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03000EE304052002

Design a P, PI and PID controller for the system with transfer function
20

G(s) = 2242906410)

by applying Zeigler-Nichols tuning method.

Draw the realisation of PID controller and explain its working.
PART C
Answer any two full questions, each carries 10 marks.

೧ „ _ [-1 0 1]. ,_ ⋅
onvert the system x = [ 0 12 + இ u,y = [1 1]% into controllable

cannonical form by applying similarity transformation.

து 7 9 1
Determine the stability of the system x = | 2 1 3 |x+]2]u, y=
-4 3 8 3

[1 1 01%.
⋅ ⋅−↥↥ 1 5
Design a state feedback controller for the system x = [ டூ + [ Ju y=
2 2 0
[0 112 to place the eigen values of the closed loop system matrix at -2+j2.
⋅ ⋅ ⋅−−↕↥ 1 5
Derive the transfer function of the system x = | 3 5 x+ A uy =

[0 1]% when the initial state of the system is zero.
Determine the stability of the system with characteristic equation z* +
0.62” + 0.6372 — 0.372 + 0.065 = 0
Write the structure of state space representation of an ‏٭ھ‎ ordered SISO system
in digital domain and specify the dimensions of each matrix.
PART D

Answer any two full questions, each carries 10 marks.

Identify the stability of limit cycle exhibited by the unity feedback system with

100

forward transfer function G(s) = ಷ್‌

when controlled by an

amplifier (P-controller) having gain 2 and it saturates when its output reaches
+2. Also determine the frequency and approximate amplitude of limit cycle.
Sketch the phase trajectory for the system x, = 2, ४2 = u, where u = ||
starting from (0,1).

Apply lyapunov stability to determine the stability of the autonomous

system x = [> शा x

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