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Control Systems > L1: Background Concepts > Flashcards

L1: Background Concepts Flashcards

1
Q

Control:

Basic Definition

A

The word control is usually taken to mean

  • Regulate
  • Direct
  • Command

Control is:

  • A key enabling technology in all branches of engineering
  • Used whenever some quantity, such as temperature, altitude or speed, must be made to behave in some desirable way over time
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2
Q

System:

Basic Definition

A

A System is defined as a collection of objects interacting with each other.

Examples

  • Mechanical Systems:
    • Robots, Airplanes, Cars, etc
  • Electrical Systems
    • Amplifiers, Filters, transformers, etc
  • Economic Systems
  • Human Body
  • Environment
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3
Q

How is a system

represented mathematically?

A

Using mathematical expressions such as

Ordinary Differential Equations

that relate some input function, u(t)

to some output function, y(t)

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4
Q

General

System Characteristics

A
  • Order: n
  • Continuous/Discrete
  • Linear/Nonlinear
  • Time Invariant/Time Variant

* There are other characteristics that are not covered in this course

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5
Q

Control System

Definition

A

A Control System is

an arrangement of physical components

connected or related in such a manner as to

command, direct, or regulate itself or another system.

A controller provides a desired system response(output).

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6
Q

Representing a Control System:

Block Diagram

A

The Block Diagram relates some Input to some Output

  • Input
    • The excitation or command applied to a control system
    • Typically from an external energy source
    • Usually in order to produce a specified response from the control system
  • Output
    • The actual response obtained from a control system.
    • May or may not be equal to the specified response implied by the input (some error)
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7
Q

Background Concepts:

Important Terms/Concepts

(15, not including subconcepts)

A
  • Control
  • System
  • Control System
  • Block Diagram
  • Open-Loop Control
  • Closed-Loop Control
    • Feedback
  • Modern Control Theory
  • Classic Control Theory
  • Time Domain
  • Frequency Domain
    • Complex Frequency
    • Poles
    • Zeros
  • Laplace Transform
    • Inverse Laplace Transform
    • Transform Table
    • Properties
  • Important Test Waveforms
  • Theorems
    • Initial Value Theorem
    • Final Value Theorem
  • Finding Inverse Transforms
    • Partial Fraction Expansion
    • Three Forms
      • Simple Poles
      • Repeated Poles
      • Complex Poles
  • Solving ODE using Laplace
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8
Q

Open-Loop Control

A

An Open-Loop Control System

utilizes an actuating device to control the process directly, without using feedback

  • Sometimes it is useful to evaluate a complex system in the open-loop configuration by temporarily removing feedback

Examples:

  • Simple Timer
  • Toaster
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9
Q

Open-Loop Control:

Characteristics/Benefits/Drawbacks

A
  • Must be closely monitored
  • No Feedback
  • Difficult to control with accuracy

​

  • Easy to design
  • More economical
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10
Q

Closed Loop Control:

Description

A

A Closed-Loop Control System

uses a measurement of the output and feedback of this signal to compare it with the desired output.

  • Must have feedback
    • Sensor on output
  • Continually adjusts the process
  • Almost always negative feedback
  • More difficult to design and costlier
  • But produces more accurate output

Example: Room Temperature Control

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11
Q

Closed-Loop Control:

Roles of Feedback

A
  • Reduce or eliminate error
    • Reduce Sensitivity
    • Enhance Robustness
  • Disturbance Rejection or Elimination
  • Improve Dynamic Performance
  • Adjust transient response
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12
Q

Applications of Control:

Various Industries and types of

systems that Control Systems Theory

can be used for

A
  • Industrial Plants
  • Transportation
  • Robotics
  • Biological Systems
  • Economic Systems
  • Biomedical Systems
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13
Q

Applications of Control:

Use in Industrial Plants

A
  • Manufacturing and Assembly Lines
  • Machining
  • Power Plants

Goals

  • Maximize efficiency
  • Minimize environmental impact
  • Meet all quality specifications

Most modern industrial plants could not operate without control systems

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14
Q

Applications of Control:

Transportation Applications

A
  • Automobiles
    • Cruise control
    • Lane keeping
    • “Ecoboost”
    • Fuel System
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15
Q

Applications of Control:

Robotics

A
  • Dextrous manipulation
  • Haptics
  • RC cars and gliders
  • Research submarines
  • Smart wheelchairs
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16
Q

Applications of Control:

General Benefits of Control Systems

A
  • Provides performance that would otherwise be unattainable
    • Feedback amplifier
    • Aircraft Autopilot
    • Disk drives, CD players
    • Cellular telephones
    • ABS in cars
    • Prosthetics
  • Operate in environments that humans can’t tolerate
    • Mars
    • Satellites (including GPS)
    • Underwater exploration and research
17
Q

Applications of Control:

Biological Systems

A
  • Cell regulation mechanisms
  • Population Dynamics
  • Epidemiology
18
Q

Applications of Control:

Economic Systems

A
  • Inflationary Mechanics
  • Fiscal Policies
19
Q

Applications of Control:

Biomedical Systems

A
  • Bone development and morphology
  • Sleep cycles
  • Seasonal Affective Disorder
  • Faulty feedback mechanisms in Parkinson’s disease
20
Q

Modern Control

vs

Classcial Control

A

Modern Control

Classical Control

  • Time Domain
  • Integrals/Derivatives
  • Easier for Computers
  • MIMO Systems
  • Internal States
  • State Variable feedback
  • Frequency Domain
  • Simple Algebra
  • Easier for Humans
  • SISO systems
  • Root Locus
  • Bode Plots
21
Q

Implementation of Control

A
  • Embedded microprocessors observe signals from sensors and provide command signals to electromechanical actuators
  • Designers use Computer-Aided design software
    • MATLAB
  • Design usually tested on simulations before implementation
  • Control engineering requires a thorough understanding of the application area
22
Q

Goals of this

Control Systems

Course

A
  • Identify how control is used in engineering systems
  • Identify benefits of feedback
  • Analyze and predict common behaviors of dynamical systems with feedback
  • Apply relevant mathematical theory
  • Solve simple control design problems
  • Use relevant computational tools
  • Recognize difficult control problems
23
Q

Important Test Waveforms/Functions

A
  • Unit Impulse Function 𝛿(t)
  • Unit Step Function u(t)
  • Ramp Function tu(t)
  • Parabola
  • Sinusoid
24
Q

What is the

Laplace Transform

used for?

A

Converts a mathematical expression

from the Time Domain to the Complex Frequency Domain.

The Inverse Laplace Transform

Converts an expression from the Frequency Domain to the Time Domain

25
Q

Laplace Transform:

General Equation

A
26
Q

Inverse Laplace Transform:

General Equation

A
27
Q

Complex Frequency

s

Important Concepts

A

The Complex Frequency is represented by:

s = 𝝈 + jω

  • 𝝈 represents the real component
  • jω represents the imaginary component
  • This is the Rectangular Form, representing the frequency as a vector in the complex plane
28
Q

Poles and Zeros:

Basic Idea

A

A function in the complex domain can be represented as a ratio of two polynomials:

F(s) = N(s) / D(s)

  • Zeros:
    • Values of s that make N(s) = 0
    • The roots of the Numerator, N(s)
  • Poles:
    • Values of s that make D(s) = 0
    • Roots of the Denominator, D(s)
29
Q

Initial and Final Value Theorems:

Basic Idea

Initial Value Theorem (IVT)

Final Value Theorem(FVT)

A

These theorems show that it is possible to get

the Initial Value, f(0)

and the Final Value, f(∞)

of a function directly from the Laplace Transfrom of the function

30
Q

Converting Back to Time Domain

Steps to finding Inverse Laplace Transform

of F(s)

A
  • Assume F(s) = N(s) / D(s)
    • Both N(s) and D(s) are polynomials
  • Decompose F(s) into simple terms
    • Use Partial Fraction Expansion
    • Find the inverse of each individual term using basic transform pairs
  • F(s) can have three possible forms:
    • Simple Poles
    • Repeated Poles
    • Complex Poles
31
Q

Inverse Laplace Transform:

Simple Poles Case

A
  • Finding Residues:
    • Mutliply function by denominator of the associated term
    • Substitute the value of s that makes it zero
    • Perform for each residue term
32
Q

Inverse Laplace Transform:

Repeated Poles Case

A

On decomposition, one or more of the terms will have a denominator raised to some power:

(s + p)n and other terms like (s + p)n-m

  • The residue kn for the (s+p)n is found in the normal way
  • Where residues kn-m for terms (s+p) are found using a derivative and factorial (see image for formula)
33
Q

Inverse Laplace Transform:

Complex Poles Case

A

F(s) has a part that includes complex poles

roots to a denominator of form: (s2 + as + b)

  • Solve this by Completing the Square
34
Q

Laplace Transform Pairs:

Unit Impulse Function 𝛿(t)

A

F(s) = 1

Control Systems (2 decks)

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