Time-optimal control of higher-order systems

Practical extension of time-optimal control to systems of higher order than three has been limited primarily by difficulties in physically representing surfaces in a phase space of these higher dimensions. A method is presented here for obtaining the forcing function as a function of the state variables without requiring use of the phase space concept. On line solution of a set of transcendental equations is required. Results of a digital simulation of a fourth-order, real-root, single-degree-of-freedom system are presented. In a digital solution the system operates as a series of short open-loop control intervals. The effect of including derivatives of the input for prediction is shown for second-order model inputs.