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Control Theory Fundamentals Seminar

This is our most popular course, providing a solid introduction to the theory and design of analogue and digital control systems.  The course has been over delivered in sixteen countries and is 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

Course Description

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, an understanding of basic engineering mathematics is strongly recommended.  At a minimum, attendees should be familiar with the theory of complex numbers, functions and limits, and linear differential equations.  A set of optional self-assessment questions is available on request.


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


A short impression of the seminar content - thirty-four seconds of a six hour Control Theory Fundamentals seminar recorded in Dallas in January 2014.  This section forms part of the introduction to root locus design.