Probabilistic analytic center cutting plane method in robust $${\mathcal{H}}_2$$H2 track following control

The present paper addresses the design of discrete time robust $${\mathcal{H}}_2$$H2 track following dynamic output feedback controller for hard disk drives where uncertain parameters enter in a non-linear fashion into plant description. Uncertain parameters are considered as random variables with uniform distribution. The controller is designed to meet the performance specification with desired probabilistic levels (accuracy and confidence). The design is benefited from convex optimization in design parameter space and randomization in the uncertainty space. A localization method based on analytic center cutting plane algorithm is employed in order to find the probabilistic robust feasible solution. As a result of randomization, the computational complexity of the algorithm does not depend on the number of uncertain parameters and no conservatism is introduced while handling uncertain parameters. The effectiveness of the designed controller is verified through simulation as well as experiment.

[1]  Johan Efberg,et al.  YALMIP : A toolbox for modeling and optimization in MATLAB , 2004 .

[2]  Roberto Horowitz,et al.  Robust Control Synthesis Techniques for Multirate and Multisensing Track-Following Servo Systems in Hard Disk Drives , 2010 .

[3]  Roberto Horowitz,et al.  Dual-stage track-following servo design for hard disk drives , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[4]  Michel Verhaegen,et al.  Robust output-feedback controller design via local BMI optimization , 2004, Autom..

[5]  Stephen P. Boyd,et al.  Method of centers for minimizing generalized eigenvalues , 1993, Linear Algebra and its Applications.

[6]  Andrew Packard,et al.  The complex structured singular value , 1993, Autom..

[7]  R. Tempo,et al.  Probabilistic robustness analysis: explicit bounds for the minimum number of samples , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[8]  Giuseppe Carlo Calafiore,et al.  Uncertain convex programs: randomized solutions and confidence levels , 2005, Math. Program..

[9]  Yasuaki Oishi,et al.  Probabilistic design of a robust state-feedback controller based on parameter-dependent Lyapunov functions , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[10]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[11]  Tong Heng Lee,et al.  Hard Disk Drive Servo Systems , 2002 .

[12]  Jean-Philippe Vial,et al.  Convex nondifferentiable optimization: A survey focused on the analytic center cutting plane method , 2002, Optim. Methods Softw..

[13]  Minyue Fu,et al.  Worst-case properties of the uniform distribution and randomized algorithms for robustness analysis , 1998, Math. Control. Signals Syst..

[14]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[15]  Giuseppe Carlo Calafiore,et al.  A probabilistic analytic center cutting plane method for feasibility of uncertain LMIs , 2007, Autom..

[16]  Robert F. Stengel,et al.  Some Effects of Parameter Variations on the Lateral-Directional Stability of Aircraft , 1980 .

[17]  John E. Mitchell,et al.  Polynomial Interior Point Cutting Plane Methods , 2003, Optim. Methods Softw..

[18]  Wei Hua,et al.  Direct Monte Carlo simulation of air bearing effects in heat-assisted magnetic recording , 2011 .

[19]  Tong Heng Lee,et al.  Hard Disk Drive Servo Systems (Advances in Industrial Control) , 2006 .

[20]  Giuseppe Carlo Calafiore,et al.  RACT: Randomized Algorithms Control Toolbox for MATLAB , 2008 .

[21]  Qing-Guo Wang,et al.  On the sample complexity of uncertain linear and bilinear matrix inequalities , 2013, 52nd IEEE Conference on Decision and Control.

[22]  Qing-Guo Wang,et al.  A statistical learning theory approach for uncertain linear and bilinear matrix inequalities , 2013, Autom..

[23]  Qing-Guo Wang,et al.  Sequential randomized algorithms for sampled convex optimization , 2013, 2013 IEEE Conference on Computer Aided Control System Design (CACSD).

[24]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[25]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[26]  Roberto Tempo,et al.  Probabilistic robust design with linear quadratic regulators , 2001, Syst. Control. Lett..

[27]  M. Overton.  On minimizing the maximum eigenvalue of a symmetric matrix , 1988 .

[28]  J. Geromel,et al.  Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems , 2002 .

[29]  R. Tempo,et al.  Randomized Algorithms for Analysis and Control of Uncertain Systems , 2004 .

[30]  Michel Verhaegen,et al.  An ellipsoid algorithm for probabilistic robust controller design , 2003, Syst. Control. Lett..