Modeling for control of an inflatable space reflector, the linear 2-D case

In this paper we develop a mathematical model for the dynamics of a linear plate with piezoelectric actuation. This model can then be used to design controllers with the goal of achieving a desired shape of the plate. This control scheme can be used for several applications, e.g., vibration control in structures or shape control for high precision structures like inflatable space reflectors. The starting point of the control design is modeling for control. We will do this in the framework of port-Hamiltonian (pH) modeling, since the pH modeling framework has very nice properties which can be exploited if one wants to design a controller for a specific task. One property for example is that it facilitates modeling multi physics systems or systems which consist of several systems by first modeling all parts separate and then interconnecting them. This is possible because any interconnection of pH systems yields again a pH system. Hence, the pH framework is useful for our multi-domain modeling purpose.