Control Theory 2b (Multivariable Control Systems)

General Data
Academic program	ECAM ENGINEERING PROGRAM			:
Type d'EC	Classes
Lectures : 6h00 Tutorials : 6h00 Lab Work : 8h00 Total duration : 32h00	Status :	Period : SEMESTER 7	Education language : English

Learning Outcomes
By the end of this module, students will be able to : 1. Modelize Multivariable systems 2. Determine the State space representation in canonical forms 3. Linearize a system 4. Design a state-feedback controller 5. Implement the designed controller and evaluate the system's performances

Content
1. System representation : the state-space representation SSR of monovariable and multivariable systems 2. Determinantion of the system's Block diagram 3. Determinantion of the State space representations in canonical forms : Controllable,Observable,Diagonal/Jordan 4. Evaluation of the Controllability and the observability of a given LTI system using the Kalman citerion 5. Design of State-feedback controller using the Ackermann's formula 6. Analysis of system performances : precision, rapidity, robustness against the presence of disturbances 7. System linearization using the Tylor expansion

Content

1. System representation : the state-space representation SSR of monovariable and multivariable systems
2. Determinantion of the system's Block diagram
3. Determinantion of the State space representations in canonical forms : Controllable,Observable,Diagonal/Jordan
4. Evaluation of the Controllability and the observability of a given LTI system using the Kalman citerion
5. Design of State-feedback controller using the Ackermann's formula
6. Analysis of system performances : precision, rapidity, robustness against the presence of disturbances
7. System linearization using the Tylor expansion

Pre-requisites / co-requisites
Introduction to control theory (S6) and Digital control (S7) Mathematics for Engineers 1 and 2 : Linear algebra : Determination of rank of matrix, the determinant

Bibliography
Ogata, K. (2010) Modern control engineering.Prentice Hall

Assessment(s)
N°	Nature	Coefficient	Observable objectives
1	This written exam stands for a Midterm. The students will be evaluated on some points that will be defined according to the progress of the lectures and tutorials sessions	0,2	Written exam
2	The practical sessions are in a form of a project that should last 8 hours. It concerns the Modeling and control of a multivariable system : case of the three-tank system, the main objectives are the following : 1.Characterise the components of the system (valves in this case) 2. If the system is non-linear, study the possibility of its linearization 3.Derive the state space model of the whole system 4. Analyse and study the model: controllability and observability 5. Develop the controller 6. Characterise the performance of the controlled system in terms of precision, and robustness to perturbations	0,3	Practical work
3	The final exam will take all the parts the student had seen during lectures, tutorials and labs	0,5	Written exam