than 1%, for a step input For sensor-noise rejection reasons, the controller's gain cannot exceed 10 (a) Find the (closed-loop) transfer function fromr to y, for a proportional controller C(s) = kp. (b) Translate the given specifications into constraints on the values of Ç, wn second-order system. and for a standard (c) Sketch by hand the root locus for the purely proportional controller. Please briefly explain the rules you applied to obtain your sketch, and show calculations for any asymptotes.

Question
Excercise 1: Controller design. The block diagram for an aircraft's attitude control system is shown
below
Controller
Plant
2s4
е
C(s)
s20.1s4
п
We will attempt to design a controller that meets the following specifications:
Rise time of less than 1.2 seconds
Settling time of less than 4 seconds
Steady-state error less than 1%, for a step input
For sensor-noise rejection reasons, the controller's gain cannot exceed 10
(a) Find the (closed-loop) transfer function fromr to y, for a proportional controller C(s) = kp.
(b) Translate the given specifications into constraints on the values of Ç, wn
second-order system.
and
for a standard
(c) Sketch by hand the root locus for the purely proportional controller. Please briefly explain the rules
you applied to obtain your sketch, and show calculations for any asymptotes.
Expand
Transcribed Image Text

Excercise 1: Controller design. The block diagram for an aircraft's attitude control system is shown below Controller Plant 2s4 е C(s) s20.1s4 п We will attempt to design a controller that meets the following specifications: Rise time of less than 1.2 seconds Settling time of less than 4 seconds Steady-state error less than 1%, for a step input For sensor-noise rejection reasons, the controller's gain cannot exceed 10 (a) Find the (closed-loop) transfer function fromr to y, for a proportional controller C(s) = kp. (b) Translate the given specifications into constraints on the values of Ç, wn second-order system. and for a standard (c) Sketch by hand the root locus for the purely proportional controller. Please briefly explain the rules you applied to obtain your sketch, and show calculations for any asymptotes.

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