Control System (EC-404) - Important Questions

Find / determine the transfer function $Y(s)/U(s)$ from a given signal flow graph using Mason's gain formula.

Define what a control system is and explain its classification with suitable real-life examples.

Develop the mathematical models (differential equations) of mechanical and electrical systems and derive their transfer functions, including electrical analogy.

Compare open-loop and closed-loop control systems with block diagrams, including advantages, disadvantages and advantages of feedback.

Explain block diagram terms: block, output, summing point, take-off point, forward path and feedback path

Find the transfer function / reduce a given block diagram to single-block form using block diagram reduction rules

Explain block diagram representation of control systems and the rules of block diagram reduction

Explain the Signal Flow Graph (SFG), state Mason's Gain Formula and explain its application.

Explain the following:

Draw block diagrams of open-loop and closed-loop control systems, compare them, and give advantages and disadvantages of each.

Define transfer function and derive the expression for closed-loop transfer function.

Find the transfer function of a given electrical circuit (numerical problem).

What is root locus and what are the steps/rules for sketching root locus?

Determine stability (and number of right-half s-plane roots) from given characteristic equation using Routh-Hurwitz criterion

Write the steps for drawing root locus and explain how stability is judged from root locus.

Determine steady-state error using error series for given $G(s)$ and input $r(t)$.

For unity feedback system with $G(s)=K/[s(1+sT_1)(1+sT_2)]$, find range/value of $K$ in terms of $T_1,T_2$ for stability using Routh-Hurwitz criterion

Explain concept of stability in linear systems and describe Routh-Hurwitz stability criterion

Explain the Standard Test Signals. Derive the Time Response of a First-Order System for a unit step input.

Explain the time response of a second-order system including steady-state error and error constants.

Discuss the effects of addition of poles and zeros on open-loop and closed-loop system performance.

For the unity-feedback closed-loop transfer function $C(s)/R(s) = 20/(s^2+16s+25)$, determine damping ratio, undamped natural frequency, percentage peak overshoot (and error response).

Explain the various standard test signals used in control systems.

Sketch the root locus for $G(s)=K/[s(s+2)(s+4)]$ and find $K$ for a specified damping ratio of 0.5.

Using Nyquist criterion, determine closed-loop stability for a given open-loop transfer function $G(s)H(s)$.

State/explain the Nyquist stability criterion and describe assessment of relative stability using Nyquist plot, including gain margin and phase margin.

Draw the Bode plot for the given open-loop transfer function and determine the gain crossover frequency, phase crossover frequency, gain margin and phase margin.

Explain polar and inverse polar plots and how they differ from Bode plot

Explain the relationship between Time Response and Frequency Response. Describe Polar Plot and Bode Plot.

Derive expressions for resonant peak and resonant frequency for a second-order system and establish correlation between time response and frequency response parameters.

Derive expressions for resonant peak and resonant frequency and establish correlation between time-domain and frequency-domain response parameters.

Sketch the Bode plot for $G(s) = \frac{K(1+0.2s)(1+0.025s)}{s^3(1+0.001s)(1+0.005s)}$.

Write a short note on polar plot

Write a short note on Bode plot.

Briefly discuss polar plots, Bode plots, and correlation between time and frequency response.

Write the Nyquist stability criterion and draw the Nyquist plot for a given $G(s)H(s)$ and decide stability.

Explain proportional (P), integral (I), derivative (D) and composite / PID controllers

What is compensation? Draw the phase-lead network / lead compensator and explain it and obtain its transfer function.

Discuss types of compensation techniques and design / describe phase-lag, phase-lead and lead-lag compensators and objectives of control system design.

Design a compensating network for $G(s)=\frac{K}{s(1+0.2s)(1+0.01s)}$ for at least $40^\circ$ phase margin and steady-state velocity error not exceeding $2\%$.

Derive the relationship between $\alpha$ and $\phi_m$ for a lead compensator.

Design a compensating network for $G(s)=1/s^2$ to achieve $45^\circ$ phase margin without sacrificing velocity error constant.

Describe types of compensation techniques.

Design compensators in time and frequency domain for phase-lag and phase lead-lag cases.

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

Explain/define the concepts of controllability and observability, their importance, with example/short note

Explain transfer function decomposition and direct decomposition method

Find controllability and calculate state transition matrix for a given 2nd-order state equation

Explain state-space representation and derive the state equation and transfer matrix.

Convert a third-order transfer function into state-space form.

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

Test controllability and/or observability of a given state-space system using Kalman's test

Determine the state-space model from a given transfer function using direct decomposition

Express the given transfer function in phase-variable state-space form.

Describe the general state-space representation and derive the state model for an $n^{th}$-order differential equation.

Discuss transfer function decomposition, State Transition Matrix, and Kalman's test

Write a short note on any two :

Write a short note on any two :

Write a short note on any two