Model reference active optimal distributed tracking system for the linear distributed parameter systems

This paper presents a technique for designing an active optimal tracking system for control of a linear distributed parameter process for applications where precise tracking of the commanded trajectories or a reference model is required. Its dynamic performance is quite satisfactory where the boundary conditions are either unpredictable or the primary cause of the instability. The type of processes considered in this study include those of structural vibrations, acoustic noises, and electromagnetic shock waves. A linear dynamic model of the distributed parameter process is developed in a discrete state-space form. The control strategy and the degree of the tracking of the commanded trajectories or the reference model are then set forth by the performance criteria. Requirements for selecting an appropriate set of weighting factors for the performance criteria are provided. Optimization of the performance criteria is in the context of the Pontrygin´s maximum principle, modified for the spatial distribution. A control law is derived based on the distributed linear quadratic regulation for infinite dimensional time-spatial invariant systems. It is composed of a feedforward and a state feedback controller. A simulation is presented.