Cancellation of Unknown Harmonic Disturbance for Nonlinear System with Input Delay* Anton A. Pyrkin 1 , Alexey A. Bobtsov 1, 2 , Artem S. Kremlev 1 , and Stanislav V. Aranovskiy 1 The Department of Control Systems and Informatics, Saint Petersburg State University of Information Technologies Mechanics and Optics, Kronverkskiy av. 49, Saint Petersburg, 197101 Russia 2 Laboratory "Control of Complex Systems", Institute for Problems of Mechanical Engineering, Bolshoy pr. V.O. 61, St.Petersburg, 199178, Russia E-mail: a.pyrkin@gmail.com, bobtsov@mail.ru, kremlev_artem@mail.ru Abstract: In this paper a new approach for cancellation of a biased harmonic disturbance is proposed. Compared with a number of known results in this paper the disturbance compensation 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 reaction wheel pendulum on a movable platform is considered as the plant to demonstrate how proposed approach can be plugged. Created by hand disturbance moves the platform in horizontal surface and the pendulum is oscillating. The second goal of this work is the development of mechatronic applications using in education. Keywords: Disturbance cancellation, time-delay systems, decision feedback, nonlinear control, output regulation, SISO systems, robust control, robustness. 1. INTRODUCTION In this article a new approach for rejection of the biased harmonic disturbance with unknown parameters acting on a nonlinear plant is proposed. There are a number of papers dealing with control in condition of an uncertain disturbance         using only the input and the output measurable signals. The paper is focused on the design of the adaptive scheme to identify the frequency of the sinusoid. For plants with no input delay many different approaches exist for adaptive identification of unknown sinusoid, see, for example, (Bobtsov, 2008: Bobtsov et al., 2008, 2009, 2011; Hou, 2005; Hsu et al., 1999; Marino et al., 2003; Xia, 2002). Some of these approaches are not restricted to the case of a single sinusoid, in particular, a biased sinusoidal signal is considered in (Bobtsov et al., 2005; Pyrkin et al., 2010, 2011; Bobtsov, 2008; Hou, 2005), and the case of multiple sinusoids with different frequencies is presented in (Xia, 2002; Bobtsov et al., 2010). This approach is based on the ideas introduced in (Aranovskiy et. al., 2010; Bobtsov, 2008; Bobtsov et al., 2008, 2009; Nikiforov, 1998; Pyrkin, 2010) and removes various limitations of these designs. In particular, (Nikiforov, 1998) and (Bobtsov et. al., 2008, 2011) deal with a minimum-phase plant, the scheme from (Bobtsov et al., 2008, 2011) is limited to strictly minimum phase plants but for unknown plant, and the result presented in (Bobtsov et al., * The article is supported by the Russian Fund of Fundamental Researches (grant 09-08-00139-a), Federal Special Program “Scientific and Research and Educational specialists of innovational Russia” for 2009-2013 (projects P498, 8.08.2010 and P127, 13.04.2010), and the General Motors Global Research and Development (ITMO-GM-Grant-2010-NV888) 2009; Pyrkin 2010) applies to plants of any relative degree. Here, our disturbance rejection scheme applies to unstable plants with non-minimum phase and arbitrary relative degree, while the dynamic order of the adaptive law is equal to three, which compares favorably with known results (Hou, 2005; Marino et al., 2003; Xia, 2002). For demonstrating efficiency of proposed algorithm the reaction wheel pendulum on a movable platform is considered as plant and disturbance is created by hand moving platform in horizontal plane. Complex of Mechatronics system Inc., disposable of Cybernetics and Control System Laboratory of Saint Petersburg State University of Information Technologies Mechanics and Optics has been used to demonstrate efficiency of proposed algorithm (see Fig. 1). Fig. 1. Mechatronic Control Kit. Mechanical part of the plant represents a single-link pendulum fixed at the pivot pin with the reaction wheel situated at the opposite end of the pendulum. The platform of the pendulum is movable (see Fig. 2). Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011 Copyright by the International Federation of Automatic Control (IFAC) 1516