Multidimensional Trajectory Tracking for Numerically Stiff Independent Metering System


  • Goran Stojanoski
  • Dimitar Ninevski
  • Gerhard Rath
  • Matthew Harker



Hydraulics, Optimal control, Independent metering, Euler-Lagrange


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.