GATE Electrical Engineering 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 GATE Electrical Engineering, not a summary of it.

1. 1

   Mathematical modelling and representation of systems

   3 topics

   • Feedback principle
   • Transfer function
   • Block diagrams and Signal flow graphs
2. 2

   Transient and Steady-state analysis of linear time invariant systems

   overview

   Examined as a single unit within Control Systems — no further topic split in the official outline.

3. 3

   Stability analysis using Routh-Hurwitz and Nyquist criteria

   overview

   Examined as a single unit within Control Systems — no further topic split in the official outline.

4. 4

   Bode plots

   overview

   Examined as a single unit within Control Systems — no further topic split in the official outline.

5. 5

   Root loci

   overview

   Examined as a single unit within Control Systems — no further topic split in the official outline.

6. 6

   Lag, Lead and Lead-Lag compensators

   overview

   Examined as a single unit within Control Systems — no further topic split in the official outline.

7. 7

   P, PI and PID controllers

   overview

   Examined as a single unit within Control Systems — no further topic split in the official outline.

8. 8

   State space model

   1 topic

   • Solution of state equations of LTI systems

Control Systems flashcards for GATE Electrical Engineering

25 of 50 cards from the Control Systems deck — real questions with worked answers.

1. What is the defining characteristic of a feedback (closed-loop) control system?

   A portion of the output is measured and fed back to be compared with the reference input; the resulting error signal drives the controller. This allows the system to self-correct based on actual output.

2. In a negative feedback system, how is the error signal $e(t)$ formed?

   $e(t) = r(t) - b(t)$, where $r(t)$ is the reference input and $b(t)$ is the feedback signal (the output passed through the feedback element $H$).

3. State the closed-loop transfer function for a single-loop negative feedback system with forward path $G(s)$ and feedback path $H(s)$.

   $$\frac{C(s)}{R(s)} = \frac{G(s)}{1 + G(s)H(s)}$$

4. For a unity-feedback system, what is the closed-loop transfer function in terms of $G(s)$?

   With $H(s)=1$: $$\frac{C(s)}{R(s)} = \frac{G(s)}{1 + G(s)}$$

5. What is the loop transfer function (open-loop gain) of a feedback system?

   It is the product $G(s)H(s)$ — the gain encountered going once around the loop, broken at any point.

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

   $1 + G(s)H(s) = 0$. Its roots are the closed-loop poles, which determine system stability and transient response.

7. List two key advantages and one disadvantage of negative feedback in control systems.

   Advantages: reduced sensitivity to parameter variations and disturbances; improved bandwidth/speed and accuracy. Disadvantage: it reduces overall gain and may introduce instability.

8. Define the sensitivity of the closed-loop gain $T$ to a change in the forward gain $G$.

   $$S^{T}_{G} = \frac{\partial T / T}{\partial G / G} = \frac{1}{1 + GH}$$ For negative feedback ($GH>0$) this is less than 1, so feedback reduces sensitivity.

9. Derive the sensitivity of the closed-loop gain to the feedback element $H$ for a unity-loop case.

   $$S^{T}_{H} = \frac{-GH}{1 + GH}$$ For large $GH$ this approaches $-1$, meaning the closed-loop response depends almost entirely on $H$.

10. How does negative feedback affect system bandwidth and gain?

    It increases bandwidth (faster response) by the factor $(1+GH)$ but decreases the DC/low-frequency gain by the same factor — the gain-bandwidth product tends to remain roughly constant.

11. Define the transfer function of a linear time-invariant (LTI) system.

    It is the ratio of the Laplace transform of the output to the Laplace transform of the input, with all initial conditions set to zero: $$G(s) = \frac{Y(s)}{X(s)} \bigg|_{\text{ICs}=0}$$

12. What is the relationship between the transfer function and the impulse response $g(t)$?

    The transfer function $G(s)$ is the Laplace transform of the impulse response: $G(s) = \mathcal{L}\{g(t)\}$, and equivalently $g(t)=\mathcal{L}^{-1}\{G(s)\}$.

13. Define the poles and zeros of a transfer function $G(s)=\dfrac{N(s)}{D(s)}$.

    Zeros are the roots of the numerator $N(s)=0$ (where $G(s)=0$); poles are the roots of the denominator $D(s)=0$ (where $G(s)\to\infty$).

14. What determines the order and the type of a system from its transfer function?

    Order = degree of the denominator polynomial $D(s)$ (number of poles). Type = number of poles located at the origin ($s=0$), i.e. the number of pure integrators in the open-loop transfer function.

15. State the condition relating the number of poles $n$ and zeros $m$ for a physically realizable (proper) transfer function.

    $m \leq n$ (degree of numerator $\leq$ degree of denominator). A strictly proper system has $m < n$.

16. What is the DC gain of a transfer function $G(s)$, and how is it computed?

    The DC (steady-state) gain is the response to a constant input, found by evaluating $G(s)$ at $s=0$: $G(0)$ (assuming no pole at the origin).

17. For a standard second-order system $G(s)=\dfrac{\omega_n^{2}}{s^{2}+2\zeta\omega_n s+\omega_n^{2}}$, name the two defining parameters.

    $\omega_n$ = undamped natural frequency; $\zeta$ = damping ratio. The poles are $s=-\zeta\omega_n \pm \omega_n\sqrt{\zeta^{2}-1}$.

18. Classify the damping of a second-order system based on the damping ratio $\zeta$.

    $\zeta = 0$: undamped; $0<\zeta<1$: underdamped (oscillatory); $\zeta = 1$: critically damped; $\zeta > 1$: overdamped (no oscillation).

19. Give the formula for the damped natural frequency $\omega_d$ of an underdamped second-order system.

    $$\omega_d = \omega_n\sqrt{1-\zeta^{2}}$$ This is the imaginary part of the complex conjugate pole pair.

20. Write the formula for the peak overshoot $M_p$ of a second-order underdamped system to a step input.

    $$M_p = e^{-\frac{\pi\zeta}{\sqrt{1-\zeta^{2}}}} \times 100\%$$

21. State the approximate settling time $t_s$ (2% criterion) for a second-order system.

    $$t_s \approx \frac{4}{\zeta\omega_n}$$ For the 5% criterion, $t_s \approx \dfrac{3}{\zeta\omega_n}$.

22. Give the peak time $t_p$ expression for an underdamped second-order system.

    $$t_p = \frac{\pi}{\omega_d} = \frac{\pi}{\omega_n\sqrt{1-\zeta^{2}}}$$

23. What is the rule for blocks connected in cascade (series) in a block diagram?

    The equivalent transfer function is the product of the individual transfer functions: $G_{eq}(s) = G_1(s)\,G_2(s)\,\cdots\,G_n(s)$ (assuming no loading effects).

24. What is the rule for blocks connected in parallel in a block diagram?

    The equivalent transfer function is the algebraic sum of the individual transfer functions: $G_{eq}(s) = G_1(s) \pm G_2(s) \pm \cdots$ depending on the summing-junction signs.

25. State the block-diagram reduction rule for a basic negative feedback loop.

    A forward block $G$ with feedback block $H$ reduces to $$\frac{G}{1+GH}$$ (use $1-GH$ for positive feedback).

See more Control Systems flashcards →

Planning Control Systems for GATE Electrical Engineering

Control Systems (GATE Electrical Engineering) FAQ