EE 250 - Assignment 8
Q. Represent the system in state space form
A. Determine the KVL equations of the circuit shown in figure. Take states x1 = vC1 , x2 = vC2 and output
y = vC2 and represent the system in state space form.
B. Equations of a RLC circuit
EE 250 - Assignment 8
Q1.
Consider a untiy feedback system whose open loop transfer function is given by
G(s) =
K
(s + 1)(s + 2)
For some value of K, the system is operating at an overshoot of 20% when it is subjected to a unit step input.
Find the dampin
EE 250 - Assignment 7
Q1.
K
Consider a second order closed loop unity feedback system with the forward path gain G(s) = s(s+4)
. The user
wants the unit step response of the system to have a peak overshoot of 16.3%. As a designer what value of gain
K will
EE 250 - Assignment 7
Q1.
Sketch the Nyquist plot for the following open loop transfer functions. Comment on the encirclement of 1 + j0
(critical point) and hence, on the stability of the closed loop system. Find the gain margin (in dB).
(a) G(s) =
1
s(s
EE 250 - Assignment 6
Q1.
Sketch the Nyquist plot for the following open loop transfer functions. Comment on the encirclement of 1 + j0
(critical point) and hence, on the stability of the closed loop system. Find the gain margin (in dB) and the phase
marg
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EE 250 - Assignment 4
Q1.
The polynomials given below are the denominator of the transfer function G(s). Construct the Routh table for
the polynomial. Comment on the type of the poles of G(s). Comment on the stability of the system.
a) s4 + 2s3 + 6s2 + 4s
Q1.
The closed loop system is represented by following characteristic equation, determine the stability of system
using the Routh Hurwitz criteria. Also comment on the types of poles of the system.
a) s4 + 4s3 + 5s2 + 7s + 3.
b) 3s4 + 2s3 + s2 + 5s + 1.
c
EE 250 - Assignment 2
Q1.
Simplify the block diagram and obtain the transfer function relating C(s) to R(s).
a)
b)
c)
1
Q2.
Find the transfer function relating C(s) to R(s).
a)
b)
c)
2
Q3.
Find the transfer function relating C(s) to R(s) for the following
EE250A - Control System
Assignment - 9
(Q.1) Check controllability and observability of the following systems
A.
0
1 1 0
x = 0 1 0 x + 2 u, y = [1, 0, 1]x
1
0 0 2
B.
1
2 1 0
x = 0 2 0 x + 0 u, y = [0, 2, 1]x
1
0 0 1
C.
1 2
2
x =
x+
u, y = [1, 1]
0 3
EE 250 - Assignment 2
Q1.
Simplify the block diagram and obtain the transfer function relating C(s) to R(s).
a)
b)
c)
1
Q2.
Find the transfer function relating C(s) to R(s).
a)
b)
c)
2
Q3.
Find the transfer function relating C(s) to R(s) for the following
EE 250 - Assignment 5
Q1.
Sketch the root locus for the closed loop unity feedback systems whose open loop transfer functions are:
(a) KG(s)H(s) =
(b) KG(s)H(s) =
K
,
s(s + 2)(s2 + 6s + 25)
s(s2
K
,
+ 4s + 4)
(c) KG(s)H(s) =
K(s + 1)
,
s2 (s + 3.6)
(d) KG
Q1.
The closed loop system is represented by following characteristic equation, determine the stability of system
using the Routh Hurwitz criteria. Also comment on the types of poles of the system.
a) s4 + 4s3 + 5s2 + 7s + 3.
b) 3s4 + 2s3 + s2 + 5s + 1.
c
EE 250 - Assignment 1
Q1.
Find the Laplace transform of the following:
a) f (t) = sin(t + ), for t 0; and f (t) = 0 f or t < 0. where is a constant.
1
2
1
b)
u(t) u(t a) + u(t 2a)
a
a
a
c) f (t) = t2 sin(t), for t 0; and f (t) = 0 f or t < 0.
Z t
d) f (t)
DEPARTMENT OF ELECTRICAL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY, KANPUR
EE 210 QUIZ #lA 2.2.16
Total Marks: 15 Total Time: 30 mins.
Name Kﬁz Section Roll No. B
Data: for M: k’N = 40 uA/VZ, vm = 0.7 v. y = 0.4 v“, 2411: = 0.6 v, 7t —> o. gage
21) Choos
EE 250 - Assignment 9
Q1.
4
. The closed loop system is operating with a unity feeds(s + 2)
back. What will be the damping ratio and undamped natural frequency of the CL system? What is the static
velocity errorcoefficient?Calculate the peak time, percent
EE 250 - Assignment 3
Q1.
n2
and
the
poles
of
the
system
are
2
j2
3. Determine
s2 + 2n s + n2
the rise time tr , peak time tp , settling time Ts and peak overshoot Mp (in percentage). For settling time
consider the 5% tolerance band.
Consider the system G
EE 250 - Assignment 1
Q1.
Find the Laplace transform of the following:
a) f (t) = sin(t + ), for t 0; and f (t) = 0 f or t < 0. where is a constant.
1
2
1
b)
u(t) u(t a) + u(t 2a)
a
a
a
c) f (t) = t2 sin(t), for t 0; and f (t) = 0 f or t < 0.
Z t
d) f (t)