| Module 1: Control System Analysis |
| 1 | Course Introduction
Course Administration, Learning Objectives, Math Resources, Linear Algebra Quiz | 1.1, 1.2, 1.3 | |
| 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 | |
| 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 | |
| 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 | |
| 7 | Transient Response and Stability
System Stability, Pole Location and Time Response, First and Second Order System Signatures | 4.4 | |
| 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 | |
| 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 | |
| 12 | State Space Modeling
State Space Model for an nth Order Differential Equation, State Space Models for Transfer Functions, Examples | 11.3 | |
| 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 | |
| 15 | Solutions of State Space Differential Equations
General Solution of State Space Differential Equations, Quanser Example for Constant Input | lecture notes | |
| 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 | | |
| 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 | |
| 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 | |
| 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 | |
| 23 | Root Locus Examples
Root Locus Examples | 6.4 | |
| 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 | |
| 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 | |
| 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 | |
| 29 | Nyquist Examples
Examples | 7.4 | Lab #2 Due |
| 30 | More Nyquist Examples | lecture notes | |
| 31 | Quiz 2
Lectures 16-27 | | Problem Set #8 Out |
| 32 | Gain and Phase Margins
The Gain and Phase Margin Criteria and Examples | 7.6 | |
| 33 | The Gain-Phase Plane and Nichols Charts
Use of Nichols Charts and Examples | 8.5 | |
| 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 | | |
| 36 | First and Second Order System Bode Diagrams | | |
| 37 | Compensation and Bode Design | | Problem Set #9 Due |
| 38 | More Bode Design | | |
| 39 | Train Lecture | | |