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Control Theory Fundamentals

This is a one day technical seminar covering the design of analogue and digital control systems.  The course will be valuable to engineers and scientists involved in the specification, design, or use of control systems of any type. 

1.  Fundamental Concepts
Linear systems, transfer functions, transient & frequency response, classification of systems
2.  Feedback Systems
Negative feedback, the Nyquist plot, phase compensation, sensitivity & tracking, robustness
3.  Transient Response
Transient specifications, steady state error, PID control, root locus design
4.  Discrete Time Systems*
Sampled systems, the z-transform, aliasing, delay & reconstruction, controller design

Control Theory Fundamentals seminar in Shenzhen, China on 24th July 2012


The course opens with a review of fundamental concepts, including linear differential equations and the Laplace transform. The behaviour of classical first and second order systems is examined in both the time and the frequency domains. The second section introduces closed loop control and the effects of negative feedback in the frequency domain. The Nyquist plot is introduced as a valuable tool to assess control loop stability and performance, and is applied to the design of phase compensators.  The section closes with a look at the effects of modelling uncertainty and how control loops can be assessed for robustness. The central theme of section three is control performance in the time domain. The design and tuning of PID controllers is explained using the step response, and various methods of assessing quality of response are presented. The root locus plot then is introduced as a method of designing complex systems to meet transient response specifications. Section four focuses on discrete time systems. The z-transform is introduced, and the relationship between the s-plane and z-plane explained in detail.  The design of digital closed loop controllers is then described using emulation and direct design methods. Also covered are some important practical considerations when implementing discrete time controllers, including aliasing, sample rate selection, the effects of computational delay, and zero order hold. The material is supported by many examples and tutorials, and includes a short question & answer session at the end of each section. Matlab is used throughout the seminar to introduce new concepts and to illustrate each major topic. 


Although there are no formal pre-requisites for the seminar an understanding of basic engineering mathematics is recommended.  At a minimum, attendees should be familiar with the theory of complex numbers, functions and limits, and linear differential equations.  All these topics are covered in Paul Dawkins' on-line math link at the foot of the home page.  

A set of optional self-assessment questions can be found below.

Hands-on Labs

A version of the seminar is available with hands-on student exercises (labs) conducted using Matlab.  In this case the presented material is reduced somewhat in length to make room for the exercises.  For a list of lab pre-requisites, see section 6 of the "Hosted Seminars" document on the downloads page.


On 28th January 2014 the Control Theory Fundamentals** seminar was recorded live at Texas Instruments, Dallas.  The video recordings are available on YouTube: 

The seminar manual and tutorials from the recorded sessions can be found in the zip file below.

*   Part 4 (discrete time systems) may be replaced by a design "case study" at some events.
** Note that the seminar materials have been updated since the recordings were made.

Richard Poley,
27 Oct 2017, 05:41
Richard Poley,
27 Sep 2017, 10:37
Richard Poley,
6 Nov 2015, 10:36