PURPOSES OF THE CORSE

The course provide the state space theoretical methods for the analysis and the control of a closed-loop linear and non linear systems, continuous and discrete-time systems, SISO and MIMO systems.

PROGRAM

1. State space dynamic models 
Dynamic systems described in the state space. State space transformations. Eigenvalues and eigenvectors. Jordan canonical form. Transfer Matrix. Modal analysis of linear systems. 

2. Dynamic modeling and simulation of physical systems 
Dynamic structure of the energetic domains: electro-magnetic, mechanical and hydraulic. Power variables and energy variables. Graphical modeling techniques:: Bond-Graphs e Power-Oriented Graphs. Introduction to Matlab and Simulink.

3. Stability of linear and nonlinear systems 
Lyapunov stability. Equilibrium points of a system. Linearization in the neighborhood of an equilibrium point. Reduced Lyapunov criterium. Quadratic forms. Direct Lyapunov criterium. 

4. Controllability and reachability
Definitions of controllability and reachability. Reachability matrix. Reachability standard form. Point to point control of linear systems. Reachability canonical form. State feedback and pole-placement design. Ackerman's formula.

5. Observability and regulator design
Definition of observability. Observability matrix. Duality of linear dynamic systems. Standard and canonical observability forms. Asymptotical state observers: open-loop, closed loop and reduced order. Regulator design. 

6. Advanced control techniques
Interconnected systems and their properties. Sampled-data control systems. System parameters identification. Least square method. Adaptive control (basic elements). Optimal control (basic elements). Sliding Mode Control (basic elements). 

7. Exercitations in laboratory 
Examples of modeling, simulation and control of physical systems using the Matlab/Simulink environment.