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This paper investigates the lementation of optimal controllers to dynamic control systems and addresses their causality. First, a one-link robot arm system is introduced as the model for which the optimal controller will be designed. This model is used in a discrete linearized for so as to ease the mathematics involved, however no generality is lost due to this simplification as dictated by the obtained results. Then a proposed time-optimal controller is first adopted in which the control requirements are reduced to merely reaching a specified set-point in the shortest possible time. This, of course, gives rise to large control signals that may not be physically attained resulting in a fictitious controller. Then a relaxation is made to overcome this problem by applying a performance index to be minimized through the use of the minimum principle of Pontryagen. Finally, a comparative analysis is briefly made supported by the response curves. |
