ASE-7556 LQG Control with Matlab, 6 cr
Additional information
Suitable for postgraduate studies.
Person responsible
Terho Jussila
Lessons
| Implementation | Period | Person responsible | Requirements |
| ASE-7556 2016-01 | 3 - 4 |
Terho Jussila |
Pen-and-Paper Exam (3h or 1h+1h+1h, totally 50% of all exam points), PC Exam (3h, 50% of all exam points) and 5 PC sessions (each 90-115 min). Four additional PC sessions (each 90-115 min) are available for compensating absences and/or gaining extra points. REMARK. The PC sessions mentioned are not the PC Lecture & Exercise combinations scheduled for each week. |
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:
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
Correspondence of content
| Course | Corresponds course | Description |
| ASE-7556 LQG Control with Matlab, 6 cr | ASE-5056 Optimal and Robust Control with Matlab, 8 cr |