A saturation based self-tuned robust control design for Euler Lagrange systems

Abstract

Control of the family of systems that can be represented in the Euler Lagrange (EL) form is both challenging from a theoretical perspective and applicable to a broad spectrum of real systems. For this type of control problem, given that any parameter estimation error and disturbances are not directly addressed, the system performance deteriorates, and stability cannot be deduced in advance. Considering these issues, this work presents the design and the corresponding analysis of a saturation function based, model-free, continuous robust controller for mechanical systems represented in the EL form. In order to avoid chattering in controller input, which is a common problem in most robust and high-gain control designs, the proposed method makes use of continuously differentiable terms. The stability of the closed-loop system is ensured via rigorous Lyapunov-based arguments. To ease the tuning of the controller gain, an adaptive gain-tuning algorithm is proposed to be applied as an add-on. The effectiveness of the controller is demonstrated by a simulation study on a twin rotor multi-input–multi-output system (TRMS) model Furthermore, the feasibility of the proposed method is then tested on an in-house built, inherently unstable, and therefore extremely sensitive mobile robotic platform. In the experimental study, satisfactory performances are attained for both the controller and the gain-tuning algorithm where less than $0.5°$ error is obtained in roll and pitch angles and less than $1°$ error is achieved in the yaw direction.