Abstract
This paper presents new theorems, which allow to design in a unified way robust proportional-derivative (PD)-type control laws without chattering for a broad class of uncertain nonlinear multi-input multi-output (MIMO) systems, subject to bounded disturbances and noises, of great theoretical and engineering relevance. These controllers are used to track a reference signal with bounded second derivative with the tracking error norm smaller than a prescribed value. The proposed control laws are simple to design and implement, above all for robotic systems, both in the case of a trajectory assigned in the joint space and in the workspace. The obtained theoretical results can have numerous applications. In this paper four significant applications are provided. The first one concerns the solution of a nonlinear equations system or the determination of an equilibrium point of a nonlinear system. The second case study deals with the inversion of a nonlinear vectorial function or the kinematic inversion of a robot. The third application concerns: (A) the tracking control of a robot with parametric uncertainties, with and without measurement noise on velocity, both in the joint space and the workspace; (B) the impedance control of a robot interacting with a human operator. The fourth case study addresses the tracking control of an uncertain nonlinear system that does not belong to the class of mechanical systems. Finally, an appendix is included, providing six easy examples, which show how the results proposed in the paper can eliminate and/or reduce serious disadvantages existing in the robust control literature for significant classes of linear and nonlinear uncertain systems.
Highlights
Since a kilowatt-hour of electrical energy transformed into mechanical energy can produce an impressive amount of human work, current and future well-being depend primarily on automatic systems concerning many key areas for humanity, including the transportation and manufacturing systems.it is of great relevance to develop control algorithms that can be implemented using modern digital and wireless technologies to force electromechanical systems to behave like skilled workers who work quickly, accurately, and cheaply despite parametric variations, nonlinearities, and persistent disturbances
The tracking control of a robot with parametric uncertainties, with and without measurement noise on velocity, both in the joint space and the workspace; (B) the impedance control of a robot interacting with a human operator
With respect to [34], it is proved that the proposed control laws are robust with respect to bounded measurement noises
Summary
Since a kilowatt-hour of electrical energy transformed into mechanical energy can produce an impressive amount of human work, current and future well-being depend primarily on automatic systems concerning many key areas for humanity, including the transportation and manufacturing systems. This paper, for a broad class of uncertain nonlinear MIMO systems much more general with respect to [34,35,38], provides a new and unified approach to design robust PD-type control laws without chattering to track a reference signal with bounded second derivative with the tracking error norm smaller than a prescribed value, despite the presence of bounded disturbances, parametric and structural uncertainties, and bounded measurement noises. The references therein) for significant classes of linear and nonlinear systems can produce unstable control system or can significantly reduce the performance of the control system, under the following realistic hypotheses: parametric uncertainties, real actuators, measurement noise, finite online computation time of the control signal.
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