Ch 1: Introduction to Control Systems

Question 1

Three Major

Theories

Answer 1

Classical Control Theory

Modern Control Theory

Robust Control Theory

Question 2

Classic Control Theory:

Important Features and Methods

Answer 2

• Use of Differential Equations to describe systems
• Analysis of stability of closed loop systems based on open-loop, steady state sinusoidal input
• Root-Locus Method
• Frequency Response
• Developed stable systems
• Did not deal with multiple input/output systems
• Primary focus on Linear Time Invariant, single input/output systems

Note: This list is NOT comprehensive

Question 3

Modern Control Theory:

Important Features/Methods

Introduced

Answer 3

• Analysis in Time Domain
• Synthesis with State Variables

Question 4

Basic Definitions:

Controlled Variable

Answer 4

The quantity or condition that is measured and controlled

Question 5

Basic Definitions:

Control Signal

Answer 5

Also called the ‘Manipulated Value’

The quantity or condition that is varied by the controller to affect the value of the controlled variable.

Question 6

Basic Definitions:

Control

Answer 6

The action of measuring the Controlled Variable, then applying the Control Signal to correct or limit deviation of the Controlled Variable from a desired value

Question 7

Basic Definitions:

Plants

Answer 7

In the context of Control Systems,

a Plant is any physical object that is to be controlled.

A piece of equipment functioning to perform some operation.

Could be anything from a simple tool to a whole factory or power grid, or financial system.

Question 8

Basic Definitions:

Process

Answer 8

Any operation that is to be controlled

Question 9

Basic Definitions:

Systems

Answer 9

A combination of components that act together to achieve a certain objective.

Question 10

Basic Definitions:

Disturbances

Answer 10

A signal that tends to adversely affect the value of the output of a system.

Two Types:

• Internal
  
  • Generated from within the system
• External
  
  • Generated from outside the system, treated as a kind of input
  • Examples: noise, kicking a robot

Question 11

Basic Definitions:

Feedback Control

Answer 11

An operation that uses the output of a system to reduce the difference between output and some Reference Input.

Makes corrections.

This reduces the impact of Disturbances in the system.

Question 12

Robust Control Theory:

Basic Idea

Answer 12

• System models don’t perfectly reflect the actual, real world system
• Robust Control Theory attempts to account for the difference by including an Uncertainty or Error Value estimate in the model

Question 13

Robust Control Theory:

Estimating Uncertainty

Very basic Mathematical Approach

Answer 13

Assume G(s) is a perfect model of a system, and ~G(s) is a model with some uncertainty ∆(s)

The error can be related as either a

• Multiplicative Factor
  
  • ~G(s) = G(s) [1 + ∆(s)]
• Additive Factor
  
  • ~G(s) = G(s) + ∆(s)

Exact uncertainty is unknowable, so we use an upper bound estimate, W(s)

Question 14

Feedback Control System:

Summary

Answer 14

A system that maintains a prescribed relationship between the output and the reference input,

by comparing them and using the difference as a means of control

Question 15

Closed-Loop Control Systems:

Summary

Answer 15

Term is used interchangeably with Feedback Control System. The ‘Loop’ IS the feedback.

The Actuating Error Signal(the difference) is fed to the controller to reduce the error and bring the output of the system to a desired value.

“Closed Loop” always implies the use of feedback

Question 16

Open-Loop Control Systems:

Summary

Answer 16

Systems in which the output has no effect on the control action.

Output is not fed back for comparison or even measured.

Accuracy of the system must depend on calibration and the system will not compensate for disturbances.

Note: Any system that operates with only time as the input is open-loop

Question 17

Compensation:

Definition

Answer 17

Modification of the system dynamics to satisfy given specifications.

This is done in three ways:

• Adjusting Gain - primary method
• Installing a Compensator device
• Performing redesign/restructuring of the system

Question 18

Control System Design:

Three Approaches to Design and Analysis used in this book

Answer 18

Root-Locus Approach

Frequency Response Approach

State-Space Approach

Question 19

Control System Design:

Basic Considerations

Answer 19

Performance Specifications

System Compensation

Design Procedures

Question 20

Control System Design:

Major Performance Specifications/Requirements and some examples

Answer 20

Define what the system must do and under which performance constraints.

Requirements may be given as numeric values, or as more general qualitative statements

• Transient Response Requirements
  
  • Maximum overshoot
  • Settling time in Step Response
• Steady State Requirements
  
  • Steady State Error following Ramp Input
• Frequency Response Requirements
  
  • Operating frequency range
  • Dealing with high/low frequency

Question 21

Control System Design:

Basic steps of designing a system

Answer 21

• Set up a mathematical model, starting as simply as possible
• Adjust parameters of a compensator
• Construct prototype and test the open-loop system
• If open-loop test goes well, close the loop and test the prototype
• Repeat steps, adjusting parameters and design based on trials
• Attempt to catch biggest issues early