Numerical Methods for Optimal Control of Hydraulic Independent Metering Systems

Goran Stojanoski

Research output: ThesisDoctoral Thesis

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This thesis encompasses various control methods for numerically stiff independent metering systems used in road-header boring machines. These machines are equipped with state-of-the-art independent metering valves with an already implemented PID control structure. The main topics covered in this thesis are: the bulk modulus as the main indicator of the mechanical stiffness of the system, the development of a new mathematical model for an intelligent independent metering valve, methods of calculus of variations for optimal control with integrated position control, a matrix-based approach for numerically stiff ODEs, and a novel method for computing the optimal PID parameters for a given system. The Wylie - Yu model for the effective bulk modulus has been improved for the temperature change of the oil and implemented in a simulation environment to observe how the fluctuations of the effective bulk modulus influence the system dynamics. It is concluded that for high pressurized system the temperature of the oil has the highest impact on the value of bulk modulus compared to the other parameters. Additionally, an adaptive controller is implemented to compensate for the energy losses. Both the optimal control and the path tracking problem have been applied and tested in a simulation environment. For this purpose, a new linear model is derived that includes the complex feedback control structure of the independent metering valves. The linear system is then discretized and solved numerically using the Euler-Lagrange equations. In addition, the mass matrix method and interstitial derivatives are used to improve the numerical stability of the solution. The optimal control method shows remarkable accuracy and improved energy efficiency compared to conventional solvers. On the other hand, the path tracking method precisely follows the given paths with a maximum deviation of 1%.
Translated title of the contributionNumerische Methoden zur optimalen Regelung von hydraulischen Systemen nach dem Prinzip der getrennten Steuerkanten
Original languageEnglish
Awarding Institution
  • Montanuniversität
  • Rath, Gerhard, Assessor A (internal)
  • Brand, Clemens, Co-Supervisor (internal)
  • O'Leary, Paul, Supervisor (internal)
  • Harker, Matthew, Assessor B (external)
Publication statusPublished - 2023

Bibliographical note

no embargo


  • Hydraulics
  • Optimal control
  • Independent metering
  • Euler-Lagrange
  • Bulk Modulus
  • Energy efficiency
  • Path tracking
  • Numerical methods.

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