EC-404 Control System - Nov 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
   aDefine open loop and closed loop systems and describe effect of feedback on external disturbances.
   How to answer

   • Define open-loop system (no feedback) with example
   • Define closed-loop system (feedback) with example/block diagram
   • Effect of feedback on external disturbance: attenuation in closed loop vs no effect in open loop
   • Formula for disturbance transfer and conclusion
2. 7 Marks
   bWrite mathematical model of electrical and mechanical system shown in figure (i) and figure (ii).

   

   How to answer

   • Draw/label electrical parallel RLC circuit and write KCL at node V
   • Derive integro-differential / transfer model for Figure (i)
   • Draw/label mechanical 2-mass system and free-body diagrams
   • Write differential equations of motion for M1, M2 / force-voltage analogy
3. 7 Marks
   aConstruct signal flow graph for block diagram shown in figure (iii) and find out transfer function.

   

   How to answer

   • Convert each block/summing point/take-off to SFG nodes and branches G1,G2,G3,H1,H2
   • Draw signal flow graph
   • Apply Mason's gain formula: list forward paths and loops
   • Obtain C(s)/R(s) transfer function
4. 7 Marks
   bDefine terminologies used in control system and classify different types of control systems with suitable examples.
   How to answer

   • Define basic terminologies: plant, controller, feedback, error, etc.
   • Classify: open vs closed loop, linear vs non-linear, time-invariant vs variant, SISO vs MIMO
   • Give suitable example for each type
   • Comparison summary
5. 7 Marks
   aFor a unity feedback system having $$G(s)=\frac{35(s+4)}{s(s+2)(s+5)}.$$ Find error constants and error for ramp input with magnitude 5.
   How to answer

   • Identify unity feedback, type and Kp, Kv, Ka formulas
   • Compute Kp, Kv, Ka for $G(s)=35(s+4)/s(s+2)(s+5)$
   • Use $e_{ss}=A/Kv$ for ramp input
   • Evaluate error for magnitude 5
6. 7 Marks
   bDiscuss time response of following :

   1. i)1st order system
   2. ii)2nd order system
   How to answer

   • Give transfer function and step/ramp response of 1st order system
   • Define time constant, steady-state value
   • Give 2nd order response for under/critical/over-damped cases
   • Mention overshoot, settling time, damping ratio
7. 7 Marks
   aDescribe following in detail

   1. i)Concept of stability of linear systems
   2. ii)Routh Hurwitz stability criteria
   How to answer

   • Define stability: BIBO, absolute vs relative
   • Explain pole locations in s-plane for linear systems
   • State Routh-Hurwitz criterion and array construction
   • Mention special cases and stability decision
8. 7 Marks
   bCalculate the angle of asymptotes and the centroid for the system having, $$G(s)H(s)=\frac{K(s+3)}{s(s+2)(s+4)(s+5)}$$
   How to answer

   • Count poles (n=4) and zeros (m=1) to get number of asymptotes
   • Compute asymptote angles $(2q+1)180/(n-m)$
   • Compute centroid $\sigma=(\sum poles-\sum zeros)/(n-m)$
   • Substitute poles -0,-2,-4,-5 and zero -3
9. 7 Marks
   aDiscuss following in brief

   1. i)Polar plots
   2. ii)Bode plots
   3. iii)Correlation between time and frequency response
   How to answer

   • Define polar plot and procedure to sketch
   • Define Bode plot: magnitude and phase vs frequency
   • Explain correlation: resonant peak, bandwidth vs transient specs
   • Give example sketches
10. 7 Marks
    bWrite Nyquist stability criterion and draw the Nyquist plot for $G(s)H(s)=\frac{1}{(s+2)}$. Also decide stability.
    How to answer

    • State Nyquist stability criterion Z = N+P
    • Map Nyquist path and plot $1/(s+2)$
    • Count encirclements of -1+j0
    • Decide closed-loop stability
11. 7 Marks
    aDescribe types of compensation techniques.
    How to answer

    • Define compensation purpose
    • List series/parallel/feedback compensation
    • Describe lag, lead, lag-lead characteristics
    • Mention applications
12. 7 Marks
    bDesign compensators in time and frequency domain for following cases.

    1. i)Phase lag
    2. ii)Phase lead lag
    How to answer

    • State design specs in time and frequency domain
    • Outline phase-lag design steps
    • Outline phase lead-lag design steps
    • Mention transfer functions and Bode shaping
13. 7 Marks
    aWrite notes on following:

    1. i)Proportional and derivative controllers
    2. ii)Integral controllers
    3. iii)Composite controllers
    How to answer

    • Explain P and PD control law and transfer function
    • Explain I control effect on steady-state error
    • Explain composite PI, PD, PID controllers
    • Mention advantages, disadvantages with diagrams
14. 7 Marks
    bExpress the following transfer function in state space phase variable form. $$\frac{Y(s)}{U(s)}=\frac{5s^2+2s+6}{s^3+7s^2+11s+8}$$
    How to answer

    • Write differential equation from $Y(s)/U(s)$
    • Choose phase variables as outputs of integrators
    • Form A in companion form, B, C from numerator coefficients
    • Write state and output equations
15. 7 Marks
    aEvaluate the controllability and observability of the system with $$A=\begin{bmatrix}0 & 1 & 0\\0 & 0 & 1\\0 & -3 & -4\end{bmatrix}, B=\begin{bmatrix}0\\0\\1\end{bmatrix} \text{and} C=\begin{bmatrix}2 & 3 & 1\end{bmatrix}$$
    How to answer

    • Form controllability matrix Qc=[B AB A^2B] and check rank
    • Form observability matrix Qo=[C; CA; CA^2] and check rank
    • Compute determinants for given A,B,C
    • Conclude controllability and observability
16. 7 Marks
    bDiscuss following in detail :

    1. i)Transfer function decomposition
    2. ii)State Transition Matrix (STM)
    3. iii)Kalman's Test
    How to answer

    • Explain partial-fraction / transfer function decomposition
    • Define STM $e^{At}$ properties and computation
    • State Kalman's test for controllability/observability
    • Give formulas and significance