Open AccessMultidimensional Trajectory Tracking for Numerically Stiff Independent Metering System
Author(s) -
Goran Stojanoski,
Dimitar Ninevski,
Gerhard Rath,
Matthew Harker
Publication year - 2021
Publication title -
linköping electronic conference proceedings
Language(s) - English
Resource type - Conference proceedings
eISSN - 1650-3740
pISSN - 1650-3686
DOI - 10.3384/ecp182p283
Subject(s) - control theory (sociology) , discretization , regularization (linguistics) , uniqueness , mathematics , trajectory , optimal control , numerical analysis , mathematical optimization , computer science , mathematical analysis , control (management) , physics , astronomy , artificial intelligence
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.