Output feedback control for unknown LTI systems driven by unknown periodic disturbances

This paper considers unknown minimum-phase LTI systems with known relative degree and system order. The main aim is to reject the unknown, unmatched sinusoidal disturbances and make the output track a given trajectory with the output feedback. The essence of the control design is composed of disturbance parametrization, K-filter technique and adaptive backstepping procedure. Firstly, the unmeasured system states are represented in terms of filtered input and output signals. Then, the disturbance information in the output signal is parametrized and the problem is converted to an adaptive control problem. After that, the K-filter approach is employed to redefine the system states that enable to use a backstepping technique. An adaptive output feedback controller is designed recursively. It is proven that the equilibrium at the origin is globally uniformly stable and the output signal tracks the reference signal asymptotically. Finally, the effectiveness of the controller is illustrated with a numerical simulation. The robustness of the closed loop system with respect to an additive unmodelled noise is also discussed.

[1]  R. Marino,et al.  Adaptive disturbance rejection for unknown stable linear systems , 2016 .

[2]  Riccardo Marino,et al.  Disturbance cancellation for linear systems by adaptive internal models , 2013, Autom..

[3]  Miroslav Krstic,et al.  Adaptive wave cancelation by acceleration feedback for ramp-connected air cushion-actuated surface effect ships , 2013, Autom..

[4]  Miroslav Krstic,et al.  State derivative feedback for adaptive cancellation of unmatched disturbances in unknown strict-feedback LTI systems , 2014, Autom..

[5]  Marc Bodson,et al.  Adaptive Algorithms for the Rejection of Sinusoidal Disturbances Acting on Unknown Plants , 2010, IEEE Transactions on Control Systems Technology.

[6]  E. Davison.  The robust control of a servomechanism problem for linear time-invariant multivariable systems , 1976 .

[7]  G. Kreisselmeier.  Adaptive observers with exponential rate of convergence , 1977 .

[8]  Scott C. Douglas,et al.  Active noise control for periodic disturbances , 2001, IEEE Trans. Control. Syst. Technol..

[9]  C. D. Johnson,et al.  Accomodation of external disturbances in linear regulator and servomechanism problems , 1971 .

[10]  Miroslav Krstic,et al.  Adaptive Cancellation of Matched Unknown Sinusoidal Disturbances for LTI Systems by State Derivative Feedback , 2013 .

[11]  Patrizio Tomei,et al.  An adaptive learning regulator for uncertain minimum phase systems with undermodeled unknown exosystems , 2011, Autom..

[12]  Sergey A. Kolyubin,et al.  Rejection of Multiharmonic Disturbance Approach Based on Simple Adaptive Control Principle , 2013, ALCOSP.

[13]  Petros A. Ioannou,et al.  Robust Adaptive Control , 2012 .

[14]  Alexey A. Bobtsov,et al.  Compensation of unknown sinusoidal disturbances in linear plants of arbitrary relative degree , 2009 .

[15]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[16]  Hyungbo Shim,et al.  Linear systems with hyperbolic zero dynamics admit output regulator rejecting unknown number of unknown sinusoids , 2015 .

[17]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[18]  Ioan Doré Landau,et al.  Adaptive narrow band disturbance rejection applied to an active suspension - an internal model principle approach , 2005, Autom..

[19]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[20]  A. Isidori,et al.  Adaptive regulation for linear systems with multiple zeros at the origin , 2013 .

[21]  A. Pyrkin,et al.  An iterative algorithm of adaptive output control with complete compensation for unknown sinusoidal disturbance , 2012 .

[22]  Vladimir O. Nikiforov,et al.  Observers of External Deterministic Disturbances. I. Objects with Known Parameters , 2004 .

[23]  Andrea Serrani,et al.  Rejection of harmonic disturbances at the controller input via hybrid adaptive external models , 2006, Autom..

[24]  Patrizio Tomei,et al.  Output Regulation for Unknown Stable Linear Systems , 2015, IEEE Transactions on Automatic Control.

[25]  W. Wonham,et al.  The internal model principle for linear multivariable regulators , 1975 .

[26]  Lorenzo Marconi,et al.  Autonomous vertical landing on an oscillating platform: an internal-model based approach , 2002, Autom..