Re: EE250 IITK
The assignments questions for the EE250 Subject Code which comprises of Control System Analysis for the Electronics Engineering Discipline at IIT Kanpur are as given below:
Assignment Questions
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 + 1.
b) 2s4 + 2s3 + s2 + 3s + 2.
c) 2s4 + 5s3 + 5s2 + 2s + 1.
d) s4 + 2s3 + 3s2 + 4s + 5.
e) s5 + s4 + 2s3 + 2s2 + 3s + 5.
f) s6 + 2s5 + 8s4 + 12s3 + 20s2 + 16s + 16.
Q2.
The open loop transfer function of unity feedback system is Ks(1 + 0.4s)(1 + 0.25s). Find the restriction of K so that the closed loop system is absolutely stable.
Q3.
Consider T(s) to be the transfer function of a system. The denominator of this transfer function is also known as the characteristic equation of the system. The characteristic equation for certain feedback control system is s4 + 20Ks3 + 5s
2 + 10s + 15. Determine the range of K for the system to be stable.
Q4.
Check whether all the roots of the equation s3 + 7s2 + 25s + 39 = 0 have real parts less than −1.
Q5.
A system oscillates with frequency ω, if it has poles at s = ±jω. Consider a unity feedback system whose forward path gain is K(s + 1)/s3 + as2 + 2s + 1. Determine the values of K and a so that the feedback system oscillates at a frequency 2rad/s.
Q6.
A unity feedback control system is characterized by open loop transfer function G(s) = K(s + 13)/s(s + 3)(s + 7). Using RouthHurwitz criterion calculate the range of K for the system to be stable.
Q7.
Sketch the root locus for the closed loop feedback systems whose open loop transfer functions are:
(a) G(s) = Ks(s + 4)(s + 5),
(b) G(s) = Ks(s + 2)(s2 + 6s + 25),
(c) G(s) = Ks(s2 + 4s + 8),
(d) G(s) = K(s + 1) s2 (s + 3.6).
Also find the value of K for which the system will become unstable.
Q8.
Sketch the bode plot (asymptotic (approx) magnitude (in dB) and asymptotic (approx) phase) for the open looptransfer functions given by
(a) G(s) = Ks(s + 4)(s + 5),
(b) G(s) = (s + 1) s2(s + 3.6),
(c) G(s) = (s + 10) s(s + 2).
For both the questions use MATLAB to verify the plots. A sample code is as follows:
Suppose the given system is G(s) = s + 1s + 3
.
MATLAB Code
s = tf(’s’);
sys = (s+1)/(s+3);
rlocus(sys); % This gives the root locus.
bode(sys); % This gives the bode plot.
grid on
For root locus take the transfer without K when using MATLAB.
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Answered By StudyChaCha Member
