Modern University for Modern Sciences and Arts

----------------------------------------------------------------------Problem 1:

Draw the nyquist diagram for the following open loop system

GH(S) = 10 (S+1) / (S+2)(S+3) GH(S) = 1/ S(S+1)(S+2)

Problem 2:

The open loop transfer unction of a unity feedback control system is given by G(S

Sketch the polarDetermine the value of w so that the phase margin of the system is 45

Problem 3:

Find the value of w such that the phase angle is system

GH Problem 4:

The logarithmic magnitude curve for a control system is

Determine the open loop transfer function

Draw the phase curve Find the value of wc Determine th again margin and phase marin

db

26

Modern University for Modern Sciences and Arts

Faculty of Engineering Automatic Control System

ESE 346/ESE416

Sheet 5 ----------------------------------------------------------------------

diagram for the following open loop system GH(S) = 10 (S+1) / (S+2)(S+3) GH(S) = 1/ S(S+1)(S+2)

The open loop transfer unction of a unity feedback control system is given byS) = 10/ (S+1)3

Sketch the polar-plot of this system the value of w so that the phase margin of the system is 45

Find the value of w such that the phase angle is -1500 for the open loop

GH(S) = 10/ [(S+1)(S+3)(S+4)]

The logarithmic magnitude curve for a control system is given as follows

Determine the open loop transfer function Draw the phase curve Find the value of wc Determine th again margin and phase marin

26

1 5 50

-20 db/decade

-40 db/decade

wc

The open loop transfer unction of a unity feedback control system is given by

the value of w so that the phase margin of the system is 450

for the open loop

given as follows

Problem 5: Sketch the Bode-diagram for the negative feedback control system shown

G1(S) = 10 G2(S) = 1/ (S+1)(S+3)

Problem 6:

From the bode diagram and the block diagram shown Write the unknown transfer function G(s) Draw the phase plot ()

Problem 7:

Obtain the state variable matrix for a system with differential equation d2y(t)/dt2 + 3 dy(t)/dt + 2 y(t) =u(t)

Problem 8:

Obtain the state space model for the following transfer function Y(s)/U(s) = 10 (s+1) / (s2+3s+2)

G1(S) G2(S)

G(s) 10/ (1+2s) R(s) Y(s) 10 / (s(s+0.05)) -

-20dB/decade

-40dB/decade

-20dB/decade

-40dB/decade

-60dB/decade

0.5 2 10 20

dB

1

25

45

Problem 9: For the following system

1 1

2 2

0 1 0

3 4 1

x x

x x

= +

&

&, [ ] 1

2

10 0x

yx

=

Obtain Transition matrix Obtain the state transition equation with unit step response of the

system Obtain the transfer function Determine the state controllability of the system Determine the state observability of the system