Compensation of Unknown Multiharmonic Disturbance for Nonlinear Plant with
Delay in Control*
Anton A. Pyrkin, Alexey A. Bobtsov, Sergey A. Chepinskiy, and Yuriy A. Kapitanyuk
Department of Control Systems and Informatics,
Saint-Petersburg State University of Information Technologies Mechanics and Optics,
Kronverkski, 49, Saint-Petersburg, 197101, RUSSIA
(e-mail: a.pyrkin@gmail.com, bobtsov@mail.ru, chepinsky_s@hotmail.com, yura.kapitanyuk@gmail.com).
Abstract: In this paper a new approach for cancellation of a multiharmonic 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 numerical example is presented to illustrate theoretical result and the reaction
wheel pendulum on a movable platform is considered as the plant to demonstrate that proposed approach is
realizable and can be plugged in practice. 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.
I. INTRODUCTION
In this article a new approach for rejection of
multiharmonic disturbance with unknown parameters acting
on a nonlinear plant is proposed. There are a number of
papers dealing with control in condition of uncertain
disturbance
using only input
and output measurable signals.
The paper is focused on the design of the adaptive scheme
to identify the frequency of the sinusoid. Many different
approaches exist for adaptive identification of unknown
sinusoid, see, for example, (Aranovskiy et al. (2010),
Bobtsov (2008)-Bobtsov et al. (2009), Hou (2005), Hsu et al.
(1999), Marino et al. (2003), Xia (2002), Pyrkin et al.
(2010)). 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), Bobtsov
(2008), Hou (2005)), and the case of multiple sinusoids with
different frequencies is presented in (Bodson et al. (1997),
Xia (2002)).
This approach is based on the ideas introduced in (Bobtsov
(2008)-Bobtsov et al. (2009), Nikiforov (1998)) and removes
various limitations of these designs. In particular, (Nikiforov
(1998)) and (Bobtsov (2008)) deal with a minimum-phase
plant, the scheme from (Bobtsov et al. (2008)) is limited to
stable plants of relative degree one but for unknown plant,
and the result presented in (Bobtsov et al. (2009)) applies to
stable plants of arbitrary relative degree. Here, our
disturbance rejection scheme applies to plants with non-
minimum phase and arbitrary relative degree, while the
dynamic order of the adaptive law is equal to three for each
harmonic, which compares favorably with known
* This work was supported by the RFBR (projects 09-08-
00139-a), the ADTP (project 2.1.2/6326), and the FTP
(projects NK-92P/5: P498/05.08.2009, NK-495P/1:
P127/13.04.2010).
results (Hou (2005), Marino et al. (2003), Xia (2002)).
To demonstrate the efficiency of control law
that can reject the unknown disturbance in condition of input
delay we construct the special mechatronic control kit (see
Fig. 1 and Fig. 2) and consider stabilization problem for
mechatronic plant represented by the reaction wheel
pendulum on movable platform. The disturbance is created
by hand moving platform in horizontal plane. Complex of
Mechatronics system Inc., disposable of Cybernetics and
Control System Laboratory of SPbSU ITMO has been used
to demonstrate efficiency of proposed algorithm (see Fig. 1).
Fig. 1. Mechatronic Control Kit
Fig. 2. Schematic sketch of the pendulum system
8th IFAC Symposium on Nonlinear Control Systems
University of Bologna, Italy, September 1-3, 2010
978-3-902661-80-7/10/$20.00 © 2010 IFAC 481 10.3182/20100901-3-IT-2016.00065