Control System (EX-405) - Important Questions

Use Mason's gain formula to determine the overall transfer function / gain from a given signal flow graph.

Explain and distinguish between open-loop and closed-loop control systems with suitable examples.

Obtain the force-voltage analogous electrical network for the given mechanical system.

Obtain the direct and inverse electrical analogous systems for a given rotational mechanical system.

Obtain the signal flow graph from a given block diagram and then apply Mason's gain formula to find C(S)/R(S).

Derive the transfer function of an A.C. servomotor stating the assumptions made.

Explain the components of control systems for servomotors and tacho-generators.

Explain the construction and working of (AC) servomotors, including advantages and disadvantages.

Write a short notes on (any two)

Discuss the significance of feedback in control systems and how it improves system performance.

Obtain the expression for $y(t)$ which is satisfying the differential equations $\frac{d^2y(t)}{dt^2}+6\frac{dy(t)}{dt}+8y(t)=16e^{-t}$ Neglect initial conditions.

Write short notes on i) Stepper motors and ii) Nyquist plot.

Find the static error coefficients $K_p, K_v, K_a$ and the steady-state error for a composite step plus ramp plus parabolic input.

Derive the time response of a second-order system to unit step input and explain the effect of damping ratio.

Explain the time response of a first-order system to unit step and unit ramp inputs and find steady-state error.

Numerical: given (open-loop/closed-loop) transfer function, determine damping factor and time-domain specifications such as rise time, peak time, overshoot and settling time for unit step input.

Derive the relation between maximum percent overshoot $M_p$ and damping ratio $\xi$ for a second-order system, with overshoot vs damping ratio plot.

Determine $T_d$ for critical damping and settling time for a PD-controlled system.

Derive the expressions for static error coefficients, explain their use in determining steady-state error, and state limitations of the method.

For a unity-feedback system $G(s)=K/[s(sT+1)]$ with given maximum overshoot and resonant frequency, determine $K$, $T$ and the resonant peak $M_r$.

Explain PI controller action with block diagram and obtain its transfer function model.

Derive expressions for peak time $T_p$ and rise time $T_r$ in terms of $\xi$ and $\omega_n$ for an underdamped second-order system with step input.

Discuss advantages and disadvantages of P, I and D (PID) controllers.

Numerical: design gains $K_1, K_2$ to meet given peak overshoot $M_p$ and peak time $T_p$ for unit step input.

Using Routh array, determine stability and number/location of roots with positive, zero and negative real parts for a given characteristic equation or open-loop transfer function.

Sketch the complete root locus for $G(s)H(s) = K/[s(s+a)(s^2+bs+c)]$ as $K$ varies from 0 to infinity.

Explain the effects of adding open-loop poles and zeros on the nature of the root locus and on system performance.

Find the range of gain $K$ for absolute stability, marginal value of $K$ and frequency of sustained oscillations.

Sketch the complete root locus with indication of breakaway points and comment on stability.

Explain the procedure to obtain the gain $K$ for a specified damping ratio $\xi$ from the root locus.

Describe the concept of stability in control system and explain why it is important.

Sketch the root locus for the system with $G(s)=\frac{k(s+1)}{(s+3)}$.

Find relation between $K$ and $T$ for absolute stability and modified relation for all roots to lie to the left of $s=-1$ using shifted Routh-Hurwitz criterion.

Define and derive the breakaway point on the root locus.

Sketch the Bode plot for a given transfer function and determine gain margin, phase margin, gain crossover frequency and phase crossover frequency, and comment on stability.

Draw the polar plot for a given open-loop transfer function $G(s)H(s)$ of a unity feedback system and determine stability margins if asked.

Sketch the Nyquist plot for $G(s)H(s) = K/[s(s+2)(s+10)]$ and determine the range of $K$ for closed-loop stability

Given a polar plot, sketch the modified polar plot after adding a pole at the origin and a pole at $s=-1/T_2$.

Derive the expressions for the frequency domain specifications (resonant peak, resonant frequency, bandwidth, etc.) of a second-order system.

What is a polar plot and what is its significance, including shapes for Type 0, Type 1 and Type 2 systems?

Sketch the Bode magnitude and phase plots for a given open-loop transfer function and find the frequency at which magnitude is 0 dB.

Find the gain margin and stability from the Nyquist plot for $G(s)H(s) = 40/[(s+4)(s^2+2s+2)]$

Draw the Nyquist plot for $G(s)H(s) = 20/[s(s+1)(s+2)]$

Explain the concept of gain margin and phase margin and how they indicate relative stability.

Explain frequency-domain analysis and describe the procedure for constructing Bode plots to represent the frequency response of a system.

Explain Nyquist stability and relative stability with examples

Explain eigenvalues and eigenvectors and compute them (and modal/eigen matrix) for a given system matrix $A$.

Explain and compare the effects of Lag, Lead and Lag-Lead compensation on frequency response.

Define the different design steps for a lag-lead compensation network.

State the properties of State Transition Matrix and compute it for a given matrix $A$.

Design a compensator for $G(s) = \frac{K}{s(1+0.2s)}$ to meet specified $K_v$ and phase margin.

Write down / state the properties of the state transition matrix.

Discuss the compensation techniques employed in the design of control systems.

What is the state transition matrix? Explain its significance in predicting the future state of a dynamic system.

What is a lag-lead compensator and under what conditions is it employed?

Write a short note on eigenvalues and eigenvectors.

Draw the electrical circuit diagram of a lead-lag / lag-lead compensator and explain it in detail.

Obtain the solution of the state equation and list the properties of the state transition matrix.