Control Systems Analysis: Master the Fundamentals for Electrical Engineers

Question 1

Which of the following is the transfer function of a first-order system with a time constant $\tau$?

Accepted Answer

$$G(s) = \frac{1}{s+\frac{1}{	au}}$$

Answer

$$G(s) = \frac{s}{s+\frac{1}{	au}}$$

Answer

$$G(s) = \frac{	au}{s+\frac{1}{	au}}$$

Answer

$$G(s) = \frac{s+\frac{1}{	au}}{	au}$$

Question 2

What is the time constant $\tau$ of a first-order system with a transfer function $$G(s) = \frac{1}{s+\frac{1}{\tau}}$$?

Accepted Answer

The reciprocal of the pole location

Answer

The time it takes for the system to reach 63% of its final value

Answer

The rate at which the system's output decays

Answer

The gain of the system at low frequencies

Question 3

Which of the following is a necessary condition for a system to be stable?

Accepted Answer

All poles of the system must be in the left half of the s-plane

Answer

All poles of the system must be in the right half of the s-plane

Answer

The system must have no poles on the imaginary axis

Answer

The system must have only one pole on the imaginary axis

Question 4

What is the resonant frequency of a second-order system with a transfer function $$G(s) = \frac{\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}$$?

Accepted Answer

$\omega_n$

Answer

$$2\zeta\omega_n$$

Answer

$$\frac{1}{2\zeta\omega_n}$$

Answer

$$\frac{1}{\omega_n}$$

Question 5

Which of the following is the damping ratio of a second-order system with a transfer function $$G(s) = \frac{\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}$$?

Accepted Answer

$\zeta$

Answer

$$\frac{1}{\zeta}$$

Answer

$$\frac{\zeta}{\omega_n}$$

Answer

$$\frac{\omega_n}{\zeta}$$

Question 6

How does the time constant affect the decay rate of a first-order system's transient response?

Accepted Answer

Determines the decay rate

Answer

Determines the initial value

Answer

Determines the frequency

Answer

Has no effect

Question 7

Which of the following is the transfer function of an ideal integrator?

Accepted Answer

1/s

Answer

1

Answer

s

Answer

s^2

Question 8

What is the unit of feedback gain in a control system?

Accepted Answer

Dimensionless

Answer

Gain (dB)

Answer

Hertz (Hz)

Answer

Seconds (s)

Question 9

In state feedback control, how is the control law designed to achieve the desired system performance?

Accepted Answer

By using the pole placement method to select the feedback gains

Answer

By minimizing a cost function via optimal control theory

Answer

By employing a Kalman filter to estimate the system's states

Answer

By implementing a proportional-integral-derivative (PID) controller

Question 10

In the pole placement method, how do you calculate the controller's gain?

Accepted Answer

Apply Ackermann's formula.

Answer

Solve the characteristic equation.

Answer

Use trial and error.

Answer

Employ the root locus technique.

Question 11

Which of the following is **not** a viable classification for control systems based solely on the nature of their input signal?

Accepted Answer

Open-loop vs. closed-loop

Answer

Continuous-time vs. discrete-time

Answer

Linear vs. nonlinear

Answer

Single-input vs. multiple-input

Question 12

The Laplace transform of a unit step function u(t) is:

Accepted Answer

1/s

Answer

s

Answer

1

Answer

s^2

Question 13

The Nyquist stability criterion is applicable to:

Accepted Answer

Closed-loop systems with negative feedback

Answer

Systems with time delay

Answer

Non-linear systems

Question 14

What is the formula for calculating the time constant (τ) of a first-order system, where 'a' represents the pole of the system?

Accepted Answer

τ = 1 / a

Answer

τ = K / a

Answer

τ = 1 / K

Answer

τ = a

Question 15

Which of the following represents the frequency response of a first-order system, where 'K' is the gain, 'f' is the frequency, and 'τ' is the time constant?

Accepted Answer

G(f) = K / (1 + j2πfτ)

Answer

G(f) = Kf / (1 + j2πfτ)

Answer

G(f) = K(1 + j2πfτ) / f

Answer

G(f) = K / f

Question 16

What is the primary purpose of the Nyquist stability criterion in control systems analysis?

Accepted Answer

To determine the stability of a closed-loop control system based on its frequency response.

Answer

To determine the phase margin of a control system.

Answer

To design a stable control system.

Answer

To determine the gain margin of a control system.

Question 17

What does a Bode stability plot visually represent in the context of a control system?

Accepted Answer

The gain and phase shift of the system's frequency response.

Answer

The root locus of a control system.

Answer

The time response of a control system.

Answer

The state space representation of a control system.

Question 18

What is the main objective of performing root locus analysis in control systems?

Accepted Answer

To investigate the stability of a control system for varying values of a specific system parameter.

Answer

To design a stable control system.

Answer

To evaluate the frequency response of a control system.

Answer

To analyze the system's time response.

Question 19

Which of the following describes the Routh-Hurwitz criterion in control systems analysis?

Accepted Answer

A mathematical method for determining system stability based on the coefficients of the characteristic equation.

Answer

A method for designing optimal control systems.

Answer

A graphical method for determining system stability.

Answer

A frequency domain analysis technique for control systems.

Question 20

What is the state variable representation of a control system?

Accepted Answer

A mathematical model that describes the system's dynamics using a set of state variables, input, and output.

Answer

A time-domain representation of a control system.

Answer

A graphical representation of a control system.

Answer

A frequency domain representation of a control system.

Question 21

What is a significant advantage of using state space analysis in control systems design?

Accepted Answer

It allows for direct manipulation of the system's internal dynamics, enabling the design of optimal controllers.

Answer

It is easier to implement compared to other methods.

Answer

It provides a more intuitive understanding of system behavior.

Answer

It simplifies the analysis of complex control systems.