This paper presents a new approach for solving an optimal control problem in a hydraulic system, using a variational calculus method. It uses a path tracking method of two different states with different units and of different magnitude. To ensure the uniqueness of the solution, two regularization terms were introduced, whose influence is regulated by regularization parameters. The system of differential equations, obtained from the Euler-Lagrange equations of the variational problem, was solved by a mass matrix method and discretized with linear differential operators at the interstitial points for numerical stability. This enabled the calculation of the control variables, despite the stiffness of the numerical problem. The results obtained show an energy-efficient performance and no oscillations. Finally, a Simulink model of the hydraulic system was created in which the calculated control variables were inserted as feed-forward inputs, to verify the results.

No abstract

Modern oil-hydraulic systems for moving heavy payloads are designed for optimised motion, but also for minimal energy loss. Individual metering technique, using separate control of the two actuator chambers, offers some advantages. A common strategy when moving the load is to control the incoming oil flow to obtain a desired speed, and the pressure at the downstream side for good efficiency. In this work analysis and design of PI (proportional-integral) pressure control is done. The adjustment of the control parameters of this loop is usually uncritical. In the worst case, the damping of the mechanical system is the only contribution. It is shown in this work, that pressure control can increase the damping of load oscillations. The influence of the P and I parameters to the system properties is investigated using the poles of the transfer function of the system. It is shown, that there is a point, where the damping factor of the system has its maximum value, and a design method for this optimisation is given. The problem ends up in a system of two equations of fourth order. A method is shown how to reduce the problem to solving one third-order equation, which is done numerically. Finally, the results are verified using simulation.