Analysis and Control of Infinite-Dimensional Systems

Abstract

Infinite dimensional port Hamiltonian systems have been introduced in Chapter 4 as a novel framework for modeling and control distributed parameter systems. In this chapter, some results regarding control applications are presented. In some sense, it is more correct to speak about preliminary results in control of distributed port Hamiltonian systems, since a general theory, as the one discussed in Chapter 5 for the finite dimensional port Hamiltonian systems, has not been completely developed, yet. We start with a short overview on the stability problem for distributed parameter systems in Sect. 6.2, together with some simple but useful stability theorems. Then, in Sect. 6.3, the control by damping injection is generalized to the infinite dimensional case and an application to the boundary and distributed control of the Timoshenko beam is presented. In Sect. 6.4, a simple generalization of the control by interconnection and energy shaping to the infinite dimensional framework is discussed. In particular, the control scheme is developed in order to cope with a simple mixed finite and infinite dimensional port Hamiltonian system. Then, an application to the dynamical control of a Timoshenko beam is discussed in Sect. 6.5.