Abstract
The so called “Quantitative Pole Placement” (QPP) identified in the context of guaranteed tracking in the sens of spheres is considered. In the prior literature this pole-placement problem was treated in a somewhat adhoc way. The primary purpose of the present work therefore is to propose a systematic procedure for such pole placement. The approach to the problem is based on a generalization of the standard LQ problem formulation. The preferred pole locations that minimize a crucial operator norm needed for the success of the QPP formulation are shown to be a perturbed version of the Butterworth pole configuration. The results are applied to a 3 d.o.f. robotic manipulator for illustrating the evolving methodology. At the center of the overall design philosophy is the need to directly satisfy performance specifications in uncertain. nonlinear systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barnard, R.D., 1980, “Controller Design Criteria for Servo Tracking in Uncertain System,” Proceedings of 23rd Midwest Symposium on Circuits and Systems, Toledo, OH.
Barnard, R.D. and Jayasuriya, S. 1982, “Controller Design for Uncertain Nonlinear Sytems,” Proceeding of 1982 American Control Conference, Alington, VA.
Freund, E., 1982, “Fast Nonlinear Control with Arbitrary pole-placement for Industrial Robots and Manipulators,” Int. J. of Robotics Research, Vol. 1, pp. 65–78.
Horowitz, I.M., 1969, “Optimum Linear Adaptive Design of Dominant-Type Systems with Large Paramenter Variations,” IEEE Trans. Automatic Control, AC-14, pp. 261–269.
Horowitz, I.M., 1976, “Synthesis of Feedback Systems with Nonlinear Time-Varying Uncertain Plants to Satisfy Quantitative Performance Specifications,” IEEE Proceedings, Vol. 64, pp. 123–130.
Horowitz, I.M, 1982, “Quantitative Feedback Theory,” IEE Proc. 129, D, pp. 215–226.
Jayasuriya, S. and Kee, C.D., 1988, “A Circle Type Criterion for the Synthesis of Robust Tracking Controllers,” Submitted to International Journal of Control, Vol. 48, No. 3, pp. 865–886.
Jayasuriya, S., Rabins, M.J. and Barnard, R.D., 1984, “Guaranteed Tracking Behaviour in the Sense of Input-Output Spheres for Systems with Uncertain Parameters,” J. of Dyn. Syst. Meas. Control. Vol. 106, pp. 273–279.
Kee, C.D., 1987, “A Quantitative Ploe-Placement Approach for Robust Tracking,” Ph. D. Dissertation, Michigan State Univ., East Lansing, MI 48823.
Kwakernaak, H. and Sivan, R., 1972, Linear Optimal Control Systems, Wiley-Interscience, New York.
Leitmann, G., 1979, “Guaranteed Asymptotic Stability for some Linear Systems with Bounded Uncertainties,” ASME J. of Dyn. Syst. Meas. Control, Vol. 101, pp. 212–216.
Leitmann, G., 1981, “On the Efficacy of Nonlinear Control in Uncertain Linear Systems,” J. of Dyn. Syst. Meas. Control. 103, pp. 95–102.
Usoro, P.E., Schweppe, F.C., Wormley, D.N. and Gould, L.A. 1982, “Ellipsoidal Set-Theoretic Control Synthesis,” Journal of Dynamic Systems, Measurement, and Control, Vol. 104, No. 4.
Zames, G., 1981, “Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses,” IEEE Trans. Automatic Control, AC-26, pp. 301–320.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kee, C.D., Hwang, W.G. & Kim, J.Y. Perturbed Butterworth pole patterns for tracking in the sense of spheres. KSME Journal 4, 141–149 (1990). https://doi.org/10.1007/BF02954036
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02954036