European Journal of Control (2010)2:129–139 # 2010 EUCA DOI:10.3166/EJC.16.129–139 Identification of Frequency of Biased Harmonic Signal Stanislav Aranovskiy 1 , Alexey Bobtsov 1,  , Artem Kremlev 1,1 , Nikolay Nikolaev 1 , Olga Slita 2 1 Department of Control Systems and Informatics, Saint-Petersburg State University of Information Technologies Mechanics and Optics, Kronverkski av. 49, 197101, Saint-Petersburg, Russia; 2 Department of Mechatronics and Robotics, Baltic State Technical University, 1-st Krasnoarmeiskaya st. 1, 190008, Saint-Petersburg, Russia We consider a problem of identification of unknown frequency of a biased sinusoidal signal yðtÞ¼ ' 0 þ ' sinð! t þ 0Þþ ðtÞ with bounded disturbance or har- monic noise ðtÞ. A new proposed approach to estimation of frequency of biased sinusoidal signal is robust with regard to unaccounted disturbances, which are present in measurement of effective signal. Unlike known analogs, this approach allows to regulate time of estimation of unknown frequency !. The proposed approach also allows online amplitude and bias estimation. The proposed identification algorithm has smaller dimension than other known analogs. Keywords: Identification, Harmonic signal, Robust- ness, Estimation, Disturbance 1. Introduction We consider the problem of frequency identification of sinusoidal signal yðtÞ¼ ' 0 þ ' sinð! t þ 0Þþ ðtÞ for any unknown constant values ' 0 , ', 0 and boun- ded disturbance ðtÞ. Problem of frequency identi- fication of a sinusoidal signal is a very important basic problem, which has different applications in theoret- ical and engineering disciplines, for instance, in rota- tional mechanical processes like induction motor, in active noise and vibration control, in helicopters, disk drivers and magnetic bearings [4, 8, 16, 26]. The estimation problem is an important problem in sys- tems theory with applications in diverse fields. Most of the existing solutions have been sought from the perspective of signal processing and/or telecommuni- cation: line enhancers [23], finite impulse response filters [21], infinite impulse response filters or notch filters [14, 18, 19] and frequency locket loop [11]. The reading of data in magnetic and optical disk drivers requires a periodic movement of the reading device, due to the eccentricity of the tracks. The effect of disturbances originating from external sources must be reduced in active noise and vibration control [5]. These sources are often rotating machines producing periodic noise and/or vibration [6]. The problem of active noise and vibration control in system, described by equation yðsÞ¼ PðsÞðuðsÞþ dðsÞÞ, where uðsÞ and dðsÞ are Laplace transform of the controller output and disturbance signals, is of particular interest. In these systems, dðtÞ is an offending noise or vibration source and PðsÞ is the transfer function of output- actuator-to error-sensor propagation path [18]. Often, the noise source consists mainly of periodic compo- nents due to rotating machinery generating the un- desired noise signal. Examples of such noises include engine noise in turboprop aircraft, engine noise in automobiles and ventilation noise in HVAC system. There are few approaches how to solve the problem of disturbance attenuation – indirect approach (see Fig. 1) and direct approach. In order to use indirect approach, it is necessary to know frequency of disturbing influence. In practice, the frequency of disturbance is usually not known and may even vary during operation. It is often impossible *Correspondence to: A. Bobtsov, E-mail: bobtsov@mail.ifmo.ru Received 2 October 2008; Accepted 9 September 2009 Recommended by S.M. Savaresi, A.J. van der Schaft