Optimal linear controller design for periodic inputs
This book provides a general design methodology for the design of linear controllers dealing with periodic reference and/or disturbance signals. The proposed design methodology can deal, in particular, with uncertainty on the input period and allows to incorporate a variety of handle additional design specifications. The controller design problem is translated into a convex optimization problem, whose global optimum can be numerically computed in an efficient way. Experimental validation of the proposed methodology as and a comparison with major current design approaches is illustrated on an active air bearing setup. The monograph is clearly written and quite complete, even if no mention of periodic system theory is made. A complete survey of analysis and synthesis problems concerning the control of processes containing periodic references and/or disturbances is presented. The presentation is not so suitable to be used for educational purposes or to study in depth any topic, but gives a general, well organized picture of the subject, with a rich and up to date bibliography. The structure of the book is the following. Chapter 1 contains an introduction with a brief motivation for studying periodic signals and disturbances, in Chapter 2 the general methodology to design a Linear Time-Invariant (LTI) controller for an LTI system with periodic signals and disturbances is presented and its fundamental concepts are discussed. A ``periodic performance index'' is defined that is a traded-off against conflicting design objectives and the multi-objective control problem is reformulated as a convex optimization problem that can be solved only numerically. In the four subsequent chapters the design methodology is applied to a specific control situations. In particular, Chapter 3 deals with feed-forward control, Chapter 4 consider the case of the Estimated Disturbance Feedback Control, Chapter 5 deals with the repetitive controller design and the focus of Chapter 6 is the general design of a feedback controller in presence of periodic inputs. Each of chapter contains numerical examples worked out in details comparing the proposed methodology with major current design approaches. Finally, in Chapter 7 the proposed approach is applied to the design of a repetitive controller for an active air bearing setup. Chapter 8 summarizes the conclusions.
scientific article; zbMATH DE number 5651406