Robust Control: Master the Art of Designing Resilient Control Systems

Question 1

For systems with significant uncertainties, which approach is preferred for designing robust controllers?

Accepted Answer

H-infinity control based on optimization techniques

Answer

Loop-shaping based on classical control techniques

Answer

Gain-scheduling based on changing controller parameters

Answer

Model-predictive control based on real-time optimization

Question 2

What is the primary objective of H-infinity control?

Accepted Answer

Minimizing the closed-loop system's vulnerability to plant uncertainties

Answer

Maximizing the system's bandwidth

Answer

Stabilizing an unstable plant

Answer

Rejecting disturbances

Question 3

What is the role of weighting functions in H-infinity control?

Accepted Answer

Prioritizing specific performance objectives

Answer

Reducing the order of the controller

Answer

Eliminating the requirement for plant identification

Answer

Guaranteed stability of the closed-loop system

Question 4

Which of the following methods is commonly used to construct a weighting function for H-infinity control?

Accepted Answer

Frequency domain analysis

Answer

State-space modeling

Answer

Root locus analysis

Answer

Pole placement

Question 5

What is the primary distinction between parametric and unstructured uncertainty?

Accepted Answer

Parametric uncertainty can be represented by a set of known parameters, while unstructured uncertainty cannot

Answer

Unstructured uncertainty is more prevalent in practical systems than parametric uncertainty

Answer

Parametric uncertainty is inherently bounded, whereas unstructured uncertainty can be unbounded

Answer

Unstructured uncertainty can be alleviated using adaptive control techniques

Question 6

What is the main advantage of using H-infinity control?

Accepted Answer

It provides guaranteed stability and performance for uncertain systems.

Answer

It is easier to design than classical control techniques.

Answer

It can handle non-linear systems.

Answer

It is less computationally intensive than other robust control methods.

Question 7

What is the main purpose of using a reference model in gain-scheduling?

Accepted Answer

To provide a desired closed-loop response.

Answer

To estimate the plant model's parameters.

Answer

To reduce the sensitivity of the system to disturbances.

Answer

To improve the robustness of the system to uncertainties.

Question 8

What is the advantage of using mixed-sensitivity loopshaping in robust control design?

Accepted Answer

It allows for simultaneous optimization of multiple performance objectives.

Answer

It simplifies the design process by reducing the number of variables.

Answer

It can handle both parametric and unmodelled uncertainties.

Answer

It guarantees that the closed-loop system will be stable.

Question 9

Which of the following is a defining characteristic of robust control systems?

Accepted Answer

Resistant to variations in plant parameters

Answer

Unaffected by any uncertainties

Answer

Guaranteed stability under all conditions

Answer

Optimal transient response

Question 10

What is the main purpose of using gain-scheduling in robust control?

Accepted Answer

To compensate for time-varying plant parameters

Answer

To improve disturbance rejection performance

Answer

To minimize the controller order

Answer

To enhance stability under all operating conditions

Question 11

Which of the following is a fundamental assumption for stability analysis of uncertain systems using Lyapunov's method?

Accepted Answer

The uncertainty is bounded

Answer

The uncertainty set is symmetrical

Answer

The system dynamics are linear

Answer

The system is time-invariant

Question 12

Which of the following techniques is not commonly employed for designing robust controllers?

Accepted Answer

Proportional-integral-derivative (PID) control

Answer

Pole placement

Answer

Linear quadratic regulator (LQR)

Answer

H-infinity control

Question 13

In H-infinity control design, how do weighting functions influence the controller's performance?

Accepted Answer

They determine the trade-off between disturbance rejection and control effort.

Answer

They affect the stability of the closed-loop system.

Answer

They have no significant impact on the controller's performance.

Answer

They only affect the transient response of the system.

Question 14

Which of the following is a potential drawback of H-infinity control?

Accepted Answer

High computational complexity

Answer

Sensitivity to time delays

Answer

Inability to handle nonlinear systems

Answer

Requirement for precise plant model knowledge

Question 15

What is the fundamental principle behind H-infinity control?

Accepted Answer

Minimizing the infinity norm of the closed-loop transfer function

Answer

Maximizing the system gain

Answer

Eliminating all uncertainties from the plant model

Answer

Designing a controller with zero steady-state error

Question 16

What is the primary goal when designing a robust controller using gain-scheduling?

Accepted Answer

To ensure stability and performance over a range of operating conditions

Answer

To minimize the need for plant model identification

Answer

To maximize the system bandwidth

Answer

To reduce the controller order

Question 17

Which of the following steps is NOT involved in gain-scheduled controller design?

Accepted Answer

Identification of the exact system model

Answer

Plant modeling

Answer

Controller synthesis

Answer

Gain scheduling logic design

Question 18

In H-infinity control, the performance measure is defined as the:

Accepted Answer

Peak singular value of the closed-loop transfer function

Answer

Integral of the squared error signal

Answer

Time constant of the system

Answer

Gain margin of the system

Question 19

In robust control design, there is an inherent compromise between:

Accepted Answer

Performance and robustness

Answer

Complexity and accuracy

Answer

Cost and reliability

Answer

Accuracy and stability

Question 20

In H-infinity control, the weighting function W1 is used to:

Accepted Answer

Shape the frequency response of the performance objective

Answer

Represent the process noise

Answer

Determine the controller structure

Answer

Set the controller sampling rate

Question 21

A gain-scheduled controller switches between multiple controllers based on:

Accepted Answer

Changes in the operating conditions

Answer

Measurements of plant parameters

Answer

Time-varying disturbances

Answer

Estimation of model uncertainties

Question 22

In robust control, the structured singular value (μ) represents:

Accepted Answer

The stability and performance of the closed-loop system

Answer

The maximum possible uncertainty in the system

Answer

The critical frequencies of the system

Answer

The optimal controller parameters