UPSC ESE E&T Control Systems Syllabus

Control Systems syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Control Systems in UPSC ESE E&T, not a summary of it.

1. 1

   Mathematical Modelling of Control Systems

   3 topics

   • Transfer Functions
   • Block Diagrams
   • Signal Flow Graphs
2. 2

   Feedback Control Systems

   4 topics

   • Stability Analysis
   • Root Locus
   • Bode Plots
   • Nyquist Plots
3. 3

   State Space Analysis

   3 topics

   • State Variables
   • State Transition Matrix
   • Controllability and Observability

Control Systems flashcards for UPSC ESE E&T

25 of 51 cards from the Control Systems deck — real questions with worked answers.

1. What is the transfer function of a linear time-invariant system?

   The ratio of the Laplace transform of the output to the Laplace transform of the input, assuming all initial conditions are zero: G(s) = C(s)/R(s).

2. In a transfer function, what are poles and zeros?

   Zeros are the roots of the numerator polynomial (values of s making the TF zero); poles are the roots of the denominator polynomial (values of s making the TF infinite).

3. What does the order of a system correspond to in its transfer function?

   The order equals the highest power of s in the denominator polynomial (the number of poles).

4. What is the type of a control system?

   The number of poles of the open-loop transfer function located at the origin (number of pure integrators, i.e., the power of s in the denominator factor s^N).

5. What is the characteristic equation of a closed-loop system?

   Obtained by setting the denominator of the closed-loop transfer function to zero: 1 + G(s)H(s) = 0.

6. For a unity-feedback system with forward path G(s), what is the closed-loop transfer function?

   T(s) = G(s) / (1 + G(s)).

7. For a system with forward path G(s) and feedback H(s), what is the closed-loop transfer function?

   T(s) = G(s) / (1 + G(s)H(s)).

8. What is the DC gain of a transfer function and how is it found?

   The steady-state gain for a constant input, found by evaluating G(s) at s = 0 (final value theorem).

9. State the rule for reducing two blocks G1 and G2 connected in cascade (series).

   They multiply: equivalent block = G1·G2 (assuming no loading).

10. State the rule for reducing two blocks G1 and G2 connected in parallel.

    They add (algebraically, per the summing point signs): equivalent block = G1 ± G2.

11. In block diagram reduction, what happens when moving a summing point ahead of (before) a block G?

    The signal entering the moved branch must be multiplied by 1/G to keep the diagram equivalent.

12. In block diagram reduction, what happens when moving a takeoff (pickoff) point beyond (after) a block G?

    The branch taken off must be multiplied by 1/G to preserve the original signal value.

13. What is the equivalent transfer function of a basic negative-feedback loop with forward gain G and feedback H?

    G / (1 + GH). For positive feedback it is G / (1 - GH).

14. What is a signal flow graph (SFG)?

    A graphical representation of a set of linear algebraic equations using nodes (variables) and directed branches (gains) connecting them.

15. State Mason's Gain Formula.

    T = (1/Δ) Σ Pk·Δk, where Pk is the gain of the k-th forward path, Δ is the graph determinant, and Δk is the determinant with loops touching path k removed.

16. In Mason's formula, how is the graph determinant Δ computed?

    Δ = 1 − (sum of all individual loop gains) + (sum of products of two non-touching loops) − (sum of products of three non-touching loops) + ...

17. In a signal flow graph, what is a forward path?

    A path from the input node to the output node along which no node is encountered more than once.

18. In a signal flow graph, what is a non-touching loop?

    Loops that share no common node (and hence no common branch) with each other.

19. What is the BIBO stability condition for an LTI system?

    A bounded input produces a bounded output if and only if all poles of the transfer function lie in the left half of the s-plane (negative real parts).

20. Where must the roots of the characteristic equation lie for a continuous LTI system to be stable?

    Strictly in the left-half s-plane (all roots have negative real parts); roots on the jω-axis give marginal stability, in the right half give instability.

21. What does the Routh-Hurwitz criterion determine?

    The number of roots of the characteristic equation in the right-half s-plane (number of sign changes in the first column) without solving for the roots, thus assessing stability.

22. In a Routh array, what does a sign change in the first column indicate?

    Each sign change corresponds to one root in the right-half s-plane; for stability there must be no sign changes in the first column.

23. How do you handle a zero in the first column of a Routh array (with nonzero rest of row)?

    Replace the zero with a small positive ε and continue; then examine signs as ε → 0.

24. What does a row of all zeros in the Routh array signify, and how is it handled?

    It indicates symmetrically located roots (e.g., on the jω-axis). Form an auxiliary polynomial from the row above and differentiate it to replace the zero row.

25. What is the root locus?

    The plot of the loci of the closed-loop poles in the s-plane as a system parameter (usually open-loop gain K) is varied from 0 to infinity.

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