Robustness studies of a proximate time-optimal controller

Two practical time-optimal controllers for rapid slewing of type-three and type-two third-order plants, PTOS3 and PTOS3τ, respectively, have been developed. The robustness of the PTOS3τ and corresponding time-optimal controller is compared to parameter variations and flexible unmodeled dynamics. It is found that the PTOS3τ controller is much more robust than the time-optimal controller. Simulation results show the increase in settling times of the PTOS3τ and time-optimal controllers as the parameter τ of the type-two third-order plant, a÷s²(τs+1), is varied from the nominal τ used in the controller designs. Simulation studies delineate the range of applicability of the PTOS3τ when there are flexible unmodeled dynamics. A numerical method to calculate the time-optimal control of higher-order systems is presented and applied to the type-two third-order plant with flexible unmodeled dynamics. The results are compared with those of applying the PTOS3τ to the same higher-order systems