Robustness of a discrete-time predictor-based controller for time-varying measurement delay

A predictor-based controller for time-varying delay systems is presented in this paper and its robustness properties for different uncertainties are analyzed. First, a time-varying delay dependent stability condition is expressed in terms of LMIs. Then, uncertainties in the knowledge of all plant-model parameters are considered and the resulting closed-loop system is shown to be robust with respect to these uncertainties. A significant improvement with respect to the same control strategy without predictor is achieved. The scheme is applicable to open-loop unstable plants and it has been tested in a real-time application to control the roll angle of a quad-rotor helicopter prototype. The experimental results show good performance and robustness of the proposed scheme even in the presence of long delay uncertainties.

[1]  José Luis Guzmán,et al.  An unified approach for DTC design using interactive tools , 2009 .

[2]  Rogelio Lozano,et al.  Robustness of a discrete-time predictor-based controller for time-varying measurement delay , 2010 .

[3]  Shaoyuan Li,et al.  New stability criterion for discrete-time systems with interval time-varying state delay , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[4]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[5]  Guo-Ping Liu,et al.  Output Feedback Stabilization for a Discrete-Time System With a Time-Varying Delay , 2008, IEEE Transactions on Automatic Control.

[6]  Wim Michiels,et al.  Finite spectrum assignment of unstable time-delay systems with a safe implementation , 2003, IEEE Trans. Autom. Control..

[7]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[8]  Ya-Jun Pan,et al.  Stabilization of remote control systems with unknown time varying delays by LMI techniques , 2006 .

[9]  Hongyong Yang,et al.  Further Results Concerning Delay-Dependent Control for Uncertain Discrete-Time Systems with Time-Varying Delay , 2009 .

[10]  Bin Jiang,et al.  Delay-dependent robust stabilisation of uncertain discrete-time switched systems with time-varying state delay , 2008, Int. J. Syst. Sci..

[11]  Ralph R. Martin,et al.  Delay-dependent robust stabilisation of discrete-time systems with time-varying delay , 2006 .

[12]  R. Lozano,et al.  Robustness with respect to delay uncertainties of a predictor-observer based discrete-time controller , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[13]  G. E. Taylor,et al.  Computer Controlled Systems: Theory and Design , 1985 .

[14]  O Smith,et al.  CLOSER CONTROL OF LOOPS WITH DEAD TIME , 1957 .

[15]  W. P. M. H. Heemels,et al.  Controller synthesis for networked control systems , 2010, Autom..

[16]  E. Boukas.  Discrete-time systems with time-varying time delay: Stability and stabilizability , 2006 .

[17]  Leonid Mirkin.  Are distributed-delay control laws intrinsically unapproximable? , 2003 .

[18]  Keqin Gu,et al.  Control of Dead- Time Processes , 2008 .

[19]  Dong Yue,et al.  Delayed feedback control of uncertain systems with time-varying input delay , 2005, Autom..

[20]  K. Vaesen,et al.  Robustness Analysis , 2006, Philosophy of Science.

[21]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[22]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[23]  Silviu-Iulian Niculescu,et al.  Survey on Recent Results in the Stability and Control of Time-Delay Systems* , 2003 .

[24]  Sabine Mondié,et al.  Approximation of control laws with distributed delays: a necessary condition for stability , 2001, Kybernetika.

[25]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[26]  Graham C. Goodwin,et al.  Fundamental Limitations in Filtering and Control , 1997 .

[27]  Qing-Chang Zhong,et al.  On distributed delay in linear control Laws-part I: discrete-delay implementations , 2004, IEEE Transactions on Automatic Control.

[28]  Rogelio Lozano,et al.  Modelling and Control of Mini-Flying Machines , 2005 .

[29]  Pedro Castillo,et al.  Robust prediction-based control for unstable delay systems: Application to the yaw control of a mini-helicopter , 2004, Autom..

[30]  Eduardo F. Camacho,et al.  Dead-time compensators: A survey , 2008 .

[31]  A. Olbrot,et al.  Finite spectrum assignment problem for systems with delays , 1979 .

[32]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[33]  Tore Hägglund,et al.  Robust tuning procedures of dead-time conpensating controllers , 2001 .

[34]  Tore Hägglund,et al.  Interactive tool for analysis of time-delay systems with dead-time compensators , 2006 .

[35]  James Lam,et al.  A delay-partitioning approach to the stability analysis of discrete-time systems , 2010, Autom..