The materials below were used in a short class consisting of 2 lectures, each 3 hours in duration. The lectures are intended for computer scientists with little or no background in mathematical modeling. The only pre-requisite is knowledge of the geometric series.
The lectures consist of six modules, each intended to be approximately 55 minutes in duration. There is about 40 minutes of lecture and 15 minutes of group problem solving. Much of the problem solving makes use of spreadsheets. Spreadsheets turn out to be a very convenient environment for evaluation of difference equations, the fundamental tool used in our approach to control theory. A simple naming convention is used to associate the spreadsheet with the slides.
Below is the syllabus with cross references to the corresponding book chapter.
- M1: Introduction (Chapter 1) M1 - Introduction v3.ppt ShortClass-M1 v2.xls
- Content: Control system architecture, goals, and metrics. Constructing ARX models (including initial conditions)
- Lab: Simulation and analysis of Notes server with a sensor
- M2: Signals and Z-Transforms (Chapter 3) M2 - Signals v2.ppt
- Content: z-Transform representation of time signals; inverse z-Transforms; manipulating signals; infinite signals; final value theorem;
- Lab: Signal analysis
- M3: Systems and transfer functions (Chapter 3) M3 -Transfer Functions v2.ppt ShortClass-M3.xls
- Content: transfer function definition; translating between transfer functions and ARX models; steady-state gain; poles; stability criteria; estimating settling times;
- Lab: Analysis of the Notes server
- M4: Analyzing composed systems (Chapter 4) M4 - Composing Systems v2.ppt
- Content: Combining transfer functions in series; simplifying block diagrams; feedback transfer functions;
- Lab: Analysis of a Notes feedback control system with and without a sensor
- M5: Control analysis (Chapters 8, 9) M5 - Control Analysis v2.ppt ShortClass-M5 v2.xls
- Content: Basic controllers; impulse response; step response
- Lab: Analysis of controllers for Notes server system
- M6: Control design (Chapters 8, 9) M6 - Control Design v2.ppt ShortClass-M6.xls
- Content: Pole placement design methodology
- Extended group lab: Analysis of a load balancing system