Dynamical Systems and Control - 2019 entry

The field of dynamical systems and control aims towards a fundamental understanding of interconnected dynamical systems (technological, biological, socioeconomic, etc), and the use of feedback to improve their performance. Feedback is a ubiquitous technology, universally applicable to situations where an outcome is desired in the presence of uncertainty. For example, central heating systems use feedback to maintain a comfortable temperature inside a building irrespective of the external temperature; blood sugar levels are tightly regulated even during periods of heavy exercise by using negative feedback in a process known as glucose homeostasis.

This module will introduce a number of key concepts and techniques from dynamical systems and control, building on material covered in ECM1906 (Dynamics) and ECM2906 (Data, Signals and Systems). The material will be illuminated by practical examples while being treated with mathematical rigour. Classical methods of linear systems analysis and control design will be introduced, such as the stability tests of Routh Hurwitz and Nyquist; notions of observability (whether you can infer the state of the system from your observations) and controllability (whether you can control the state of the system); and also methods of linear feedback design. This will be complemented with material on nonlinear systems, notably Lyapunov’s methods of stability analysis. The appreciation of the theoretical material will be reinforced through practical sessions and computational examples which use Matlab Simulink for control system design.

Prerequisite modules: “Vectors and Matrices” (ECM1902), “Dynamics” (ECM1906), “Linear Algebra” (ECM2902), “Data, Signals and Systems” (ECM2906), and familiarity with MATLAB.

The intention of the module is to provide an introduction to several tools and techniques in Dynamical Systems and Control; an appreciation and understanding of the underlying mathematics; hands-on experience with practical control system design using state of the art software; and an awareness of the relevance and importance of control to a diverse range of disciplines.

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 Demonstrate a sound understanding of the mathematics underlying dynamical systems and control;

2 Develop familiarity with the representation and manipulation of interconnected dynamical systems described by differential equations, difference equations, state space equations or transfer functions; and a range of techniques for their analysis and control;

3 Develop a basic understanding of feedback control and how to apply designs to simple example models motivated by scientific and engineering questions;

Discipline Specific Skills and Knowledge:

4 Demonstrate competence in the application of various techniques in dynamical systems and control, an awareness of their relevance to different disciplines, and a thorough understanding of the underlying mathematics;

5 Synthesize a range of mathematical and computational techniques in MATLAB and Simulink for the analysis of dynamical systems and the design of control systems;

Personal and Key Transferable / Employment Skills and Knowledge:

6 Formulate and solve problems;

7 Communicate reasoning and solutions effectively in writing;

8 Demonstrate appropriate use of learning resources;

9 Demonstrate self-management and time-management skills.

- Dynamical systems preliminaries: differential equations and continuous time dynamical systems; difference equations and discrete time dynamical systems; state space; linear systems; linearization of nonlinear systems; numerical and analytical solution of differential and difference equations; impulse response; Laplace transforms; z transforms; transfer functions; equilibria; stability [7 hours];

- Linear single-input single-output systems: Routh Hurwitz stability condition; block diagram algebra; closed loop transfer functions; steady state and frequency response; Nyquist stability condition; proportional and integral control [7 hours]:

- Linear input-state-output systems: variation of the constants formula; state feedback; controllability; stabilizability; pole placement; observability; detectability; observers; state space isomorphism theory; formulation of optimal control problems [6 hours];

- Nonlinear systems: linearization and Lyapunov’s indirect method; invariant sets, equilibria and limit cycles; Poincaré Bendixson theorem; Lyapunov’s direct method; LaSalle’s invariance principle [7 hours];

- Systems analysis and controller design using MATLAB and Simulink: representations of continuous and discrete time dynamical systems using MATLAB and Simulink; block diagrams in Simulink; simulation; linearization; control system design [8 hours].

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

Basic reading:

ELE: http://vle.exeter.ac.uk

Reading list for this module: