Improving Intersample Behavior in Discrete-Time System Inversion: With Application to LTI and LPTV Systems

Discrete-time system inversion for perfect tracking goes at the expense of intersample behavior. The aim of this article is the development of a discrete-time inversion approach that improves continuous-time performance by also addressing the intersample behavior. The approach balances the on-sample and intersample behavior and provides a whole range of new solutions, with stable inversion and multirate inversion as special cases. The approach is successfully applied to a linear periodically time-varying system in both simulations and experiments. The approach improves the intersample behavior through discrete-time system inversion and outperforms existing approaches.

[1]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[2]  Tae Tom Oomen,et al.  Resource-efficient ILC for LTI/LTV systems through LQ tracking and stable inversion: enabling large feedforward tasks on a position-dependent printer , 2016 .

[3]  Tom Oomen,et al.  Suppressing intersample behavior in Iterative Learning Control , 2008, 2008 47th IEEE Conference on Decision and Control.

[4]  Richard H. Bartels,et al.  Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4] , 1972, Commun. ACM.

[5]  Tae Tom Oomen,et al.  On inversion-based approaches for feedforward and ILC , 2017 .

[6]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

[7]  Atsuo Kawamura,et al.  Perfect tracking control based on multirate feedforward control with generalized sampling periods , 2001, IEEE Trans. Ind. Electron..

[8]  Hiroshi Fujimoto,et al.  Tracking control method for a plant with continuous time unstable zeros: Finite preactuation based on state trajectory regeneration by using redundant order polynomial , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[9]  Naim A. Kheir,et al.  Control system design , 2001, Autom..

[10]  Yuen Kuan Yong,et al.  Monolithic Piezoelectric Insect With Resonance Walking , 2018, IEEE/ASME Transactions on Mechatronics.

[11]  Hiroshi Fujimoto,et al.  Preactuated Multirate Feedforward Control for Independent Stable Inversion of Unstable Intrinsic and Discretization Zeros , 2019, IEEE/ASME Transactions on Mechatronics.

[12]  Jinjun Shan,et al.  Modeling and Inverse Compensation for Coupled Hysteresis in Piezo-Actuated Fabry–Perot Spectrometer , 2017, IEEE/ASME Transactions on Mechatronics.

[13]  H. Fujimoto,et al.  Preactuated multirate feedforward for a high-precision stage with continuous time unstable zeros , 2017 .

[14]  Hiroshi Fujimoto,et al.  Multirate feedforward control with state trajectory generation based on time axis reversal for plant with continuous time unstable zeros , 2016, 2016 IEEE International Conference on Advanced Intelligent Mechatronics (AIM).

[15]  Santosh Devasia,et al.  Output tracking with nonhyperbolic and near nonhyperbolic internal dynamics: helicopter hover control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[16]  R. Sarpong,et al.  Bio-inspired synthesis of xishacorenes A, B, and C, and a new congener from fuscol† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc02572c , 2019, Chemical science.

[17]  Tom Oomen,et al.  LPTV loop-shaping with application to non-equidistantly sampled precision mechatronics , 2018, 2018 IEEE 15th International Workshop on Advanced Motion Control (AMC).

[18]  Tae Tom Oomen,et al.  Stable inversion of LPTV systems with application in position-dependent and non-equidistantly sampled systems , 2019, Int. J. Control.

[19]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[20]  Yoichi Hori,et al.  High-performance servo systems based on multirate sampling control $ , 2002 .

[21]  T. Hughes,et al.  Signals and systems , 2006, Genome Biology.

[22]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[23]  Masayoshi Tomizuka,et al.  Zero Phase Error Tracking Algorithm for Digital Control , 1987 .

[24]  Israel Gohberg,et al.  Schur complements and state space realizations , 2005 .

[25]  B. Paden,et al.  Nonlinear inversion-based output tracking , 1996, IEEE Trans. Autom. Control..

[26]  H. Fujimoto,et al.  Basic examination on simultaneous optimization of mechanism and control for high precision single axis stage and experimental verification , 2008, 2008 34th Annual Conference of IEEE Industrial Electronics.

[27]  Bassam Bamieh,et al.  A general framework for linear periodic systems with applications to H/sup infinity / sampled-data control , 1992 .

[28]  Lennart Blanken,et al.  Batch-to-Batch Rational Feedforward Control: From Iterative Learning to Identification Approaches, With Application to a Wafer Stage , 2017, IEEE/ASME Transactions on Mechatronics.

[29]  Kevin L. Moore,et al.  Capabilities and limitations of multirate control schemes , 1993, Autom..

[30]  W. Messner,et al.  Cancellation of Discrete Time Unstable Zeros by Feedforward Control , 1994 .

[31]  Yutaka Yamamoto,et al.  A function space approach to sampled data control systems and tracking problems , 1994, IEEE Trans. Autom. Control..