modules

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; and 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 ), and familiarity with MATLAB.

Note: The module will also touch on concepts from 'Linear Algebra' (ECM2902 ), 'Differential Equations' (ECM2903 ), and 'Data, Signals and Systems' (ECM2906 ), although these are not essential prerequisites.