An Approach to Design Robust Tracking Controllers for Nonlinear Uncertain Systems

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 50; no. 8; pp. 3010 - 3023
• Main Authors: Celentano, Laura, Basin, Michael V.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Control design; Control of robots with real actuators; Control systems design; Control theory; Controllers; Eigenvalues; Industrial robots; Mathematical model; Noise measurement; Nonlinear control; Nonlinear systems; nonlinear uncertain systems; practical robust stability; Robots; Robust control; robust control of mechanical uncertain systems; robust tracking control; Robustness; Tracking control; Tracking errors; Uncertain systems; Velocity measurement
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2018.2834908

This paper provides an approach to design robust smooth controllers that allow a plant belonging to a broad class of nonlinear uncertain systems, with possible real actuators and subject to bounded or rate-bounded disturbances, to track a sufficiently smooth reference signal with an error norm smaller than a prescribed value. The proposed control laws are based on the concept of majorant systems and allow one to establish asymptotic bounds for the tracking error and its first and second derivatives. The proposed controller design is based on two parameters: the first is related to the minimum eigenvalue of an appropriate matrix, which the practical stability depends on, and the second is determined by the desired maximum norm of the tracking error and its convergence velocity. If the trajectories to be tracked are not sufficiently smooth, suitable filtering laws are proposed to facilitate implementation of the control laws and reduce the control magnitude, especially during the transient phase. The obtained theoretical results are validated in two case studies. The first one presents a tracking control design for an industrial robot, both in the joint space and workspace, with and without real actuators or velocity measurement noise. The second one deals with tracking control design for a complex uncertain nonlinear system.