Globally optimal control of self-adjoint distributed systems

The partial differential equations of motion for an uncontrolled distributed structure can be transformed into a set of independent modal equations in terms of natural co-ordinates. It is common practice to design control forces that recouple the modal equations so that the natural co-ordinates for the open-loop (uncontrolled) system cease to be natural co-ordinates for the closed-loop (controlled) system. This approach is referred to as coupled control. In contrast, the independent modal-space control method is a natural control method, i.e. natural co-ordinates for the open-loop system remain natural co-ordinates for the closed-loop system. Moreover, natural control provides a unique and globally optimal closed-form solution to the linear optimal control problem for the distributed structure. Indeed, discretization is not necessary. The optimal control forces are ideally distributed. The distributed control can be approximated by finite-dimensional control, a process that does not require truncation of the plant. Two numerical examples are presented.