2024 question paper

Robotics Control System

23 questions

1. Q1a. For LQR, the cost function is J = \int (x^TQx + u^TRu)dt, minimize for Q = I, R = 1. What is the control input u? (i) -Kx (ii) -K (iii) Qx (iv) Ru20242m

   Unit 6.0: Design of Controllers

   For LQR, the cost function is $J = \int (x^TQx + u^TRu)dt$, minimize for $Q = I, R = 1$. What is the control input u?
   (i) $-Kx$
   (ii) $-K$
   (iii) $Qx$
   (iv) $Ru$

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2. Q1b. A system is observable if: (i) States can be measured from outputs (ii) Inputs are visible (iii) Poles are real (iv) Transfer function exists20242m

   Unit 2.0: Mathematical Modelling

   A system is observable if:
   (i) States can be measured from outputs
   (ii) Inputs are visible
   (iii) Poles are real
   (iv) Transfer function exists

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3. Q1c. Which sensor is used for measuring displacement? (i) Thermistor (ii) LVDT (iii) Photodiode (iv) Bimetallic strip20242m

   Unit 1.0: Introduction to Control System

   Which sensor is used for measuring displacement?
   (i) Thermistor
   (ii) LVDT
   (iii) Photodiode
   (iv) Bimetallic strip

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4. Q1d. Why are electrical analogies used in control systems? (i) For heating purposes (ii) To make the system unstable (iii) For simplified modeling (iv) To avoid complexity20242m

   Unit 2.0: Mathematical Modelling

   Why are electrical analogies used in control systems?
   (i) For heating purposes
   (ii) To make the system unstable
   (iii) For simplified modeling
   (iv) To avoid complexity

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5. Q1e. Why is feedback used in a control system? (i) To reduce the cost (ii) To eliminate the use of actuators (iii) To increase accuracy and stability (iv) To increase time delay20242m

   Unit 1.0: Introduction to Control System

   Why is feedback used in a control system?
   (i) To reduce the cost
   (ii) To eliminate the use of actuators
   (iii) To increase accuracy and stability
   (iv) To increase time delay

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6. Q1f. What is the function of a relay in a control system? (i) Power supply (ii) Sensor feedback (iii) Switching device (iv) None of these20242m

   Unit 1.0: Introduction to Control System

   What is the function of a relay in a control system?
   (i) Power supply
   (ii) Sensor feedback
   (iii) Switching device
   (iv) None of these

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7. Q1g. A system has poles at -2 and -4. What can be said about its time response? (i) Oscillatory (ii) Slow response (iii) Overdamped (iv) Underdamped20242m

   Unit 3.0: Time Response Analysis

   A system has poles at $-2$ and $-4$. What can be said about its time response?
   (i) Oscillatory
   (ii) Slow response
   (iii) Overdamped
   (iv) Underdamped

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8. Q1h. What is the primary effect of a derivative controller? (i) Increase steady-state error (ii) Increase rise time (iii) Reduce overshoot (iv) Increase error20242m

   Unit 6.0: Design of Controllers

   What is the primary effect of a derivative controller?
   (i) Increase steady-state error
   (ii) Increase rise time
   (iii) Reduce overshoot
   (iv) Increase error

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9. Q1i. For system A = \begin{bmatrix} 0 & 1 \\ -1 & -3 \end{bmatrix}, B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}, check controllability using rank. (i) Rank = 2, controllable (ii) Rank = 1, uncontrollable (iii) Rank = 2, not observable (iv) Rank = 1, observable20242m

   Unit 2.0: Mathematical Modelling

   For system $A = \begin{bmatrix} 0 & 1 \\ -1 & -3 \end{bmatrix}$, $B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}$, check controllability using rank.
   (i) Rank = 2, controllable
   (ii) Rank = 1, uncontrollable
   (iii) Rank = 2, not observable
   (iv) Rank = 1, observable

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10. Q1j. In the Sketch for Nyquist plot of G(s)H(s) = 1 - (s + 1), Will it encircle (-1+j0) point? (i) Yes (ii) No (iii) Only at high gain (iv) none20242m

    Unit 5.0: Stability & Frequency Response Analysis-II

    In the Sketch for Nyquist plot of $G(s)H(s) = 1 - (s + 1)$, Will it encircle ($-1+j0$) point?
    (i) Yes
    (ii) No
    (iii) Only at high gain
    (iv) none

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12. Q2a. Draw the root locus for G(s)H(s) = \frac{k}{s(s^2 + 2s + 5)} and find the range of 'k' for stability.20247m

    Unit 4.0: Stability & Frequency Response Analysis-I

    Draw the root locus for $$G(s)H(s) = \frac{k}{s(s^2 + 2s + 5)}$$ and find the range of 'k' for stability.

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13. Q2b. Find the number of poles in the left half-plane, the right half-plane, and on the j\omega-axis for the characteristic equation p(s) = 2s^5 + 3s^4 + 2s^3 + 3s^2 + 2s + 1 = 020247m

    Unit 4.0: Stability & Frequency Response Analysis-I

    Find the number of poles in the left half-plane, the right half-plane, and on the $j\omega$-axis for the characteristic equation $$p(s) = 2s^5 + 3s^4 + 2s^3 + 3s^2 + 2s + 1 = 0$$

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14. Q3a. The block diagram of a simple servo system is shown below  (i) If k = 10, determine the values of 'a' and 'b' to give an overshoot of 16\% and a time constant of 0.1 sec to a unit step input. (ii) Determine t_r, t_p, \omega_d and t_{ss} if k = 40.20247m

    Unit 3.0: Time Response Analysis

    The block diagram of a simple servo system is shown below

    

    (i) If $k = 10$, determine the values of 'a' and 'b' to give an overshoot of $16\%$ and a time constant of $0.1$ sec to a unit step input.
    (ii) Determine $t_r$, $t_p$, $\omega_d$ and $t_{ss}$ if $k = 40$.

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15. Q3b. Design a basic block diagram of a temperature control system and identify the sensor, controller, and actuator in the system.20247m

    Unit 1.0: Introduction to Control System

    Design a basic block diagram of a temperature control system and identify the sensor, controller, and actuator in the system.

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16. Q4. Draw the Bode plot for the transfer function and find the P.M. & G.M. G(s) = \frac{200(s + 2)}{s(s^2 + 10s + 100)}202414m

    Unit 4.0: Stability & Frequency Response Analysis-I

    Draw the Bode plot for the transfer function and find the P.M. & G.M.
    $$G(s) = \frac{200(s + 2)}{s(s^2 + 10s + 100)}$$

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17. Q5a. With the help of a block diagram, explain the working of a liquid level control system.20247m

    Unit 1.0: Introduction to Control System

    With the help of a block diagram, explain the working of a liquid level control system.

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18. Q5b. The SFG of a control system is shown in the figure below. Find the transfer function C/R. 20247m

    Unit 2.0: Mathematical Modelling

    The SFG of a control system is shown in the figure below. Find the transfer function $C/R$.

    

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19. Q6a. The open-loop transfer function of a unity feedback system is given by G(s) = \frac{k}{s(1 + sT)} where k and T are positive constants. By what factor should the amplifier gain be reduced so that the peak overshoot of the unit-step response of the system is reduced from 75\% to 25\%.20247m

    Unit 3.0: Time Response Analysis

    The open-loop transfer function of a unity feedback system is given by
    $$G(s) = \frac{k}{s(1 + sT)}$$
    where $k$ and $T$ are positive constants. By what factor should the amplifier gain be reduced so that the peak overshoot of the unit-step response of the system is reduced from $75\%$ to $25\%$.

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20. Q6b. Explain how relays, switches, and contactors are used in implementing simple and sequential control systems. Provide a schematic example of a motor control circuit.20247m

    Unit 1.0: Introduction to Control System

    Explain how relays, switches, and contactors are used in implementing simple and sequential control systems. Provide a schematic example of a motor control circuit.

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21. Q7. Consider a closed-loop system with an open-loop transfer function G(s)H(s) = \frac{10(s + 0.5)}{s^2(s + 2)(s + 10)} Apply the Nyquist stability criterion to determine the closed-loop stability of the system.202414m

    Unit 5.0: Stability & Frequency Response Analysis-II

    Consider a closed-loop system with an open-loop transfer function
    $$G(s)H(s) = \frac{10(s + 0.5)}{s^2(s + 2)(s + 10)}$$
    Apply the Nyquist stability criterion to determine the closed-loop stability of the system.

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23. Q8a. Explore the impact of proportional (P), Integral (I) and Derivate (D) Control modes, individually and in combination (PI, PD, PID) on system performance.20247m

    Unit 6.0: Design of Controllers

    Explore the impact of proportional (P), Integral (I) and Derivate (D) Control modes, individually and in combination (PI, PD, PID) on system performance.

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24. Q8b. Consider the mechanical system shown in the figure below. Find the transfer function G(s) = \frac{V_1(s)}{F(s)} 20247m

    Unit 2.0: Mathematical Modelling

    Consider the mechanical system shown in the figure below. Find the transfer function $G(s) = \frac{V_1(s)}{F(s)}$

    

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25. Q9. Write short notes on any two of the following: (a) Significance of actuators and sensors (b) Phase Margin and Gain Margin (c) LQR control (d) Sensitivity of open-loop & closed-loop control system & its effects202414m

    Unit 1.0: Introduction to Control System

    Write short notes on any two of the following:
    (a) Significance of actuators and sensors
    (b) Phase Margin and Gain Margin
    (c) LQR control
    (d) Sensitivity of open-loop & closed-loop control system & its effects

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