Cancelation of unknown multiharmonic disturbance for nonlinear plant with input delay

Abstract

SUMMARYIn this paper, a new approach for cancelation of a multiharmonic disturbance is proposed. Compared with a number of known results in this paper, the disturbance cancelation problem is solved when the output variable is measured only, a relative degree of the plant is arbitrary and the control channel has delay. The numerical example is presented to illustrate the theoretical result. The reaction wheel pendulum on a movable platform is considered as the plant to demonstrate that the proposed approach is realizable and can be plugged in practice. The second goal is the development of mechatronic applications for use in education. Copyright © 2011 John Wiley & Sons, Ltd.

Rejection of sinusoidal disturbance approach based on high-gain principle

“…Thus, identification scheme of the parameter ω can be based on [2], [3], [8]- [10], [12], [27], [28]. Following the ideas [13], [27], [28] we introduce the second order filter…”

“…In contrast to [21] in [7] the same task for non-minimum phase plant with known parameters, but arbitrary relative degree was solved. In [10], [12], [28] improved approach was extended for time-delay systems with known parameters. Works [8], [11] are devoted to output control with sinusoidal disturbance rejection under conditions of plant parametric uncertainty.…”

An Adaptive-Observer-Based Robust Estimator of Multi-sinusoidal Signals

“…The adaptive observer is another key methodology exploited to track multiple frequencies because of its notable feature in terms of stability: global or semi-global stability is ensured in most cases (see [23], [24], [25], [26], [27] and [28]). In particular, [26] presents a simplified global stability analysis by using contraction theory rather than traditional Lyapunov analysis; and, on the other hand, [28] proposes a hybrid observer to identify the n frequencies from a multi-frequency signal with saturated amplitudes.…”

An adaptive observer-based estimator for multi-sinusoidal signals

“…However, due to re-parametrization, the estimated frequencies are usually not directly adapted. Instead, the parameter adaptation laws regard a set of parameters related in a nonlinear to the frequency such as the coefficients of the characteristic polynomial of the autonomous signal-generator system (see [14], [15], [16], [17], [18] and [19]). Among these methods, [15], [17], [18] are capable to handle a biased multi-sinusoidal signal, while [19] has been applied in a nonlinear plant for disturbance cancellation.…”

“…Instead, the parameter adaptation laws regard a set of parameters related in a nonlinear to the frequency such as the coefficients of the characteristic polynomial of the autonomous signal-generator system (see [14], [15], [16], [17], [18] and [19]). Among these methods, [15], [17], [18] are capable to handle a biased multi-sinusoidal signal, while [19] has been applied in a nonlinear plant for disturbance cancellation. In addition to the aforementioned adaptive observer-based techniques, an asymptotically convergent estimator for n-frequencies using contraction theory is proposed in [20] Motivated by the adaptive observer proposed in [21] and its extension to the single sinusoidal case [13], the presented paper deals with a new methodology that is capable to offer reliable estimates of amplitudes, frequencies, phases and offset from a biased signal comprising n sinusoids.…”