ASE-7556 LQG Control with Matlab, 6 cr
Additional information
All the sessions include a lecture part and use of Matlab. Two subexams or a single total exam with Matlab are the only exams. In the exams one has access to Matlab documentation, Exam Tables and all the lecture files used by the teacher during the sessions.
Suitable for postgraduate studies.
Person responsible
Terho Jussila
Lessons
| Implementation | Period | Person responsible | Requirements |
| ASE-7556 2018-02 | 1 - 2 |
Terho Jussila |
Two partial exams called Tests A-B (each of 2h) or a single Total Exam (4h) with Matlab. 4 PC works, each of 120 minutes. A practical LAB session is possible. |
Learning Outcomes
To learn use of Matlab to design, analyze and implement CT and DT (Continuous-Time and Discrete-Time) deterministic H2/LQ (Linear Quadratic) and LQG (LQ Gaussian) controllers for LTI (Linear Time-Invariant) CT and DT state space systems and PID controllers for CT and DT LTI plants with delays. This includes e.g. the ability to compute suitable performance indices both in time domain and frequency domain, model integration and simulation skills, stability analysis techniques using Simulink, Control System Toolbox and Symbolic Toolbox, developing reliable algorithms for on-line use and programming of simple Matlab tools.
Content
| Content | Core content | Complementary knowledge | Specialist knowledge |
| 1. | Effective Matlab modelling: equilibriums, linearization, least squares methods, model reduction, model conversions, building models from subsystem models.Time domain simulation of various model types. | Diagonalization & Jordan, Schur and Hessenberg conversions of state models | Use of ode45 and dde23. Solvers (fzero, fsolve) and optimizers (fminbnd, fminsearch). |
| 2. | Quadratic performance indices and signal norms. Observability and Controllability Grammians. Quadratic performance indices with exponential time-weighting. Linear Quadratic deterministic state-feedback control and quadratic optimal parametric control. Use of Algebraic Lyapunov equations. | Quadratic performance indices 1) with polynomial time weighting and 2) for LTI delay-in-loop systems. | Algebraic Sylvester Equation. |
| 3. | Vector random processes in time domain. Identification, Mean and variance calculus, variance minimization. Stochastic regulator, Kalman filtering, LQG control. | Parseval formulae for cost computations. | Spectral factorization. |
| 4. | Transfer function matrix, frequency response. Classical and modern studies of robust stability: classical margins and studies of unstructured uncertainty. | ||
| 5. | Improving reliability of the computations. |
Instructions for students on how to achieve the learning outcomes
Usual.
Assessment scale:
Numerical evaluation scale (0-5)
Partial passing:
Study material
| Type | Name | Author | ISBN | URL | Additional information | Examination material |
| Book | AEM = Advanced Engineering Mathematics | Glyn James | No | |||
| Book | AMOC = Optimal Control ... | Brian D. O. Anderson & Joh B. Moore | No | |||
| Book | AMOF = Optimal Filtering | Brian D. O. Andersson & John B. Moore | No | |||
| Book | CEHB1 = The Control Handbook. Control System Fundamentals | William S. Levine & al. | No | |||
| Book | CEHB2 = Control Engineering Handbook. Advanced Methods. | William S. Levine | No | |||
| Book | Control Theory. Multivariable and Nonlinear Methods. | Lennart Ljung & Torkel Glad | 0-7484-0878-9 | No | ||
| Book | Linear Controller Design | Boyd & Barrat | No | |||
| Book | OBC = Optimization Based Control | Richard M. Murrays | No | |||
| Book | ÅM = Feedback Systems. An Introduction for Scientists and Engineers | K. J. Åström & R. M. Murray | No | |||
| Lecture slides | Lecture Slides | Terho Jussila | In slides.zip | Yes | ||
| Summary of lectures | TJ | Terho Jussila | TJ.pdf | Yes |
Prerequisites
| Course | Mandatory/Advisable | Description |
| ASE-1130 Automaatio | Mandatory | 1 |
| ASE-1251 Järjestelmien ohjaus | Mandatory | 1 |
| ASE-1258 Introduction to Control | Mandatory | 1 |
1 . ASE-1130/1251/1258
Additional information about prerequisites
ASE-1130, ASE-1251 or ASE-1258 is not needed if one has had a basic course on analog control.
Correspondence of content
| Course | Corresponds course | Description |
| ASE-7556 LQG Control with Matlab, 6 cr | ASE-7557 LQG Control with Matlab, 5-7 cr | |
| ASE-7556 LQG Control with Matlab, 6 cr | ASE-5056 Optimal and Robust Control with Matlab, 8 cr |