| Module 1: Control System Analysis |
| 1 |
Course Introduction
Course Administration, Learning Objectives, Math Resources, Linear Algebra Quiz |
1.1, 1.2, 1.3 |
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| 2 |
Introduction to Control Systems
First Classification and Examples of Control Systems (Open and Closed Loop), Disturbances, Parameter Variations, Linearized Models and Block Diagrams |
1.1, 1.2, 1.3 |
Problem Set #1 Out |
| 3 |
Control System Analysis and Design
Control System Analysis and Design, The Performance of a System, Motivations for Feedback, The Concept of Gain, Transfer Functions, Block Diagrams |
1.2, 1.4, 1.7 (to top of page 14), 3.7(Chapters 2 & 3 for reference), lecture notes |
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| 4 |
Disturbances and Sensitivity
The Performance of Feedback Systems, Motivations for Feedback, Sensitivity to Parameter Variations and Model Uncertainty, Sensitivity Functions, Effects of Disturbances |
4.1, 4.2 |
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| 5 |
Steady-State Errors
Steady-State Errors, The Importance of Integrators as Fundamental Building Blocks and the Steady-State Disposition of Information in a Closed Loop System |
4.3, lecture notes |
Problem Set #1 Due
Problem Set #2 Out |
| 6 |
S-Plane, Poles and Zeroes
Transient Performance and the S-Plane, Poles and Zeroes, Graphical Determination of Residues |
1.7 (from top of pg. 14), 1.8, 1.9 |
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| 7 |
Transient Response and Stability
System Stability, Pole Location and Time Response, First and Second Order System Signatures |
4.4 |
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| 8 |
Dominant Modes
Concept of a Dominant Mode, Invading Poles, High-Order Systems, The Importance of Magnitude of Residues and Time Constants of Terms |
1.8, 4.4, lecture notes |
Problem Set #2 Due
Problem Set #3 Out |
| 9 |
Transient Response and Performance
Transient Response Performance Criteria (aka Metrics), Sources of System Zeros, Feedback Poles and Closed Loop Zeros |
5.1, 5.2 |
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| 10 |
Effects of Zeroes
The Effects of Adding a Zero to Various Pole Patterns, The Long Tail |
5.3 |
Problem Set #3 Due
Lab #1 Out |
| Module 2: State-Space Methods |
| 11 |
State Space
The Concept of System State, State Vector Definition and State Space Representation of LTI Systems |
11.1, 11.2 |
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| 12 |
State Space Modeling
State Space Model for an nth Order Differential Equation, State Space Models for Transfer Functions, Examples |
11.3 |
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| 13 |
More State Space Modeling and Transfer Function Matrices
Transfer Functions with Zeros, Laplace Transforms for Vector/Matrix Differential Equations |
11.4 |
Lab #1 Due
Problem Set #4 Out |
| 14 |
Quanser Model and State Transition Matrices
State Space Model of the Quanser, Homogeneous Solution of State Differential Equations and State Transition Matrices |
11.5 |
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| 15 |
Solutions of State Space Differential Equations
General Solution of State Space Differential Equations, Quanser Example for Constant Input |
lecture notes |
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| 16 |
Controllability
Simple Examples of Controllable and Uncontrollable Systems, Formal Definition of Controllability and Controllability Conditions for Single Input Systems |
11.7 |
Problem Set #4 Due |
| 17 |
Quiz 1
Lectures 1-15 |
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| 18 |
Controllability Continued
Controllability for Systems with Multiple Inputs |
lecture notes |
Problem Set #5 Out |
| 19 |
State Space Design
Pole Assignment with Full State Feedback, Design with Sensor Feedback |
12.1, 12.2 |
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| Module 3: Time Domain System Design |
| 20 |
Proportional Control
Effects of Proportional Control with First, Second and Third Order Systems, The Case for a Better Controller |
lecture notes |
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| 21 |
Control System Design (Time Domain)
General System Analysis in the Time Domain - Introduction to the Root Locus Method, Angle and Magnitude Conditions |
6.1, 6.2 |
Problem Set #5 Due
Problem Set #6 Out |
| 22 |
Root Locus Rules
Root Locus Rules |
6.3 |
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| 23 |
Root Locus Examples
Root Locus Examples |
6.4 |
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| 24 |
Root Locus Design
Root Loci and System Design, Pole-Zero Cancellation, Motor Position Servo with Velocity Feedback, Phase-Lead Compensator Design Using Root Loci |
6.5, 6.6 |
Problem Set #6 Due
Problem Set #7 Out |
| 25 |
Compensator Design
Phase Lag Compensator Design Using Root Loci, Introduction to PID Control Using Root Loci |
6.7, 6.8 |
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| Module 4: Frequency Domain System Design |
| 26 |
Frequency Response Analysis
Steady State System Responses to Sinusoidal Inputs, Second Order System Example |
7.1, 7.2 |
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| 27 |
Polar Plots
First and Second Order Polar Plots, Other Examples |
lecture notes |
Problem Set #7 Due
Lab #2 Out |
| 28 |
Principle of the Argument and the Nyquist Stability Criterion
Development of the Nyquist Stability Criterion |
7.3 |
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| 29 |
Nyquist Examples
Examples |
7.4 |
Lab #2 Due |
| 30 |
More Nyquist Examples |
lecture notes |
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| 31 |
Quiz 2
Lectures 16-27 |
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Problem Set #8 Out |
| 32 |
Gain and Phase Margins
The Gain and Phase Margin Criteria and Examples |
7.6 |
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| 33 |
The Gain-Phase Plane and Nichols Charts
Use of Nichols Charts and Examples |
8.5 |
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| 34 |
Open and Closed Loop Behavior and the Second Order System Paradigm
Frequency Response Criteria Based on Second Order System Paradigm |
8.3 |
Problem Set #8 Due
Problem Set #9 Out |
| 35 |
Bode Diagrams |
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| 36 |
First and Second Order System Bode Diagrams |
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| 37 |
Compensation and Bode Design |
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Problem Set #9 Due |
| 38 |
More Bode Design |
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| 39 |
Train Lecture |
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