Chapter three
Introduction to feedback
Section six: Introduction to Feedback with MATLAB
This chapter is on the theme of linear feedback control, for example with G(s) representing a system, M(s) a compensator and d an input disturbance signal:
MATLAB tools are are valuable for modelling, simulating and analysing feedback loops. This section gives a brief introduction to the most important tools.
1. Solving ODEs and other skills
A number of resources are already provided on the main MATLAB resources page and moreover a concise feedback tool summary (PDF, 522 KB).
It is useful to be proficient with MATLAB syntax for handling polynomials, so some extra notes are provided here (PDF, 900 KB).
A MATLAB live script for doing modelling, analysis and PI control of a 1st order system.
2. Defining transfer function objects
MATLAB has a number of built in functions for handling the analysis of systems represented by transfer function objects, so creating these objects is a core skill.
Continuous time transfer functions video and notes (PDF, 918 KB).
Discrete time transfer functions notes (PDF, 708 KB).
Transfer functions with a delay notes (PDF, 655 KB).
3. Control analysis tools
A number of built in functions allow simple analysis of feedback-loops and transfer functions.
Closed-loop transfer functions video and notes (PDF, 575 KB).
Step responses (open- or closed-loop) video and notes (PDF, 558 KB).
Overlaying step-response plots (PDF, 687 KB) and code1 (M-file), code2 (M-file).
Closed-loop poles and iterative design notes (PDF, 739 KB).
4. Videos with useful illustrations
Demonstrates real time examples of MATLAB use to analyse and design feedback loops.
Responses with arbitrary inputs
Trial and error design: