EC-404 Control System - Jun 2024 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aWhat is control system? Briefly explain the classification of control system.
   How to answer

   • Define control system as interconnection of components to obtain desired output
   • Classify by open-loop vs closed-loop, linear vs non-linear, time-invariant vs time-variant, continuous vs discrete
   • Give examples and block diagrams for each class
   • Summarize advantages/disadvantages
2. 7 Marks
   bReduce the given block diagram into

   1. i)A form having one block in the forward path and one in the feedback path
   2. ii)Single block representation

   

   How to answer

   • Apply block diagram reduction rules stepwise
   • Obtain equivalent with one forward block and one feedback block
   • Further reduce to single block transfer function C/R
   • State final transfer function
3. 7 Marks
   aFor the system with negative feedback, discuss the effect of feedback on the following Obtain mathematical expression in each case

   1. i)Disturbance
   2. ii)System parameter variation
   3. iii)System time constant
   How to answer

   • Write closed-loop model with feedback H(s) and disturbance
   • Derive effect on disturbance rejection: divided by 1+GH
   • Derive sensitivity to parameter variation
   • Derive effective time constant reduction
4. 7 Marks
   bDiscuss about the effect of addition of poles and zeros to open loop and close loop system.
   How to answer

   • Define poles and zeros of open-loop transfer function
   • Explain effect of added pole: stability decreases, root locus shifts right
   • Explain effect of added zero: stability improves, root locus shifts left
   • Contrast for open-loop vs closed-loop response
5. 7 Marks
   aDetermine the stability of a system having following characteristics equation using Routh Hurwitz criterion $$S^5 + S^4 + 2S^3 + 2S^2 + 11S + 10 = 0$$
   How to answer

   • Form Routh array for $S^5+S^4+2S^3+2S^2+11S+10=0$
   • Check first column sign changes
   • Identify rows of zeros / auxiliary equation if any
   • Conclude stability / number of RHP poles
6. 7 Marks
   bSketch the root locus of the system whose open loop transfer function is $$G(s) = \frac{K}{s(s+2)(s+4)}$$ Find the value of K so that the damping ratio of the closed loop system is 0.5.
   How to answer

   • Identify poles at 0, -2, -4 and asymptotes, centroid, breakaway points
   • Sketch root locus for $K>0$
   • Use angle condition for damping ratio 0.5 line intersection
   • Calculate gain K at intersection point
7. 7 Marks
   aDerive the expressing for resonant peak and resonant frequency. Establish correlation between time and frequency response parameters.
   How to answer

   • Write standard second-order closed-loop frequency response
   • Differentiate magnitude to get resonant frequency and resonant peak formulas
   • Relate resonant peak/frequency to damping ratio
   • Correlate with time-domain Mp, ts, tr
8. 7 Marks
   bSketch the bode plot for the following open loop control system. $$G(s) = \frac{K(1+0.2S)(1+0.025 S)}{S^3(1+0.001 S)(1+0.005 S)}$$
   How to answer

   • Identify corner frequencies from time constants 0.2, 0.025, 0.001, 0.005 and triple pole at origin
   • Draw asymptotic magnitude and phase plots
   • Combine to get complete Bode magnitude and phase
   • Determine gain/phase margins if required
9. 7 Marks
   aUsing Nyquist criterion investigate the closed loop stability of the system whose open loop transfer function is $$G(s)H(s) = \frac{K(s+1)}{(s+0.5)(s-2)}$$ Consider K = 1.25
   How to answer

   • Identify open-loop poles: -0.5 and +2, so P=1
   • Plot Nyquist path and mapping of G(s)H(s) with K=1.25
   • Count encirclements N of -1+j0
   • Apply Z=N+P to decide closed-loop stability
10. 7 Marks
    bDraw the diagram of lead compensator and find the expression for its transfer function.
    How to answer

    • Draw circuit diagram of lead compensator (R-C network)
    • Derive transfer function using voltage division / Laplace
    • Express in form (1+T s)/(1+alpha T s) with alpha<1
    • Mention pole-zero locations
11. 7 Marks
    aA unity feedback control system has an open loop transfer function of $G(s) = 1/s^2$. Design a suitable compensating network such that a phase margin of $45^\circ$ is achieved without sacrificing system velocity error constant.
    How to answer

    • Analyze G(s)=1/s^2: double integrator, velocity constant needs
    • Choose lag-lead or lead compensator to get 45 deg phase margin
    • Calculate compensator parameters without reducing Kv
    • Verify phase margin and Kv
12. 7 Marks
    bExplain in brief propositional, derivative, integral and composite controllers.
    How to answer

    • Define P, D, I control actions with transfer functions
    • Explain composite PI, PD, PID controllers
    • Give response characteristics and applications
    • Summarize comparison table
13. 7 Marks
    aDiscuss the concept of controllability and observability with suitable example.
    How to answer

    • Define controllability and observability matrices
    • State Kalman rank conditions
    • Illustrate with suitable example calculation
    • Explain physical significance
14. 7 Marks
    bThe transfer function of a system is given by $$\frac{Y(s)}{U(s)} = \frac{s^2 + 3s + 2}{s^3 + 9s^2 + 26s + 24}$$ Determine the state model by using direct decomposition method.
    How to answer

    • Factor numerator and denominator or use direct decomposition
    • Assign state variables to integrator outputs
    • Write state equations in controllable / observable form
    • Obtain A, B, C, D matrices
15. 14 Marks
    Write a short note on any two

    1. a)Open loop and close loop systems
    2. b)Effect of location of poles on stability
    3. c)Log magnitude versus phase plot
    4. d)State space representation of system
    How to answer

    • Select any two topics from a-d
    • Give definition, diagram/formula and key points for each
    • Mention applications / significance
    • Conclude briefly