Active vibration control for harmonic disturbances with time-varying frequencies through LPV gain scheduling

Abstract

A design method for a discrete-time ∞ H -optimal gain-scheduling controller that rejects harmonic disturbances with time-varying, known frequencies is presented. This is motivated by active vibration control and the controller is experimentally validated on an active vibration control test bench. The harmonic disturbances are modeled as outputs of a linear parameter varying system (LPV) where the frequencies are the varying parameters. The design method and the controller synthesis are discussed and experimental results for constant and time-varying frequencies are shown. The design method leads to a controller that stabilizes the closed-loop system even for arbitrarily fast changes in the disturbance frequencies. In the real-time experiment, the controller suppresses a disturbance consisting of six independent harmonics with frequencies that vary over ranges of 20 Hz.

Rejection of Harmonic and Transient Disturbances of a Smart Structure With Piezoelectric Actuators

“…It might affect the disturbance attenuation for fast changes in the disturbance frequency, although this simplifi ed model has been used for the rejection of time-varying frequencies (Shu et al 2011, Ballesteros and Bohn 2011a, 2011b, Heins et al 2011, 2012a, 2012b, Duarte et al 2013. In most practical applications with time--varying frequencies, however, the measured frequency will not correspond exactly to the instantaneous frequency due to measurement delays and the transmission of the disturbance to the plant.…”

“…Dettori and Scherer (2001), Du et al (2003), Bohn (2011a, 2011b), Shu et al (2011) and Duarte et al (2012Duarte et al ( , 2013 employed gain-scheduling output-feedback controllers. In the work done by Heins et al (2011Heins et al ( , 2012aHeins et al ( , 2012b and Ballesteros et al (2012) gain--scheduling observer-based controllers were implemented.…”

LPV Gain-Scheduled Observer-Based State Feedback for Active Control of Harmonic Disturbances with Time-Varying Frequencies

“…For example, for LPV systems where the parameter dependence is expressed as a linear fractional transformation (LFT), the uncertain parameters also enter the controller through an LFT [2]. For harmonic disturbances, an LPV-LFT approach has been suggested and applied in real time by Ballesteros & Bohn [4,5] and Shu et al [26]. Another example for direct scheduling is a controller based on a time-varying state estimator, for example a Kalman filter, where the scheduling parameters enter the controller through the recursive equations for the state estimate and the error covariance matrix.…”

“…In direct scheduling, the dependence of the controller on the scheduling parameter does not correspond to a simple interpolation or switching law [2,4,5,21,23,26]. For example, for LPV systems where the parameter dependence is expressed as a linear fractional transformation (LFT), the uncertain parameters also enter the controller through an LFT [2].…”

“…It is therefore not surprising that the continuous-time controllers of Darengosse & Chevrel [10], Du et al [12], Kinney & de Callafon [19] and Köroglu & Scherer [23] are only tested in simulation studies with a very simple system as a plant and a single frequency in the disturbance signal. The design methods that are tested in real time are usually formulated in discrete time [4,5,7,8,16,17,20,21,26]. Exceptions are Witte et al [28] and Balini et al [6], who designed continuous-time controllers which then are approximately discretized.…”