EC-404 Control System - Jun 2025 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
   aExplain the following terms with reference to block diagram representation

   1. i)Block Diagram
   2. ii)Output
   3. iii)Summing Point
   4. iv)Take-off Point
   5. v)Forward path
   6. vi)Feedback Path
   How to answer

   • Define block diagram representation purpose
   • Explain each term: block, output, summing point, take-off point, forward and feedback path
   • Mention symbols/sign conventions with small sketches
   • Relate to closed-loop structure
2. 7 Marks
   bThe signal flow graph for a system is given below. Find the transfer function Y(s)/U(s)

   

   How to answer

   • Identify forward paths and individual loops from signal flow graph
   • Apply Mason's gain formula $\Delta = 1-\sum L_1+\sum L_2-...$
   • Compute path determinants $\Delta_k$
   • Obtain $Y(s)/U(s)=\sum P_k\Delta_k/\Delta$ and simplify
3. 7 Marks
   aDraw the block diagram of open loop and close loop control system and compare them. Give the advantages and disadvantages of each.
   How to answer

   • Draw labelled block diagrams of open-loop and closed-loop systems
   • Compare on basis of feedback, accuracy, stability, cost, sensitivity
   • List advantages of each
   • List disadvantages of each
4. 7 Marks
   bWrite down the steps of drawing the root locus of any system. How the stability can be judged by the root locus.
   How to answer

   • List standard root locus construction rules (poles, zeros, asymptotes, breakaway, angles)
   • Describe step-by-step procedure
   • Explain how pole locations in s-plane indicate stability
   • Mention crossing of imaginary axis and gain margin
5. 7 Marks
   aThe open loop transfer function of a unity feedback is given by $$G(s) = \frac{40}{[s(0.2s+1)]}$$ Determine steady state error using error series for the input $r(t) = (3+4t)t$
   How to answer

   • Write $G(s)=40/[s(0.2s+1)]$ and input $r(t)=(3+4t)t$
   • Find error constants or error series coefficients
   • Compute steady-state error for ramp and parabolic components
   • Obtain total steady-state error
6. 7 Marks
   bThe open loop transfer function of a unity feedback control system is given by $$G(s) = \frac{K}{s(1+sT_1)(1+sT_2)}$$ Applying Routh Hurwitz criterion, determine the value of K in term of $T_1$ and $T_2$ for the system to be stable.
   How to answer

   • Form closed-loop characteristic equation $1+G(s)=0$
   • Construct Routh array in terms of $K, T_1, T_2$
   • Apply Routh-Hurwitz conditions for no sign change
   • Derive range/condition for K for stability
7. 7 Marks
   aWhat do you understand by polar and inverse polar plots. How do they differ from bode plot.
   How to answer

   • Define polar plot and inverse polar plot
   • Explain procedure to obtain them from frequency response
   • Differentiate from Bode plot (gain-phase vs log magnitude/phase vs log frequency)
   • Mention uses and limitations
8. 7 Marks
   bA unity feedback control system with open loop transfer function $$G(s)\frac{50(s+60)}{(s+2)(s+10)}$$ Draw the bode plot and find the gain crossover frequency, phase crossover frequency, gain margin as well as phase margin.
   How to answer

   • Rewrite $G(s)=50(s+60)/((s+2)(s+10))$ in Bode standard form
   • Draw magnitude and phase plots vs log frequency
   • Identify gain crossover and phase crossover frequencies
   • Determine gain margin and phase margin
9. 7 Marks
   aAscertain stability by Nyquist criterion for the following open loop control system $$G(s)H(s) = \frac{(4s+1)}{s^2(1+s)(1+2s)}$$
   How to answer

   • State Nyquist stability criterion $Z = P - N$
   • Plot Nyquist path for $G(s)H(s)=(4s+1)/(s^2(1+s)(1+2s))$
   • Count encirclements of -1+j0
   • Conclude stability
10. 7 Marks
    bWhat is Compensation? Draw the phase lead network and explain phase lead compensation.
    How to answer

    • Define compensation in control systems
    • Draw circuit of phase lead network
    • Derive its transfer function
    • Explain effect on phase, gain margin and transient response
11. 7 Marks
    aExplain in brief propositional, derivative, integral and composite controllers.
    How to answer

    • Define proportional, derivative, integral actions
    • Give transfer function/output equation of each
    • Explain composite (PI, PD, PID) controllers
    • Mention effects on steady-state and transient response
12. 7 Marks
    bDesign a compensating network for $$G(s) = \frac{K}{s(1+0.2s)(1+0.01s)}$$ So that its phase margin at least will be $40^{\circ}$ and the steady state error will not exceed 2% of the final velocity.
    How to answer

    • Determine K from velocity error requirement (2% of final velocity)
    • Plot Bode of uncompensated system and find phase margin
    • Design lead/lag compensator to achieve >=40 deg phase margin
    • Verify compensated frequency response
13. 7 Marks
    aWhat do you mean by transfer function decomposition and discuss about direct decomposition.
    How to answer

    • Define transfer function decomposition
    • Explain need for state-space realization
    • Discuss direct decomposition (parallel/series) method
    • Mention example of splitting into first-order terms
14. 7 Marks
    bThe state equation of a linear time invariant system is given below $$\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} -2 & 0 \\ 1 & -1 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} 0 \\ 1 \end{bmatrix} u(t); t > 0$$ Find the controllability of the system and calculate the state transition matrix.
    How to answer

    • Write state matrices A, B from given equation
    • Test controllability via $Q_c=[B\ AB]$ rank
    • Compute $\Phi(s)=(sI-A)^{-1}$ then inverse Laplace
    • Obtain state transition matrix $e^{At}$
15. 14 Marks
    Write a short note on any two :

    1. a)Linearization effect of feedback
    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 and key concepts for each
    • Add relevant formulas/diagrams/examples
    • Conclude with significance in control systems