Abstract
In this paper we discuss the time optimal control problem of an electrohydraulic servo system. This system is described by the 16th order nonlinear ordinary differential equations with multi-discontinuities. The control variables are inputs to the two servovalves with different nonlinear flow gains and dynamics. The performance index to be minimized is made up of integrated square errors of allowable system pressures, load displacement and velocity around the origin, and response time.
This problem is solved by applying a hillclimbing algorithm to the 4th order Runge-Kutta method simulation of the state equations. As the pattern of this control is bang-bang, it is important to find the switching criteria as well as stability conditions. In this numericall experiment, a square root function is taken as closing control to a valve, and the amplitude of a feedback variable is limited to ensure reasonable stability.
In spite of the several assumptions made throughout with the system, such that the valve dynamics is simple and the liquid flow is steady, the computational results have shown fairly good coincidence with the experimental results.
