Integrated actuator placement and fault tolerant controller design for a class of distributed parameter systems

In the current work we present an integrated actuator placement and fault tolerant controller design based on the concept of spatial H₂ norm and combined with a fault tolerant controller design concepts for DPS presented in earlier work by the authors. Specifically, a nonlinear optimization problem is formulated to identify and rank spatially independent actuator groups that may control a distributed process with minimal actuator power. The optimization problem is based on the concept of the spatial H₂ norm and guarantees a minimum amount of controllability for each group. The augmented fault monitoring scheme employs a time varying threshold in order to minimize detection time, and the fault accommodating scheme simply switches off the faulty actuator and activates a healthy group without reconfiguring the control signal, as the latter by design is the same for all possible actuator groups. The simplicity of the proposed methodology lies in the unique property of transport reaction processes that properly chosen actuators at physically different locations have an identical effect on the system long term behavior.