Digital Technique for Optimal Control of Third-Order Systems

The time optimal control of higher order systems based on available mathematical theories requires tedious mathematical manipulations to determine the switching instants for optimum performance. Even for the third-order system the computations are involved and become intricate if the parameters vary during the system performance. A simple digital technique is presented for time optimal control of third-order systems and takes into consideration any change in system parameters. Sections of actual system trajectories are stored in the computer memory in the form of tables, and projections of optimum switching curves are generated by effectively shifting these stored trajectories to pass through the origin. By continually updating its own optimum trajectories the system has sufficient intelligence to discern proper switching instants in case of any parameter changes without any mathematical calculations. A simple method is proposed to avoid any measurements of derivatives of error. Simulation results are presented to establish the usefulness of of the control technique.