Optimal output transitions for linear systems

Abstract

Addresses the optimal output transition problem for linear systems. The goal is to transfer the system output from an initial value to a final output value with zero residual vibrations in the output. Such problems arise in the point-to-point positioning applications such as positioning of disk drive heads. Methods have been developed (previously) to achieve such output transition by constraining the internal states to be zero at the beginning and at the end of the output transition. The output transition problem is then solved as an optimal state transition problem. However, the output transition cost is not minimal. Output transition costs can be further reduced if the internal states are not constrained to be zero at the beginning and at the end of the output transition. The optimal output transition is posed and analytical solution is presented by (a) using the standard optimal state transition approach to obtain the control law during the output transition and then (b) integrating this with the inversion-based approach to find inputs that maintain perfect output tracking before the initiation and after the completion of the output transition by using pre- and post-actuation. An example system is studied and simulation results are presented to illustrate the performance improvement over approaches to point-to-point output transition, which do not use pre- and post-actuation.