Abstract
This paper provides a unified approach via majorant systems, which allows one to easily design a family of robust, smooth and effective control laws of proportional - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h$ </tex-math></inline-formula> order integral - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> order derivative <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(PI_{h} D_{k})$ </tex-math></inline-formula> -type for broad classes of uncertain nonlinear multi-input multi-output (MIMO) systems, including mechatronic and transportation processes with ideal or real actuators, subject to bounded disturbances and measurement errors. The proposed control laws are simple to design and implement and are used, acting on a single design parameter, to track a sufficiently smooth but generic reference signal, yielding a tracking error norm less than a prescribed value, with a good transient phase and feasible control signals, despite the presence of disturbances, parametric and structural uncertainties, measurement errors, and in case of real actuators and amplifiers. Moreover, some guidelines to easily design the proposed controllers are given. Finally, the stated unified methodology and various performance comparisons are illustrated and validated in two case studies.
Highlights
Nowadays, in a deeply mechanized and computerized global society, one of the challenging problems is to develop reliable control techniques for mechatronic and transportation processes, that can be implemented using modern digital and wireless technologies to force them to behave like skilled workers who work quickly, accurately, and cheaply, despite parametric variations, nonlinearities, and persistent disturbances
The mainly used tracking control laws are based on such well-known techniques as feedback linearization, inverse model, and model predictive control (MPC) ones
This paper presents a comprehensive and unified approach via majorant systems that can be successfully applied to numerous engineering systems (e.g., control of rolling mills, conveyor belts, automatic guided vehicles (AGVs), unicycles, cars, trains, ships, airplanes, drones, missiles, satellites, manufacturing and surgical robots)
Summary
In a deeply mechanized and computerized global society, one of the challenging problems is to develop reliable control techniques for mechatronic and transportation processes, that can be implemented using modern digital and wireless technologies to force them to behave like skilled workers who work quickly, accurately, and cheaply, despite parametric variations, nonlinearities, and persistent disturbances. The proposed controllers allow one to track reference signals r(t), with bounded i-th derivatives, with a tracking error norm e(t) = r(t) − y(t) less than a prescribed value, with a good transient phase, and feasible control signals without chattering, despite parametric and structural uncertainties, disturbances, and measurement errors. It holds for the norm of the first derivative, and, in some cases, of the second derivative, of the error e(t)
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