On the linear Active Rejection Control of Thomson's Jumping Ring

Abstract

The problem of tracking a smooth time-varying reference trajectory for Thomson's ring is addressed from the perspective of Active Disturbance Rejection Control (ADRC). The tracking controller is designed on the basis of the tangent linearization model of the nonlinear system around a constant equilibrium point. The large height deviations, outside the region of validity of the approximate linearization, trigger the effect of unknown nonlinearities and exogenous perturbations. These disturbances are properly on-line estimated and canceled with the help of a linear extended observer-linear controller based output feedback control scheme. Experimental results are presented which validate the effectiveness of the proposed control scheme.

Active Disturbance Rejection Control for Reference Trajectory Tracking Tasks in the Pendubot System

“…Similarly, this result holds for all its time derivatives modulo a small error due to the approximate nature of signal z 1 with respect to the actual total disturbance. The coefficients for the ESO are chosen in accordance with the procedure developed in [28] this methodology for tuning gains has been successfully applied in [29] and [30]. Consider a characteristic polynomial p(s) of the form:…”

On the sliding mode control of MIMO nonlinear systems: An input‐output approach

“…A slight modification of GPI control, known as flat filtering control, consists in using a standard classical feedback compensation block, inspired in the GPI controller, adding an extra suitable linear combination of iterated integrations of the output error, beyond those required to properly compensate the effects of neglected arbitrary initial conditions. This modification allows the resulting controller to handle, and efficiently attenuate, the effects of arbitrary additive disturbances in closed loop, thus rendering a practical (ie, closely approximate) solution to output reference trajectory tracking problems in linear and, more surprisingly, in nonlinear flat and controllable linearizations of non flat systems …”

“…This modification allows the resulting controller to handle, and efficiently attenuate, the effects of arbitrary additive disturbances in closed loop, thus rendering a practical (ie, closely approximate) solution to output reference trajectory tracking problems in linear and, more surprisingly, in nonlinear flat and controllable linearizations of non flat systems. [6][7][8][9][10][11][12][13] Multivariable (MIMO) sliding mode control of smooth nonlinear systems, of state dimension n, typically contain a certain number, m, of independent control inputs in charge of nonconflicting intelligent individuals. Sliding mode control, for the MIMO case, assumes the prescription of m functionally independent, smooth, switching manifolds with an n − m dimensional smooth, nonempty, intersection.…”

On frequency response analysis of GPIO

“…Based on the rigorous theoretical foundation and good performances of ESO, ADRC has been successfully applied in a number of industrial areas, such as motion control, DC-DC power converter, inverted pendulum systems, and integrated flight-propulsion control, and so on ( [20]- [23] In contrast, the Generalized Proportional Integral Observers (GPIO), also known as the high order ESO, which is used to estimate the aggregate effects of the exogenous and endogenous additive disturbances in a self-updated manner [25], could make the LESO error dynamics of asymptotic convergence for a class of disturbances that are time-varying but can be expressed in time polynomial function forms [26]- [27]. The GPIO technique has been successfully applied to chaotic systems [28]- [29], induction motors [30]- [31], robots [32]- [33] and many other fields [34]- [35]. The objective of this paper is to explore the good tracking performances and disturbances rejection ability using frequency-domain analysis and compare them under different numbers of extended state variables in GPIO, which will be of value for the engineers and researchers.…”