ASE-7557 LQG Control with Matlab, 5-7 cr
Additional information
The extensions to 6-7 cr are available for ony exchange students whose home university requires more than 5cr. All the sessions assume a pre-study and include both a short lecture part and use of Matlab to solve exercise problems. Three subexams with Matlab form an alternative to a single Total Exam with Matlab. In the exams one has access to Matlab documentation, Exam Tables and all the pre-study & lecture files created & used by the teacher during the sessions.
Suitable for postgraduate studies.
Person responsible
Terho Jussila
Lessons
| Implementation | Period | Person responsible | Requirements |
| ASE-7557 2019-01 | 1 - 2 |
Terho Jussila |
Examination in 2, 3 or 4 Matlab tests and 4, 5 or 6 mandatory PC sessions/assignments depending on the course width. In the tests the student has access to all internal documentation of Matlab and to all pdf slides and lecture notes used. |
Learning Outcomes
In Period 2 the students should be able to modify the results of DT systems studied in Period 1 to CT systems as a member of a team. After the course the student should be able to: use of Matlab to design, analyze and implement CT and DT (Continuous-Time and Discrete-Time) deterministic LQ (Linear Quadratic) Controllers, Kalman Filters and LQG (LQ Gaussian) controllers for LTI (Linear Time-Invariant) CT and DT state space systems as well as PID controllers for CT and DT LTI plants, even for delayed ones. This includes e.g. the ability to compute suitable performance indices both in time domain and frequency domain, model integrations 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 and communication of the results to other members of the engineering & business community.
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. Spectral factorization. | Parseval formulae for cost computations. | |
| 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. | ||
| 6. | +1cr: CT H2 control, CT Non-Stationary Kalman Filter, CT Extended Kalman Filter, Solution of CT Two-Point-Boundary Value Problem. | ||
| 7. | +1cr: DT Kalman Filter for Recursive Identification, Special Lyapunov and Riccati Algorithms, Morf-Kailath Algorithm, Schur Decomposition in solving Lyapunov Equations. |
Instructions for students on how to achieve the learning outcomes
Usual: Sufficient early enough work, even before the sessions, active participation in the sessions.
Assessment scale:
Numerical evaluation scale (0-5)
Partial passing:
Study material
| Type | Name | Author | ISBN | URL | Additional information | Examination material |
| Book | AMOC = Optimal Control | Brian D. O. Anderson & John B. Moore | No | |||
| Book | AMOF = Optimal Filtering | Brian D. O. Andersson & John B. Moore | No | |||
| Book | Control Theory. Multivariable and Nonlinear Methods. | Lennart Ljung & Torkel Glad | 0-7484-0878-9 | No | ||
| Book | Feedback Systems | K.J. Åström & R.M. Murray | No | |||
| Book | Linear Controller Design | Stephen Boyd & Craig Barrat | No | |||
| Summary of lectures | OBC = Optimization Based Control | Richard M. Murray | No | |||
| Online book | Control Engineering Handbook | William Levine et al. | No |
Prerequisites
| Course | Mandatory/Advisable | Description |
| ASE-1252 Järjestelmien ohjaus | Mandatory | 1 |
| ASE-1259 Introduction to Control | Mandatory | 1 |
| ASE-1131 Automaatio | Mandatory |
1 . ASE-1130/1251/1258
Additional information about prerequisites
ASE-1131/1130, ASE-1252/1251 or ASE-1259/1258 is not needed if one has had a basic course on analog control.
Correspondence of content
| Course | Corresponds course | Description |
| ASE-7557 LQG Control with Matlab, 5-7 cr | ASE-7556 LQG Control with Matlab, 6 cr |