Design of a sliding mode controller with model-based switching functions applied to robotic systems

Abstract

This thesis presents an in-depth study sliding mode control applied on electromechanical systems which dynamic model can be formalized according to the standard mathematical structure of robotic manipulator arms. More specifically, this research work focuses on an innovative design of nonlinear sliding surfaces based on the dynamic model of robotic systems. The design of the nonlinear model-based surfaces consists in simplifying the nonlinear terms of the torque control input including the inertia, accelerations and gravity matrices by using them in the sliding surfaces themselves. Thus, compared to the typical design of linear sliding surfaces, the resulting torque control law is considerably simplified, and becomes linear as a function of the position and velocity error vectors. This simplification thus leads to a reduction in transient dynamic constraints and in digital and analog noise levels originating from the signals of the sensors that are part of the closed-loop control system. In addition, the compensation of the inertia matrix in the sliding surfaces ensures a total decoupling of the high-frequency chattering phenomenon originating from the discontinuous term of the torques control law. This decoupling in turn induces a general reduction in the chattering levels on all axes. In addition, the design of model-based sliding surfaces also generates a complementary study on the gravity matrix of the robotic system. Indeed, this complementary study makes it possible to characterize novel algebraic properties linked to the gravity matrix which serve to establish a compensation criterion for the latter in the very design of sliding surfaces. It is also possible to use the characteristics of the gravity matrix to mathematically validate the latter, thus providing a way to complement the traditional mathematical validation of the inertia and acceleration matrices of the robot model. In order to experimentally validate the model-based sliding surface design approach, a test bench including a prototype of an exoskeleton arm with 7 degrees of freedom is first used. Compared to the conventional approach, the proposed approach demonstrates a significant reduction in dynamic constraints as well as in the chattering levels on the torque inputs of the exoskeleton, while ensuring very good trajectory tracking performance. In order to subsequently demonstrate the generalization of the approach on other robotic systems, an experimental application has also been validated on a commercial quad copter drone. Lastly, the literature review positions our research work with relation to recent scientific publications, and proves the originality of the proposed approach, since to the best of our knowledge, no similar method using the design of model-based sliding surfaces on robotic systems has been developed to date.

Date	7 May 2021
Original language	American English
Awarding Institution	École de technologie supérieure
Supervisor	Maarouf Saad (Supervisor)