Below are a set of links to notes and equation sheets on elementary control systems. The topics covered are those typically covered in a first course in control systems in engineering curricula. Selected examples are included in the notes. Some schools also cover state-space methods, but these methods are not presented here at this time.

Reference: Dorf & Bishop, Modern Control Systems, 12th edition, Prentice-Hall, Inc, 2011

Trademarks: MATLAB is a registered trademark of The MathWorks, Inc. The MathWorks does not warrant the accuracy of the examples given in these notes.

#### Knowledge Map

Map of Areas Related to Control Systems

#### Introduction to Control Systems

#### Introduction to Mathematical Modeling of Dynamic Systems

- Mathematical Models
- Linearity Principles
- Linearization of Algebraic Models
- Linearization of Equations of Motion of Pendulum and Accelerating Pendulum
- Model for a Hydraulic Positioning System

#### Short Review of Laplace Transforms

- Using Laplace Transforms to Solve Linear, Ordinary Differential Equations
- Laplace Transform Table
- Laplace Transform Examples
- Introduction to Partial Fraction Expansions
- Examples using Partial Fraction Expansions

#### Introduction to Transfer Functions and Block Diagrams

- Transfer Functions
- Cramer’s Rule for Solving a System of Linear Equations
- Block Diagrams and Transfer Functions
- Block Diagrams & Transfer Functions Example
- Block Diagram Reduction Transformations
- Block Diagram Reduction Examples
- Armature-Controlled DC Motor Transfer Function

#### Proportional Control of a the Position of a Spring-Mass-Damper

- Position Control of Spring-Mass-Damper using Proportional Control
- Plotting a Step Response Using MATLAB

#### General Characteristics of Systems with Feedback

- Characteristics of Open-Loop and Closed-Loop Systems
- Design Problem – Roll Control of a Small Aircraft

#### Performance Characteristics of Systems with Feedback

- First Order System Step Response
- Using Feedback to Modify Transient Response of a First Order System
- Characteristics of Under-damped, Second Order System Step Response
- Second Order System Step Response
- Dominant (or Insignificant) Poles
- System Type and Steady-State Error
- Performance Indices
- Performance Examples
- Performance Design Problem – Aircraft Roll Control

#### Stability Analysis using the Routh-Hurwitz Method

#### Closed-loop System Analysis using Root Locus Diagrams

- What is a Root Locus Diagram?
- Introduction to Root Locus Diagrams
- Root Locus Diagrams
- Summary Procedure for Root Locus Diagrams
- Root Locus Diagram Examples
- Using MATLAB for a Root Locus Analysis

#### Closed-loop System Analysis using Bode Diagrams

- Introduction to Bode Diagrams
- Summary of Bode Diagram Terms
- Bode Diagram of a 2nd Order System
- Bode Magnitude Diagram Examples
- Blank Bode Magnitude Diagram (for practice sketches)
- Frequency Domain Analysis

#### Control of Spring-Mass-Damper Position using PID Control

PID Control of a Spring-Mass-Damper Position

#### Implementation of PID Controllers using Operational Amplifiers

Implementation of PID Controllers in Electronic Circuits