


Politecnico di Torino  
Academic Year 2015/16  
01PDXOV, 01PDXND, 01PDXQW Modern design of control systems 

Master of sciencelevel of the Bologna process in Computer Engineering  Torino Master of sciencelevel of the Bologna process in Energy And Nuclear Engineering  Torino Master of sciencelevel of the Bologna process in Mechatronic Engineering  Torino 





Esclusioni: 01PDC; 04CFI; 01OUV; 01NNE 
Subject fundamentals
The course is taught in English.
One of the most useful qualities of a properly designed feedback control system is robustness, i.e., the ability of the closedloop system to perform satisfactorily despite large variations in the (openloop) plant dynamics. The aim of the course is to provide methodologies and tools for the analysis and design of robust feedback control systems. 
Expected learning outcomes
By the end of this course, students will gain the following knowledge and skill:
 Knowledge of the concept of a dynamical system together with its mathematical representations such as state equations and transfer functions.  Skill in deriving mathematical models of linear dynamical systems.  Skill in computing the solution of the system state equations.  Skill in evaluating the behaviour of a dynamical system through numeric simulation.  Knowledge of structural properties (stability, reachability, observability) of dynamical systems  Skill in studying the structural properties of dynamical systems.  Knowledge of the concept of feedback control of dynamical systems.  Knowledge of the main performance requirements of feedback systems.  Knowledge of the main analysis techniques in the frequency domain for the study of stability and performance of feedback control systems.  Skill in analyzing stability and performance of feedback control systems.  Knowledge of the design techniques of feedback controllers based on lead and lag functions.  Skill in designing feedback controllers for single input single output systems through lead, lag and PID functions.  Skill in evaluating the behaviour and performance of controlled systems through numerical simulation.  Knowledge of unstructured uncertainty models.  Skill in deriving weighting functions from performance specifications.  Knowledge of nominal and robust stability; nominal and robust performance.  Skill in the study of nominal and robust stability; nominal and robust performance.  Knowledge of the theory of robust control through H_infinity norm minimization.  Skill in the design of controllers through H_infinity norm minimization.  Knowledge of structured uncertainty modelling and the generalized plant.  Skill in representing structured uncertainty.  Skill in deriving the generalized plant.  Knowledge of robust stability and robust performance analysis through structured singular values.  Skill in the analysis of robust stability and robust performance through structured singular values.  Knowledge of Mubounds computation  Basic Knowledge of musynthesis.  Skill in the computation of mubounds. 
Prerequisites / Assumed knowledge
Knowledge of differential and integral calculus of vector valued real functions. Basic results of complex numbers, functions of a complex variable, the Laplace transform and a good knowledge of linear algebra and the theory of polynomial and rational functions. Linear system theory. Knowledge of basic feedback control systems analysis and design. Skill in the design of controllers in the frequency domain. Basic skill of Matlab and Simulink.

Contents
Course organization. Prerequisites. Course description. Exam rules. Major topics and course outline (1.5 hr).
Control problem formulation and systems representations (3 hr). Internal stability and Bibo stability (1.5 hr). Frequency response representations (Bode plot and polar plot) and Nyquist stability criterion (6 hr). Feedback control systems steadystate response to polynomial references and disturbances, and to sinusoidal disturbances (6 hr). Transient requirements translation and the Nichols chart (1.5 hr). Frequency domain controllers design through loopshaping (3 hr). Performance specifications and weighting functions (4.5 hr). Unstructured uncertainty models (4.5 hr). Nominal and robust stability; nominal and robust performance (4.5 hr). Robust control through H_infinity norm minimization (6 hr). Structured uncertainty modelling and the generalized plant (6 hr) Robust stability and robust performance analysis through structured singular values (7.5 hr). Mubounds computation and introduction to musynthesis (3 hr). Exam simulation: guidelines and solution (1.5 hr). 