Chapter four

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:

Core skills include:

• How do I analyse the expected behaviour of the closed-loop?

• How do I use analysis tools to facilitate control design?

• Are there classical controller structures which are simple and easy to use?

The focus is on root-loci and frequency response tools alongside lead and lag compensators. It is implicit that students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials, logarithms, behaviours and Laplace.

Sections in chapter four

Section one: Root-loci

What are root-loci? How can I use root-loci for analysis and design? What software tools might be useful?

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Section two: Frequency response and Bode diagrams

What is frequency response and how do I compute it? What is a Bode diagram and sketching rules for insight? How are Bode diagrams affected by standard compensator structures?

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Section three: Nyquist diagrams

What is a Nyquist diagram and how can I use this to assess closed-loop stability? What insights do I gain which lend themselves to control design?

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Section four: Gain and phase margins

What are gain and phase margins and why are they important? How do I use these to facilitate systematic analysis and design of expected closed-loop behaviour? How are margins exploited in lead/lag compensator design?

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Section five: Classical feedback analysis tools with MATLAB

Much of control analysis and design requires tedious numerical manipulations which are best handled using computer tools. This section gives an overview of some basic MATLAB tools.

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