EC-404 Control System - Jun 2026 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
   aDefine a Control System. Classify control systems with suitable real-life examples.
   How to answer

   • Definition of control system as interconnection of components to obtain desired output
   • Classification: open-loop vs closed-loop, linear vs non-linear, time-invariant vs time-variant, SISO vs MIMO
   • Classification: continuous vs discrete, deterministic vs stochastic
   • Real-life examples for each type e.g. traffic signal, room heater, servo, refrigerator
2. 7 Marks
   bDevelop the mathematical models of Mechanical and Electrical Systems. Derive their Transfer Functions.
   How to answer

   • Mechanical elements: mass, damper, spring and force balance equations
   • Electrical elements: R, L, C and KVL/KCL equations
   • Force-voltage and force-current analogous circuits
   • Derivation of transfer function $C(s)/R(s)$ via Laplace transform
3. 7 Marks
   aExplain the block diagram representation of control systems. Discuss the rules of Block diagram Reduction.
   How to answer

   • Block diagram elements: summing point, take-off point, forward path, feedback
   • Canonical closed-loop representation and transfer function
   • Rules of block diagram reduction: series, parallel, feedback, shifting points
   • Stepwise reduction example to single block
4. 7 Marks
   bExplain the Signal Flow Graph (SFG). State Mason's Gain Formula and explain its application.
   How to answer

   • Definition of SFG: nodes, branches, transmittance, source and sink
   • Terminology: forward path, loop, non-touching loops
   • Statement of Mason's gain formula $T = \frac{1}{\Delta}\sum P_k \Delta_k$
   • Application procedure to find overall transfer function
5. 7 Marks
   aCompare Open-Loop and Closed-Loop Control Systems. Explain the advantages of feedback.
   How to answer

   • Definitions and block diagrams of open-loop vs closed-loop
   • Comparison table: feedback, accuracy, stability, cost, sensitivity
   • Advantages of feedback: reduced sensitivity, disturbance rejection, improved dynamics
   • Examples of each system
6. 7 Marks
   bExplain the following:

   1. (i))Regenerative Feedback
   2. (ii))Linearization by Feedback
   3. (iii))Sensitivity
   4. (iv))Disturbance Rejection
   How to answer

   • Regenerative feedback: positive feedback concept and effect
   • Linearization by feedback: handling non-linearities
   • Sensitivity: definition $S = \frac{\partial T/T}{\partial G/G}$ and reduction
   • Disturbance rejection: how feedback suppresses disturbances
7. 7 Marks
   aExplain the Standard Test Signals. Derive the Time Response of a First-Order System for a unit step input.
   How to answer

   • Standard test signals: step, ramp, parabolic, impulse and sinusoidal
   • Laplace transforms of test signals
   • First-order transfer function $1/(Ts+1)$ with unit step
   • Derivation of time response $c(t)=1-e^{-t/T}$ and time constant
8. 7 Marks
   bExplain the Time Response of a second order system. Discuss Steady-state Error and Error constants.
   How to answer

   • Second-order model $\omega_n^2/(s^2+2\zeta\omega_n s+\omega_n^2)$ and damping cases
   • Transient specifications: rise time, peak time, overshoot, settling time
   • Steady-state error $e_{ss}$ for step, ramp, parabolic inputs
   • Error constants $K_p, K_v, K_a$ and system type
9. 7 Marks
   aExplain the concept of Stability in linear control systems. Describe the Routh-Hurwitz Stability Criterion.
   How to answer

   • Stability concept: bounded input bounded output, pole locations
   • Necessary and sufficient conditions for linear systems
   • Routh-Hurwitz table construction procedure
   • Stability determination and special cases
10. 7 Marks
    bExplain the Root Locus Technique. State the rules for constructing the Root Locus.
    How to answer

    • Root locus concept: variation of closed-loop poles with gain K
    • Angle and magnitude conditions
    • Rules for construction: asymptotes, breakaway, centroid, crossings
    • Sketching procedure and stability inference
11. 7 Marks
    aExplain the relationship between Time Response and Frequency Response. Describe Polar Plot and Bode Plot.
    How to answer

    • Correlation between time-domain specs and frequency-domain specs
    • Polar plot: magnitude-phase locus for $\omega:0$ to $\infty$
    • Bode plot: log magnitude and phase vs log frequency
    • Gain crossover, phase crossover and stability margins
12. 7 Marks
    bExplain the Nyquist Stability Criterion. Discuss Gain Margin, Phase Margin, and Relative Stability.
    How to answer

    • Nyquist criterion: $Z = N+P$ encirclement of -1+j0
    • Mapping of Nyquist path and stability determination
    • Gain margin and phase margin definitions
    • Relative stability interpretation from margins
13. 7 Marks
    aExplain the objectives of control systems design. Describe Phase-Lag, Phase-Lead, and Lead-Lag compensation techniques.
    How to answer

    • Design objectives: stability, accuracy, speed, robustness
    • Phase-lag compensation: characteristics and transfer function
    • Phase-lead compensation: characteristics and design
    • Lead-lag compensation: combined improvement
14. 7 Marks
    bExplain the following controllers:

    1. (i))Proportional (P) Controller
    2. (ii))Integral (I) Controller
    3. (iii))Derivative (D) Controller
    4. (iv))PID Controller
    How to answer

    • P controller: $u=K_p e$ effect on steady-state and stability
    • I controller: elimination of steady-state error
    • D controller: predictive action and damping improvement
    • PID combination: tuning and overall performance
15. 7 Marks
    aExplain the state-space representation of control systems. Derive the State Equation and Transfer Matrix.
    How to answer

    • State, state vector, state-space model $\dot{x}=Ax+Bu, y=Cx+Du$
    • Derivation of state equation from differential equation / transfer function
    • Transfer matrix $G(s)=C(sI-A)^{-1}B+D$
    • Block diagram of state model
16. 7 Marks
    bDefine Controllability and Observability. Explain their importance in modern control systems.
    How to answer

    • Definitions of controllability and observability
    • Kalman tests using controllability and observability matrices
    • Importance for state feedback and observer design
    • Role in modern control: pole placement, minimal realization