Frequency domain approach to solve the time-optimal control of a distributed parameter system

In this paper, the time-optimal control of the wave equation k derived in closed form. A frequency domain approach k used to obtain the time-optimal solution which k bang-off-bang. The system studied in thk paper k a uniform flexible rod with a control input at each end, whose dynamics in axial vibration is represented by the wave equation. In order to verify the optimality of the control profile derived for the dktributed parameter system, the system k discretized in space and a series of time-optimal control problems are solved for the finite dimensional model, with increasing number of flexible modes. In the limit, the controllers show the convergence of the first and final switch of the bang-bang controller of the finite dimensional system to the first and final switch of the bang-off-bang controller of the dktributed parameter system, in etddition to the convergence of the maneuver time. The number of switches in between the first and final switch k a function of the order of the finite dimensional system. The maneuver time of the dktributed parameter system k compared to that of an equivalent rigid system and the coincidence of the time-optimal controller for the flexible and rigidized systems k illustrated for certain maneuvers.