As the storage capacity of hard disk drives (HDDs) increases dramatically, the demand for positioning control accuracy of a read/write head of HDD is becoming more stringent. This paper presents a tuning methodology for fixed-structure controllers using the optimization. The tuning of a PID (Proportional plus Integral plus Derivative) controller for head positioning of an HDD is presented as an application example. The optimization problem of fixed-structure controllers can be locally solved by using the transformation into an synthesis problem of static output feedback control. Simulation and experimental results show the effectiveness of the proposed approach as a fine tuning method to improve controller performance without requiring profound knowledge and experiences in manual loop-shaping.
Issue Section:
Technical Briefs
Keywords:
disc drives,
hard discs,
servomechanisms,
three-term control,
position control,
feedback,
tuning,
optimisation
1.
Grochowski
, E. G.
, and Hoyt
, R. F.
, 1996
, “Future trends in hard disk drives
,” IEEE Trans. Magn.
, 32
, No. 5
, pp. 1850
–1854
.2.
Steinbuch
, M.
, and Norg
, M. L.
, 1998
, “Advanced motion control: An industrial perspective
,” European Journal of Control
, 4
, pp. 278
–293
.3.
Chew
, K. K.
, 1995
, “Control system challenges to high track density magnetic disk Storage
,” IEEE Trans. Magn.
, 32
, No. 3
, pp. 1799
–1804
.4.
Gahinet
, P.
, and Apkarian
, P.
, 1994
, “A linear matrix inequality approach to H∞ control
,” Int. J. Robust Nonlinear Control
, 4
, pp. 421
–448
.5.
Iwasaki
, T.
, and Skelton
, R. E.
, 1994
, “All controllers for the general H∞ control problem: LMI existence conditions and state space formulas
,” Automatica
, 30
, No. 8
, pp. 1307
–1317
.6.
A˚stro¨m
, K. J.
, Panagopoulos
, H.
, and Ha¨gglund
, T.
, 1998
, “Design of PI controllers based on non-convex optimization
,” Automatica
, 34
, No. 5
, pp. 585
–601
.7.
Grassi, E., and Tsakali, K., 1996, “PID controller tuning by frequency loop-shaping,” Proc. of the 35th Conf. on Decision and Control, Kobe, Japan, pp. 4776–4781.
8.
Kawabe, T., and Tagami, T., 1997, “A real coded genetic algorithm for matrix inequality design approach of robust PID controller with two degree of freedom,” Proc. of the 12th IEEE International Symposium on Intelligent Control, Istanbul, Turkey, pp. 119–124, July.
9.
Goh, K.-C., Safonov, M. G., and Papavassilopoulos, G. P., 1994, “A global optimization approach for the BMI problem,” Proc. of the 33rd Conf. on Decision and Control, Lake Buena Vista, FL, U.S.A, pp. 2009–2014, Dec.
10.
Wenk
, C. J.
, and Knapp
, C. H.
, 1980
, “Parameter optimization in linear systems with arbitrarily constrained controller structure
,” IEEE Trans. Autom. Control
, AC-25
, No. 3
, pp. 496
–500
.11.
Takahashi
, R. H. C.
, Peres
, P. L. D.
, and Ferreira
, P. A. V.
, 1997
, “Multiobjective H2/H∞ guaranteed cost PID design
,” IEEE Control Syst. Mag.
, 17
, No. 5
, pp. 37
–47
.12.
Collins
, E. G.
, Jr., Sadhukhan
, D.
, and Watson
, L. T.
, 1999
, “Robust controller synthesis via nonlinear matrix inequalities
,” Int. J. Control
, 72
, No. 11
, pp. 971
–980
.13.
Hassibi, A., How, J., and Boyd, S., 1999, “A path following method for solving BMI problems in control,” Proc. of the American Control Conference, San Diego, CA, pp. 1385–9.
14.
Nett, C. N., Bernstein, D. S., and Hadded, W. M., 1989, “Minimal complexity control law synthesis, part 1: Problem formulation and reduction to optimal static output feedback,” Proc. of the American Control Conf., Pittsburgh, PS, pp. 2056–2064, June.
15.
Bernstein, D. S., Haddad, W. M., and Nett, C. N., 1989, “Minimal complexity control law synthesis, part 2: Problem solution via H2/H∞ optimal static output feedback” Proc. of the American Control Conf., Pittsburgh, PS, pp. 2506–2511, June.
16.
Erwin
, R. S.
, Sparks
, A. G.
, and Bernstein
, D. S.
, 1998
, “Fixed-structure robust controller synthesis via decentralized static output feedback
,” Int. J. Robust Nonlinear Control
, 8
, pp. 499
–522
.17.
Syrmos
, V.
, Abdallah
, C.
, Dorato
, P.
, and Grigoriadis
, K.
, 1997
, “Static Output Feedback-A Survey
,” Automatica
, 33
, No. 2
, pp. 125
–137
.18.
Grigoriadis
, K. M.
, and Skelton
, R. E.
, 1995
, “Low order control design for LMI problems using alternating projection methods
,” Automatica
, 32
, No. 8
, pp. 1117
–1125
.19.
Geromel, J. C., de Souza, C. C., and Skelton, R. E., 1994, “LMI numerical solution for output feedback stabilization,” Proc. of the American Control Conference, Baltimore, MD, June, pp. 40–44.
20.
Iwasaki
, T.
, and Rotea
, M. A.
, 1997
, “Fixed-order scaled H∞ synthesis
,” Opt. Control Appl. Methods
, 18
, pp. 381
–398
.21.
Ghaoui
, L. E.
, Oustry
, F.
, and AitRami
, M.
, 1997
, “A cone complementarity linearization algorithm for static output-feedback and related problem
,” IEEE Trans. Autom. Control
, 42
, No. 8
, pp. 1171
–1176
.22.
Ibaraki, S., and Tomizuka, M., 2000, “H∞ Optimization of Fixed Structure Controllers,” Proc. of the 2000 International Mechanical Engineering Congress and Exposition, Orlando, FL, Nov.
23.
Gahinet, P., Nemirovskii, A., Laub, A. J., and Chilali, M., 1994, “The LMI Control Toolbox,” Proc. of the 33rd Conf. on Decision and Control, Lake Buena Vista, FL, pp. 2038–2041.
24.
Ding, J., Tomizuka, M., and Numasato, H., 2000, “Design and robustness analysis of dual stage servo system,” Proc. of the American Control Conf., Chicago, IL, pp. 2605–2609, June.
Copyright © 2001
by ASME
You do not currently have access to this content.
