The course aims to provide mathematical tools dor the analysis and
design of feedback control systems.
The main topics are:
1) STABILITY OF FEEDBACK CONTROL SYSTEMS AND STABILIZATION
2) DIRECT SYNTHESIS METHODS
3) PERFORMANCE LIMITATIONS OF FEEDBACK CONTROL SYSTEMS
4) SAMPLED-DATA CONTROL SYSTEMS
5) CONTROL DESIGN VIA STATE-SPACE METHODS
6) OPTIMAL CONTROL
Basso, Chisci, Falugi. Fondamenti di Automatica, De Agostini-UTET, 2007.
Bolzern, Scattolini, Schiavoni. Fondamenti di controlli automatici, 3a edizione, Mc Graw-Hill Italia, Milano, 2015.
Doyle, Francis, Tannenbaum. Feedback Control Theory. Maxwell McMillan, 1992.
Goodwin, Graebe, Salgado. Control System Design. Prentice-Hall, 2001.
Isidori. Sistemi di Controllo: seconda edizione, Vol. I. Siderea, Roma, 1993.
Learning Objectives
To provide mathematical tools for the analysis and design of feedback
control systems to be applied to the solution of practical engineering
control problems.
Prerequisites
Math analysis.
Linear algebra.
Elements of control engineering.
Teaching Methods
Lectures and practice in class.
Type of Assessment
Oral exam after a written test.
Course program
1. INTRODUCTION
Background on linear system theory. The internal model principle and its applications.
2. STABILITY OF FEEDBACK CONTROL SYSTEMS AND STABILIZATION
Internal stability: definition, mathematical conditions and connection with the Nyquist criterion. Characterization of stabilizing controllers: case of stable process and general case.
3. DIRECT SYNTHESIS TECHNIQUES
Choice of the closed-loop transfer function. Controller design meeting desired control specifications. Hints on possible extensions of direct synthesis.
4. PERFORMANCE LIMITATIONS ON FEEDBACK CONTROL SYSTEMS AND ROBUST CONTROL
Influence of open-loop right half-plane poles and zeros on the control system bandpass and step-response. Bode's theorem on the sensitivity function.
5. SAMPLED-DATA SYSTEMS
Structure of sampled-data control systems: sampling and reconstruction of signals. Discretization of a continuous-time linear time-invariant process; analysis of the dynamic behaviour via z-transform. Design of digital controllers: integration, matching and direct discretization techniques.
6. REGULATOR PROBLEM
Background on state-space representations. Observability and controllability. Static state feedback and eigenvalue/pole placement. Asymptotic state observers. Regulator design.
7. OPTIMAL CONTROL
Optimal control and dynamic programming. Linear Quadratic (LQ) regulator on a finite control horizon for discrete-time systems. Infinite-horizon LQ regulators. LQ regulators for continuous-time systems.