Linear Systems Theory

EEEN40221 Linear Systems Theory 15 Semester 1 Undergraduate Level 4 Lanlan Su Unit coordinator Joaquin Carrasco Gomez Unit coordinator 1 FHEQ level (Framework for Higher Education Qualifications) ' Masters/Integrated Masters P4 ' European Credit Transfer & Accumulation System Rating : 7.5 Brief description of the unit:Part 1 - Linear AlgebraLinear subspaces Eigenvalues and Eigenvectors Matrix inversion formulas Invariate subspaces Vector norms and matrix norms Singular value decomposition Generalised inverses Semidefinite matricesPart 2 - Linear Dynamical SystemsDescription of linear dynamical systems Solutions of linear dynamical systems and their stability Controllability and observability Observers and observer-based controllers Operation on systems State-space realisations for transfer functions Hidden modes and pole-zero cancellationPart 3 - Feedback SystemFeedback structure Well-posedness of feedback system Closed-loop stability Brief description of the unit:Part 1 - Linear AlgebraLinear subspaces Eigenvalues and Eigenvectors Matrix inversion formulas Invariate subspaces Vector norms and matrix norms Singular value decomposition Generalised inverses Semidefinite matricesPart 2 - Linear Dynamical SystemsDescription of linear dynamical systems Solutions of linear dynamical systems and their stability Controllability and observability Observers and observer-based controllers Operation on systems State-space realisations for transfer functions Hidden modes and pole-zero cancellationPart 3 - Feedback SystemFeedback structure Well-posedness of feedback system Closed-loop stability The unit aims to introduce the essential linear algebra concepts used in the development of the mathematical descriptions of linear system theory; to establish the mathematical foundations of linear dynamical systems used in control system theory; to give students a sound understanding of the state-space representation of linear dynamical systems and to formulate the stability of closed-loop systems. ILO1: Analyse the preoerties of a matrix such as eigenvalues, norms, and singular values in the context of dynamical systems. [Developed and Assessed].ILO2: Compute the invariate subspaces of a matrix and other significant properties.ILO3: Describe dynamical systems in mathematical terms using state-space representations.ILO4: Analyse dynamical system properties of state-space models.ILO5: Develop feedback controllers for state-space models using state-feedback and observer techniques.ILO6: Analyse feedback dynamical systems and their properties. Assessment Methods Lectures, tutorials, practical/ laboratory work and private study. 1 Written exam 80% 3 Report 20% Examination - four questions, answer all questions. Feedback is provided after the examination board.Laboratories - Quiz and Report. Feedback is provided two weeks after report submission. EEEN30231 Control Systems II Pre-Requisite Compulsory To select unit EEEN40221 you must have taken EEEN30231 Control Systems II in your 3rd year. MEng (Hons) Electrical and Ele MEng (Hons) Electrical and Ele Fourth Year Optional MEng (Hons) Mechatronic Engine MEng (Hons) Mechatronic Engine Fourth Year Optional MEng (Hons) Electronic Enginee MEng (Hons) Electronic Engine Fourth Year Optional N “Robust and Optimal Control” by Zhou, Doyle, and Glover.“Linear Systems Theory” by Joao P. Hespanha“Feedback control of dynamic systems” by Franklin and Powell, Prentice-Hall.“Modern control systems” by Dorf and Bishop, Prentice-Hall. Lectures 30 Practical classes & workshops 3 Tutorials 6 0 111