CONTROL SYSTEMS

A control system with feedback generally has

1. Lower stability
2. Reduced steady-state error
3. Increased nonlinearity
4. Higher sensitivity to parameter variations

In signal flow graph analysis, a loop in contact with another loop is called

1. Forward path
2. Self-loop
3. Non-touching loop
4. Touching loop

For a second-order underdamped system, increasing damping ratio decreases

1. Rise time only
2. Peak overshoot
3. Settling time only
4. Natural frequency

The number of branches in a root locus equals the number of

1. Zeros
2. Closed-loop poles
3. Open-loop poles
4. Gain constants

Breakaway points in root locus occur where

1. Gain becomes zero
2. Multiple roots exist
3. Poles cross imaginary axis
4. Characteristic equation changes sign

A Type-1 system has zero steady-state error for

1. Step input
2. Ramp input
3. Parabolic input
4. Impulse input

The slope of magnitude plot for a single pole in Bode plot is

1. +20 dB/decade
2. −20 dB/decade
3. −40 dB/decade
4. +40 dB/decade

Phase margin is the additional phase lag required to make the system

1. Critically damped
2. Oscillatory
3. Unstable
4. Faster

Root-locus based controller design mainly involves adjustment of

1. Pole-zero locations
2. Sampling frequency
3. Input amplitude
4. State variables

State-space analysis is particularly useful for

1. Nonlinear algebraic equations
2. Single-input single-output systems only
3. Multi-variable systems
4. Frequency response only

Explain signal flow graphs and derive Mason’s Gain Formula. Determine the transfer function (C(s)/R(s)) for given signal flow graph.

Discuss the effects of feedback on stability, sensitivity, bandwidth, and steady-state error of a control system.

A unity feedback system has:
G(S) = 25/[S(S+5)]
Determine: (i) Damping ratio (ii) Natural frequency (iii) Peak overshoot (iv) Settling time.

Derive expressions for rise time and maximum overshoot for a standard second-order system.

Using the Routh–Hurwitz criterion, determine the stability of the system whose characteristic equation is: S⁴ + 2S³ + S² + 2S + 1 = 0.

Sketch the root locus for:
G(S)H(S) = K/[S(S+2)(S+4)]
Determine the breakaway points and imaginary-axis crossings.

Explain the effect of adding poles and zeros on the transient response and stability of a control system.

State and explain the Nyquist stability criterion. Also draw the Nyquist Plots for:
G(S)H(S) = 3/[(S+2)(S−1)]

Discuss gain margin and phase margin and explain their significance in relative stability analysis.

Explain lag compensation and discuss its effect on steady-state accuracy and bandwidth.

Discuss the concept of robustness in control systems and explain how controller design improves robustness.

Explain the concepts of state variables, state equations, and state-space representation with suitable example.

Discuss the stability of discrete-time systems and explain the role of eigenvalues in determining system stability.

Test the controllability and observability of the system:
A = [0 1; −2 −3], B = [0; 1], C = [1 0]

Routh–Hurwitz stability criterion and its significance

Gain margin and phase margin in frequency response analysis

Initial value theorem and final value theorem

closed-loop control systems