Systems and Control (5cr)

Objectives

Thinking, concepts, analysis and synthesis needed to control deterministic systems of various complexity, especially for LTI systems in DT (Discrete-Time) but also for CT (Continuous-Time). The student should (for grade 3/5):1. Recognize the basic concepts and elements of systems control needed and relate the methods studied to them.2. Master model conversions between CT and DT models and between state space models and transfer function models.3. Analyze stability, controllability (reachability) and observability of a DT LTI state space model.4. Design and analyze LTI State Feedback Controllers including Integrating and Repetitive Control.5. Design Smith Predictor and Ragazzini Controllers.6. Design LTI State Observers for LTI DT state space systems. 7. Apply z transforms, z transfer functions and LTI state space models in analysis and synthesis8. Know the similarities and differences in the CT and DT time domain and frequency domain theory of systems (due to elementary knowledge from a course of CT control)9. Master Root-Locus Theory excluding angle rules.Grade (1/5): At least four of the goals listed are reached

Content

Core contentLinear Time Invariant. Elements of Discrete-Time aka DT systems control. Non-experimental Modelling. Model conversions. Simulation. Similarities and Differences of Continuous-Time systems and DT systems. Nyquist-Shannon Sampling Theorem.Elementary Block Diagram. z Transform, z Transfer Function, DT Operator Transfer Functions. State-Space Models.Stability, Root Locus, Controllability, Observability and Frequency Response of DT Systems. Möbius-Routh Stability Test. Intersample behavior.Analysis and Synthesis of DT Feedback Controllers. Root Locus.DT State Feedback Control, State Observers and Observer Based Feedback Control using eigenvalue assignment designs including analysis of Relative Stability and Sensitivities.Complementary knowledge• Further simulation tools of Matlab• Efficient Stability Tests• Sensitivity of eigenvalue, DC gain and the system response• LTI and LPV systems• State space model and Transfer Function Matrix from such model of the subsystems• Improving accuracy of the computations• Two skills from the list of 5 skills listed elsewhere

Prerequisites

Basic knowledge on analog control of Linear Time-Invariant Single-Input-Single-Output systems including PID control, differential equations, time-delay models, Laplace transform, transfer function, frequency response and matrices.

Further information

The course AUT.200 in Finnish corresponds to the course. The contents of the mandatory seminars will not imply exam questions for the fair participants.The examination of Topics 01-12 and the mandatory PC works is offered using Open Book Tests (sub-exams) A, B and C in EXAM classes with access to Matlab and the text files of the lectures, Exam Tables, Math notes and Matlab's documentation. The Matlab problems are solved using basic commands, Simulink, Control System Toolbox, Matlab scripts and Mathwork's Matlab functions . Symbolic Math Toolbox may be used to replace manual calculus. Guarantee Points and Extra Points may be earned in voluntary weekly PC exercisesPossible videos are shared in Panopto service, other files in Moodle.Partial completions of the course must be carried out during the same implementation round.