B.TECH - Semester 6 control systems Question Paper 2013 (apr)
Practice authentic previous year university questions for better exam preparation.
Sample Questions
- Distinguish open loop and closed loop control systems.
- Explain Mason's gain formula
- What do you mean by type and order of system. Cite with an example.
- Explain generalized error coefficients.
- Define observability of a system
- Predict the stability of a given system using Routh-Hurwitz stability criterion $$ s^{4}+8 s^{3}+18 s^{2}+16 s+5=0 $$
- Define gain margin and phase margin
- State Nyquist stability criterion.
- Find the meeting point of the asymptotes on the real axis for the unity feedback control system with an open loop transfer function given as $$ G(s)=\frac{K(s+5)}{s(s+2)(s+4)\left(s^{2}+2 s+2\right)} $$
- Find the characteristic equation of the given matrix. $$ A=\left[\begin{array}{cc} 0 & 1 \\ -2 & 3 \end{array}\right] $$ ( $\mathbf{1 0} \boldsymbol{\times} \mathbf{2} \boldsymbol{=} \mathbf{2 0}$ Marks) P.T.O. Answer any one question from each mo...
- (a) Measurements conducted on a servomechanism show the system response to be $C(t)=1+0.2 e^{-60 t}-1.2 e^{-10 t}$ when subjected to a unit step input. Obtain the expression for closed loop transfer function, the damping ratio and undamped natural fr...
- (b) Ascertain the stability of the system with characteristic equation using Routh-Hurwitz stability criterion. Find also the roots of the equation. $s^{5}+2 s^{4}+24 s^{3}+48 s^{2}-25 s-50=0$ OR
- (a) The closed loop transfer function of a unity feedback control system is given by $\frac{C(s)}{R(s)}=\frac{10}{s(0.5 s+1)}$ Determine
- (i) Damping ratio (ii) Natural undammed resonance frequency (iii) Percentage peak overshoot (iv) Expression for error response.
- (b) For a unity feedback system whose open loop transfer function is $$ G(s)=\frac{20(s+2)}{s(s+3)(s+4)} $$ Find the static error constants and the steady state error for $r(t)=3 u(t)+5 t u(t)$ constants.
- (a) Define the frequency domain specifications of a system.
- (b) Sketch the Bode Plot for a unity feedback system characterized by the open loop transfer function $$ G(s)=\frac{1000(s+1)}{s(s+2)(s+5)(s+10)} $$ Find
- (i) Gain Margin (ii) Phase Margin (iii) Stability of the System. OR
- (a) Investigate the stability of a closed loop system with the following open loop transfer function using Nyquist stability criterion. $$ G(s)=\frac{K}{(s+1)(s+2)(S+3)} $$
- (b) Explain the procedures for construction Root Locus.
- (a) Determine the state observability of the system described by $$ \dot{x}=\left[\begin{array}{ccc} -3 & 1 & 1 \\ -1 & 0 & 1 \\ 0 & 0 & 1 \end{array}\right] x+\left[\begin{array}{ll} 0 & 1 \\ 0 & 0 \\ 2 & 1 \end{array}\right] u \quad \dot{y}=\left[...
- (b) Design a PI controller for an unity feedback system with open loop transfer function to have phase margin of 60 degrees at a frequency of $0.5 \mathrm{rad} / \mathrm{sec} .10$ $$ G(s)=\frac{100}{(s+1)(s+2)(s+5)} $$
- (a) Construct signal flow graph and state model for a system whose transfer function is $$ T(s)=\frac{s^{2}+3 s+3}{s^{3}+2 s^{2}+3 s+1} $$
- (b) Derive a mathematical model of Zero order. Derive the pulse transfer function of the closed loop control system. Figure 4 $$ (4 \times 20=80 \text { Marks }) $$