ASE-7557 LQG Control with Matlab, 5-7 cr


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.


Terho Jussila


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.


Sisältö Ydinsisältö Täydentävä tietämys Erityistietämys
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.     

Ohjeita opiskelijalle osaamisen tasojen saavuttamiseksi

Usual: Sufficient early enough work, even before the sessions, active participation in the sessions.


Numerical evaluation scale (0-5)


Completion parts must belong to the same implementation


Tyyppi Nimi Tekijä ISBN URL Lisätiedot Tenttimateriaali
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   


Opintojakso P/S Selite
ASE-1252 Järjestelmien ohjaus Mandatory   1
ASE-1259 Introduction to Control Mandatory   1
ASE-1131 Automaatio Mandatory    

1 . ASE-1130/1251/1258

Tietoa esitietovaatimuksista
ASE-1131/1130, ASE-1252/1251 or ASE-1259/1258 is not needed if one has had a basic course on analog control.


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ASE-7557 LQG Control with Matlab, 5-7 cr ASE-7556 LQG Control with Matlab, 6 cr  

Päivittäjä: Laine Marja-Liisa, 06.03.2019