Optimal control simulation of elliptical shaft center orbit with the hydraulic servo system

To bore elliptical hole, the present research proposes hydraulic servo system and the control method to control the shaft center movement orbit. Considering the control difficulty when there are a small number of collocation points, the present research uses optimal control method to solve the control difficulty. Gauss pseudospectral method, which is often used in aerospace field, is applied to obtain relation between shaft center coordinate and load capacity of bearing. And the relation between load capacity and servo valve spool displacement is deduced with flow continuity equation. After the two steps above, the mathematic relation between shaft center coordinate and spool displacement is eventually obtained. The simulation results indicate that compared to the Eulerian control method, optimal control method has better self-adaptation, faster control rate, and higher control accuracy. Even if the starting movement point of shaft center is not on the expected elliptical orbit, or shaft is disturbed by instantaneous external force or dynamical force, the optimal control method still makes the shaft center orbit quickly get close to the expected ellipse. The present research lays theoretical foundation for new boring method of elliptical hole