Minimal control configuration for descriptor systems

Considers the problem of choosing a decentralized information flow constraint (DIFC), or equivalently, the choice of input/output pairing, so as to minimize the complexity of a controller required for the system. In particular, DIFC is analyzed for the generalized robust servomechanism problem where the necessary controller structure is well defined. For the case of constant y^ref, constant disturbance ω, and open-loop stable plants, it can be readily shown that the servocompensator gain matrix generally contains mr nonzero parameters. In large scale system problems, this number may be unrealistically large and therefore not practical. It is of interest then, to determine if a minimal interconnection/pairing exists for the sensors and actuators. This problem is known as the minimal sensor actuator placement problem (MSAPP). Since a large number of industrial processes are characterized by poorly modeled plant dynamics, e.g. chemical systems, electric power networks, the MSAPP is discussed in the context of unknown systems where the existence conditions for the MSAPP and the corresponding controller structure are determined by some steady-state parameters of the plant, calculated by performing a limited number of steady-state experiments on the plant. Since the plant is “unknown”, it is assumed that it is open-loop stable and that y^ref, ω are constant-the most common class of signals encountered in industrial processes