×

Non-linear control based on physical models. Electrical, mechanical and hydraulic systems. (English) Zbl 0965.93003

Lecture Notes in Control and Information Sciences. 260. London: Springer. xv, 172 p. (2001).
The book is a compact introduction to nonlinear control theory and its applications in electromagnetic systems, finite- and infinite-dimensional mechanical systems and hydraulic drive systems.
Chapter 1 summarizes some principal theoretical concepts of nonlinear control, such as Lyapunov stability, dissipativity, passivity, positive realness and absolute stability. Physical backgrounds and connections between these concepts are discussed. Some results are given without proofs, but the reader is referred to the corresponding literature. The port-controlled Hamiltonian system with dissipation (PCHD-system) and the port-controlled Hamiltonian system (PCH-system) are defined too; they are generalizations of the well-known Hamiltonian systems. Some nonlinear model-based control design strategies are briefly described in Chapter 2. These are the nonlinear state feedback \(H_2\)-design for affine systems with and without integral terms, the non-linear state feedback \(H_{\infty}\)-design for affine systems and the passivity-based control concept. There exist a number of other different nonlinear control design strategies, but all the model-based nonlinear control approaches have one fact in common, namely that somehow the knowledge of the underlying physical structure helps to solve the design problems.
In Chapter 3 an extension of the Brayton-Moser theory is used for setting up the electric network equations by means of mixed potentials. The combination of this energy-based concept with graph theory allows to derive the mathematical model of an electric network in the form of a PCHD-system. The modelling process is illustrated by means of a terminal model of a power generator and a three-phase application. Finally, for a laboratory model of a Ćuk-converter it is shown how the presented theory can contribute to the design of a nonlinear \(H_2\)-controller.
Chapter 4 is devoted to finite- and infinite-dimensional mechanical systems, which can be presented as PCH-systems. On the basis of the Poisson bracket approach, the nonlinear \(H_2\)-design, the nonlinear \(H_{\infty}\)-design, the PD-(proportional differential) controller design and the idea of disturbance compensation for such systems are formulated. The different control strategies developed for PCH-systems are applied to an infinite-dimensional piezoelectric composite beam structure.
In Chapter 5 a pump-displacement controlled rotational piston actuator and a valve controlled translational piston actuator are considered. An analytic mathematical description and a controller design are presented for these two hydraulic drives. Finally, two industrial applications, namely the hydraulic gap control with eccentricity compensation for rolling mills and the swash-plate mechanism of a hydrostatic drive unit are investigated.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93C85 Automated systems (robots, etc.) in control theory
74M05 Control, switches and devices (“smart materials”) in solid mechanics
70Q05 Control of mechanical systems
93C95 Application models in control theory
93C10 Nonlinear systems in control theory
93B36 \(H^\infty\)-control
93D10 Popov-type stability of feedback systems
PDFBibTeX XMLCite