B.TECH - Semester 6 control systems Question Paper 2021 (dec)
Practice authentic previous year university questions for better exam preparation.
- What is gain margin and phase margin? Why these parameters are important?
- Compare controllability and observability of a system.
- (b) A unity feedback system has the open loop transfer function $G(s)=K(s+12) /\{(s+14)(s+18)\}$. Find the value of K to so that the steady state error is $12 \%$. Derive any formula you may use.
- Compare closed loop and open loop systems with examples.
- Consider the mechanical system shown in Figure 1. The initially relaxed system is set into motion by a unit impulse force. Find the resulting oscillation. Figure 1
- Obtain a state space model of the system with transfer function $C(s) / R(s)=10(s+8) /\{(s+7)(s+9)\}$. Discuss the properties of the state model you derived. Is this the unique model of the system?
- Obtain the transfer function of the system represented by the signal flow graph Figure (Q.12) using Masons' gain formula. Verify the result by reduction of the signal flow graph also. Figure Q. 12
- Sketch the root locus of the system with forward transfer function $G(s)=K(s+2) /\left(s^{2}-4 s+13\right)$. Determine the critical value of K , the corresponding value of frequency, break away point and angle of departure.
- Use Rouths' Criterion to determine the stability of the system with characteristic equation $F(s)=s^{3}+10 s^{2}+31 s+1030=0$.
- Given the closed loop pole locations of a system as $-3 \pm \mathrm{j} 7$. Find the transient response specifications.
- Draw the bode plot of a unity feedback system with feed forward gain $G(s)=10 /\{s(0.5 s+1)(0.1 s+1)\}$. Analyse the stability of the system.
- Design a lag compensator for the unity feedback system with open loop transfer function $G(s)=1 /\{s(s+1)(0.5 s+1)\}$ so that the compensated system will have static velocity error coefficient of $5 / \mathrm{sec}$ phase margin at least 50 degrees and gain margin at least 10 dB .
- What do you understand by steady state error? Explain.
- How will you determine the steady state error coefficients from the Bode plot? P.T.O.
- (a) What do you mean by steady state error and error coefficients?
- Derive the transfer function of a lead compensator.
- Briefly explain Liapunov method of stability analysis. ( $10 \times 4=40$ Marks) Answer any two questions from each module. Each question carries 10 marks.
- Sketch the Nyquist diagram of a unity feedback system with open loop transfer function $G(s)=K /\{s(s+3)(s+5)\}$ Find the range of gain K for stability. Explain how stability can be determined from Nyquist plot.
- What is Jury's stability criterion? What are the conditions for stability of a LTIV discrete time system? Discuss the stability of the discrete time system with characteristic equation $F(z)=2 z^{4}+7 z^{3}+10 z^{2}+4 z+1$.
- Find $y[k]$. Given $x[k+1]=G x[k]+H u[k] ; y[k]=x_{1}[x]$; with $x_{0}=\binom{1}{1}$ $$ G=\left(\begin{array}{cc} 0 & 1 \\ -2 & -3 \end{array}\right) H=\binom{0}{1} $$
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