Linear Observer‐Based Active Disturbance Rejection Control of the Omnidirectional Mobile Robot

Abstract

This article describes the design of a linear observer‐linear controller‐based robust output feedback scheme for output reference trajectory tracking tasks in an omnidirectional mobile robot. The unknown, possibly state‐dependent, additive nonlinearities influencing the input‐output tracking error dynamics are modeled as an absolutely bounded, additive, unknown “time‐varying disturbance” input signal. This procedure simplifies the system tracking error description to that of three independent chains of second order integrators with, known, position‐dependent control gains. These simplified systems are additively perturbed by the unknown, smooth, time‐varying signal which is proven to be trivially observable. Generalized proportional integral (GPI) observers, are shown to naturally estimate, in an arbitrarily close manner, the unknown perturbation input of the simplified system and a certain number of its time derivatives. This information is used to advantage on the linear, observer‐based, feedback controller design via a simple cancellation effort. The results are implemented on a laboratory prototype of an omnidirectional mobile robot.

Control GPI-repetitivo para sistemas lineales con incertidumbre/variación en los parámetros

“…34, enero-junio de 2015, pp. [13][14][15][16][17][18][19][20][21][22][23][24] rriente directa, ampliamente utilizados para el control de movimiento; circuitos RLC, base fundamental de muchos dispositivos eléctricos; modelos de tanques hidráulicos para el control de nivel.…”

“…Ya se reportan resultados experimentales de la utilización de la técnica GPI para el manejo de dinámicas no modeladas e incertidumbre en los parámetros con excelentes resultados en su desempeño [14]- [17], que dieron motivación a esta investigación y garantía de los resultados esperados con este trabajo. Este trabajo forma parte de una serie de trabajos, aun preliminares, que buscan explorar capacidades y funcionalidades de la combinación de ambas técnicas con el fin de alcanzar sistemas de control que sean capaces de gestionar adecuadamente la incertidumbre/variación de planta.…”

Comparison of linear and nonlinear active disturbance rejection control method for hypersonic vehicle

“…However, compared with the traditional ADRC method which is nonlinear, a linear active disturbance rejection control (LADRC) method has also been developed for controller design. The experiment results of [17,18,19,20,21] which used linear ADRC method all have achieved good results. In this paper, we clarify and analysis the structure differences, characteristic differences etc.…”

“…However, the ADRC method and the LADRC method both have more tuning parameters than the traditional PID method, while the appropriate controller parameters depend on the experiences of experts. Sometime, the number of the ADRC method parameters can be reduced to one or two [16,20]. To compare the traditional ADRC method and the LADRC method clearly, this paper does not reduce parameters.…”

Dynamic surface tracking controller design for a constrained hypersonic vehicle based on disturbance observer

“…For ESO, it only has a firstorder extension, that is, one integrator to estimate the disturbance. 34 But GPI observer is characterized by a higher dimensional extension, 35 and thereby has a better estimation performance of disturbances than ESO. Besides, GPI observers are most naturally applicable to the control of perturbed differentially flat nonlinear systems with measurable flat outputs.…”