1.sketch the root locus plot of unity feedback system with an open loop transfer function G(s)= K/s(s+2)(s+4), find the range of values of K for which the system has damped oscillatory response. what is the greatest value of K which can be used before continuous oscillations occur. also, determine the frequency of continuous oscillations?
2.sketch the bode plot for a unity feedback system characterised by the open-loop transfer function G(S)=K(1+0.2S)(1+0.025S)/S^3 (1+0.001S)(1+0.005S).
3.The openloop transfer function of a unity feedback control system is given by G(S)H(S)=K(S+5)(S+40)/S^3(S+200)(S+1000) Discuss the stability of closed loop system as a function of K. Determine values of K which will cause sustained oscillations in the closed loop system. what are the frequencies of oscillations.use nyquist approach.
4. using R-H stability criteria determine the stability of the following systems a) it's loop transfer function has poles at s=0,s=-1,s=-3 and zero at s=-5,gain k of forward path is 10 b) it is a type-1 system with an error constant of 10/sec and poles at s=-3 and s=-6.
5.what are the frequency response specifications and explain how to obtain resonant peak,resonant frequency,bandwidth,cutoff rate,gain crossover frequency,phase crossover frequency,gain margin,phase margin and find for a second order system with unity feedback G(s)=200/s (s+8), find various frequency domain specifications, explian the principle of argument or mapping theorem as applied to nyquist plot?
6.write a short notes on steps to find transfer function from the given bode plot and explian the nyquist stability criterion applied to minimum phase and non minimum phase transfer function?
10 comments:
refer jairat for problems and nagoor kani for theory
SIR PLEASE UPDATE THE BLOG WITH THE SOLUTIONS SOON:-)
for first problem the centroid=-2,valid breakaway point is at s=-0.846 now at this break away point if you find k using(k=-s^3-6s^2-8s)it is 3.079 which is k minimum.next using rouths array k(marginal)=48 and jw crossing points are at s=+-j2.828 so range of values of k 3.079<k<48, greatest value of k=48,frequency of oscillations 2.828 rad/sec.
remaining procedure for root locus as it is.
for second and third refer jairath
for fourth problem
a) GH=10(S+5)/S(S+1)(S+3) given using rouths array for 1+GH the system is stable. b)kv error constant=10 GH=K/S(S+3)(S+6) given for type-1 system. kv=Lt s-0 (s*G*H)find K=180 substitute K and using R-H find stability and system is unsatble with one root in RHS plane
for 5th problem mr=1.86,wr=12.98,wb=20.74,phase margin=209.38,gain margin is infinite(explain how will u suggest this) for mapping theorem or principle of argument refer bakshi
for 6th one explain minimum and non minimum phase functions and explain using nyquist stability i.e N=P-Z to each system and explain stability considering the encirclements of -1+j0 point.
OH THANK YOU SIR!
I WILL FINISH REST OF THEM!
GOOD NIGHT :-)
The questions are of really good standard...Hope this will help us...Thank you sir for updating the solutions...
good problems we liked it enjoying it doing
sir what does the terms called sink mode & path gain ?
important questions of 2nd chap..!!
in first question ..while writing individual equations ..should we consider (m1+m2)as a whole or individually..?
2nd question..do the B1 B2 B3 connected to the ground will effect the adjacent blocks..or only K component will come into picture as it is connected in between the blocks...?
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