Time optimal control of a second order system with hydraulic fluidic implementation

Abstract

This study was undertaken to determine the requirements for fluidic implementation of a time optimal “target acquisition” control system. Analytic expressions for the optimal control function u ∗ , the systems trajectory curve, switch curve and minimum transition time are determined for a given plant. The optimal control u ∗ is obtained as a function of the system state variables u ∗[x(t)] so that u ∗ is generated in a feedback sense. The component requirements for hydraulic fluidic implementation of this minimum time control system are stringent. Therefore, linear proportional and sub-optimal control systems are also considered. The decision to use optimal, sub-optimal or proportional control requires, among other things, weighing the advantages of high performance against the complexity of the control circuit. In this case the sub-optimal control appears to be the best choice because it requires simple control circuitry and its transition time is nearly optimal. The use of this type of control eliminates the need for a number of components required in the optimal system.