An approximate minimal time closed-loop controller for processes with bounded control amplitudes and rates

This paper presents a method for designing an approximate minimal time closed-loop controller for linear systems with bounded control amplitudes and rates. The method is based on obtaining an approximate functional expression (explicitly in terms of the state variables) that describes the minimal time isochrones of the system. This expression is obtained by a series of least-squares fits to the computed system states on the various isochrones. The computation of the system states on the isochrones and the determination of the approximate expressions are achieved off-line. For on-line operation, it is only required to store a limited number of coefficients of the approximate expressions, and to compute the closed-loop control function by some algebraic manipulation. Consequently, the on-line computer storage requirement as well as the on-line computation requirement is relatively small. Thus, the method is feasible for high-order practical systems. To evaluate its usefulness in applications, the scheme is used to design a fourth-order Ranger Block III Attitude Control System. The results are compared to those obtained by applying the minimal time open-loop control.