Abstract—Control Lyapunov Function (CLF) is a powerful tool for synthesizing nonlinear control laws. Several control laws may be deduced from the same CLF. In the Electro-hydraulic Servo Systems (EHSS) literature, two types of CLF are distinguished, especially for tracking control problems. The first type is a sum of a quadratic function of the errors while the second type is the quadratic function of the weighted sum of the errors. In this paper, we extend the second type of CLF by adding a power factor to appreciate its influence on closed-loop performances. Thus, we obtain three CLFs instead of the classic quadratic function by varying the power factors 2, 4 and 6. The three deducing control laws are compared under the presence of Coulomb friction. The study is carried out both for an angular velocity tracking control and an angular position tracking control. The numerical results show that the control laws using the CLFs of orders 2 and 4 have the best performances. Moreover, the closed-loop systems based on both controllers exhibit the best robust results under friction disturbance.

Keywords—Control Lyapunov Function (CLF), Sontag formula, Electro-hydraulic Servo Systems (EHSS), Lyapunov redesign control, friction, weighted tracking errors sum

Cite: Honorine Angue Mintsa, Gérémino Ella Eny, Rolland Michel Assoumou Nzué, and Nzamba Senouveau, "Power Factor in Control Lyapunov Functions for Electro-hydraulic Tracking Problem under the Influence of Friction," International Journal of Mechanical Engineering and Robotics Research, Vol. 13, No. 1, pp. 85-93, 2024. 

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