Title: Second-Order Systems with Acceleration Measurements (1 hour)
Abstract: A number of systems are modelled by partial differential equations that include second-order derivatives with respect to time. Flexible structures, acoustic waves in cavities as well as coupled acoustic-structure systems are examples of systems modelled by equations of this type. Accelerometers are a very popular choice of sensor for these systems. However, the systems theory for acceleration systems has not been well-studied. Several examples are given to show that in general choosing acceleration as the output leads to an ill-posed system. Conditions under which these systems are well-posed will be given, as well as a representation for the input/output map and transfer function for situations where the control system may not be well-posed. A model for acceleration measurements that includes a model for the micro-electrical-mechanical systems (MEMS) devices used to measure acceleration is developed and analyzed. With this more complex model, the control system is in general well-posed with a natural choice of state space. Part of this talk will include a discussion of the meaning of well-posedness and its importance for control systems.