EC-404 Control System - Jun 2023 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 are effects of feedback? Classify different types of control systems with examples.
   How to answer

   • Define feedback and list its effects: sensitivity, stability, bandwidth, noise, steady-state error
   • Classify control systems: open-loop vs closed-loop, linear vs non-linear, time-invariant vs variant, SISO vs MIMO, continuous vs discrete
   • Give examples for each type
2. 7 Marks
   bWrite mathematical model of mechanical system shown in figure (i) and write analogous electrical equations.

   

   How to answer

   • Draw free-body diagrams for masses M1, M2 with displacements x1, x2
   • Write force equilibrium differential equations with dampers D1, D2 and spring K2
   • Draw analogous electrical circuits using force-voltage and force-current analogy
   • Write loop/node electrical equations
3. 7 Marks
   aCompare open loop and closed loop systems and find transfer function of block diagram shown in figure (ii) by reduction rules

   

   How to answer

   • Compare open-loop vs closed-loop: definition, feedback, accuracy, stability, cost, examples
   • Apply block reduction rules stepwise: shift takeoffs, combine G2+G3 parallel, inner loop with H1
   • Reduce outer loop with H2 to get C/R
4. 7 Marks
   bDetermine transfer function of signal flow graph as shown in figure (iii) by using Mason's gain formula.

   

   How to answer

   • Identify forward paths, individual loops, non-touching loops from signal flow graph
   • Compute graph determinant Delta and path cofactors Delta_k
   • Apply Mason's gain formula C(s)/R(s) = sum(Pk*Delta_k)/Delta
5. 7 Marks
   aDescribe standard test signals, steady state errors and error constants in detail.
   How to answer

   • Define step, ramp, parabolic, impulse test signals with Laplace forms
   • Define steady-state error ess and static error constants Kp, Kv, Ka
   • Give ess formulas for type 0,1,2 systems
6. 7 Marks
   bDiscuss effects of additions of poles and zeros to open loop and closed loop system.
   How to answer

   • Explain effect of adding pole on stability, transient response and steady-state
   • Explain effect of adding zero on damping, peak overshoot and stability
   • Contrast effects for open-loop vs closed-loop systems
7. 7 Marks
   aApply Routh Hurwitz stability criteria to determine the stability and find the number of roots lying in the right half of the s-plane if characteristic equation of the two systems are given as follows:

   1. i)$s^4 + 21s^3 + 21s^2 + 36s + 20 = 0$
   2. ii)$s^5 + 6s^4 + 3s^3 + 2s^2 + s + 1 = 0$
   How to answer

   • Construct Routh array for each characteristic equation
   • Check first-column sign changes for stability
   • Count sign changes to get number of roots in right-half s-plane
8. 7 Marks
   bWhat is root locus? Describe steps involved in sketching root locus.
   How to answer

   • Define root locus as plot of closed-loop poles vs gain K
   • List construction rules: poles/zeros, real axis, asymptotes, breakaway, angles
   • Explain steps to sketch root locus
9. 7 Marks
   aEstablish correlation between time response and frequency response parameters.
   How to answer

   • Define time-domain specs: Mp, tp, tr, ts and frequency specs: Mr, wr, bandwidth, phase margin
   • Derive relations for second-order system: Mr vs damping ratio, bandwidth vs natural frequency
   • State correlation formulas
10. 7 Marks
    bDefine gain margin, phase margin and draw bode plot for the system having open loop transfer function. $$G(s)H(s)=\frac{50}{(s+1)(s+2)}$$
    How to answer

    • Define gain margin and phase margin with formulas
    • Compute magnitude and phase for G(s)H(s)=50/((s+1)(s+2))
    • Sketch Bode magnitude and phase plots and mark GM, PM
11. 7 Marks
    aState Nyquist stability criterion and describe procedure of assessment of relative stability using Nyquist plot.
    How to answer

    • State Nyquist stability criterion Z = N+P
    • Explain Nyquist contour and encirclement of -1+j0
    • Describe gain margin, phase margin and relative stability from Nyquist plot
12. 7 Marks
    bDiscuss types of compensation techniques and design of phase - lag and phase lead compensators.
    How to answer

    • Classify compensators: lag, lead, lag-lead
    • Give transfer functions and pole-zero locations
    • Explain design procedure for phase-lag and phase-lead compensators
13. 7 Marks
    aCompare proportional, derivative, integral and composite controllers.
    How to answer

    • Define P, I, D actions with transfer functions
    • Compare effects on error, speed, stability and noise
    • Describe composite PI, PD, PID controllers
14. 7 Marks
    bDescribe general state space representation and write state model for $n^{th}$ order differential equation.
    How to answer

    • Define state vector, state equation x_dot=Ax+Bu, output y=Cx+Du
    • Explain nth-order differential equation to first-order form
    • Write companion/state model matrices
15. 7 Marks
    aConvert the following transfer function into state - space form: $$\frac{Y(s)}{R(s)} = \frac{s^2 + 2s + 4}{s^3 + 3s^2 + 6s + 10}$$
    How to answer

    • Express transfer function in controllable/observable canonical form
    • Choose state variables and write A, B, C, D matrices
    • Verify by C(sI-A)^-1B+D
16. 7 Marks
    bWrite short note on following

    1. i)Controllability and observability
    2. ii)Transfer function decomposition
    3. iii)Solution of state equation
    4. iv)All-pass and minimum - phase systems.
    How to answer

    • Define controllability/observability tests with matrices
    • Explain transfer function decomposition methods
    • Give solution x(t) using state transition matrix; define all-pass and minimum-phase