Controllability and Observability

Controllability and observability are structural properties that carry useful information for structural testing and control, yet are often overlooked by structural engineers. A structure is controllable if the installed actuators excite all its structural modes. It is observable if the installed sensors detect the motions of all the modes. This information, although essential in many applications, is too limited: it answers the question of excitation or detection in terms of yes or no. The quantitative answer is supplied by the controllability and observability grammians, which represent a degree of controllability and observability of each mode. In this chapter the controllability and observability properties of flexible structures are discussed. The fundamental property of a flexible structure in modal coordinates consists of a set of weakly coupling of the modes, as shown in Property 2.1. The weak coupling allows one to treat each individual mode separately specifically, to combine the controllability and observability properties of the whole system out of the properties of individual modes. These controllability and observability properties are used later in this book in the evaluation of structural testing and in control analysis and design.