Abstract
Periodicity frequently occurs in hard disk drives (HDDs) whose servo systems with periodic phenomena can be usually modeled as linear periodically time-varying (LPTV) systems. This paper discusses optimal <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$H_{\infty}$</tex></formula> control synthesis for discrete-time LPTV systems via discrete Riccati equations. First, an explicit minimum entropy <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$H_{\infty}$</tex> </formula> controller for general time-varying systems is obtained. Subsequently, the developed control synthesis algorithm is applied to LPTV systems and it is shown that the resulting controllers are periodic. The proposed control synthesis technique is evaluated through both single and multirate optimal <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"> $H_{\infty}$</tex></formula> track-following control designs. The single-rate servo design shows that our proposed control synthesis technique is more numerically robust in calculating optimal <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"> $H_{\infty}$</tex></formula> controllers for discrete-time linear time-invariant systems than the MATLAB function of “hinfsyn,” while the multirate servo design validates its ability of synthesizing multirate controllers to achieve the robust performance of a desired error-rejection function. Moreover, an experimental study—in which the developed control synthesis algorithm on a real HDD with missing position error signal sampling data is implemented—further demonstrates its effectiveness in handling LPTV systems with a large period and attaining desirable disturbance attenuation.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
