Ripple-Free Sampled-Data Output Regulation: Stability Analysis and Sampling Period Estimation

Consider the robust output regulation of linear continuous-time multivariable systems by sampled-error feedback. It is known that by the internal model principle for sampled-data systems, a controller should incorporate a continuous internal model of the exogenous signals for validating the ripple-free error response condition. This study revisits the problem, and particularly, we reformulate the relevant closed-loop regulation system as a specific hybrid representation. This enables us to address a monodromy matrix-based direct method for the stability analysis. Moreover, we can estimate the valid sampling periods assuring the system stability. We also observe that the set of all the allowable sampling periods in general is not connected in the time axis. As a consequence, we propose a line-search algorithm for estimating the local maximum allowable sampling periods (LMASPs).

[1]  Edward Davison,et al.  The design of controllers for the multivariable robust servomechanism problem using parameter optimization methods , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[2]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

[3]  B. Francis,et al.  Input-output stability of sampled-data systems , 1991 .

[4]  Dragan Nesic,et al.  Explicit Computation of the Sampling Period in Emulation of Controllers for Nonlinear Sampled-Data Systems , 2009, IEEE Transactions on Automatic Control.

[5]  Corrado Possieri,et al.  Structural Properties of a Class of Linear Hybrid Systems and Output Feedback Stabilization , 2017, IEEE Transactions on Automatic Control.

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

[7]  Laura Menini,et al.  Output regulation for a class of linear hybrid systems. Part 2: stabilization , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[8]  Dragan Nesic,et al.  Open- and Closed-Loop Dissipation Inequalities Under Sampling and Controller Emulation , 2002, Eur. J. Control.

[9]  G. Franklin,et al.  Design of ripple-free multivariable robust servomechanisms , 1984, IEEE Conference on Decision and Control.

[10]  Jie Huang,et al.  Nonlinear Output Regulation: Theory and Applications , 2004 .

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

[12]  B. Francis.  The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[13]  Laura Menini,et al.  Output regulation for a class of linear hybrid systems. Part 1: trajectory generation , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

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

[15]  Laura Menini,et al.  Robust Hybrid Output Regulation for Linear Systems With Periodic Jumps: Semiclassical Internal Model Design , 2017, IEEE Transactions on Automatic Control.

[16]  Yung-Chun Wu,et al.  A ripple free sampled-data robust servomechanism controller using exponential hold , 1994, IEEE Trans. Autom. Control..

[17]  Rafal Goebel,et al.  Solutions to hybrid inclusions via set and graphical convergence with stability theory applications , 2006, Autom..

[18]  C. Kravaris,et al.  Global stability results for systems under sampled-data control , 2006, 2007 European Control Conference (ECC).

[19]  Danna Zhou,et al.  d. , 1840, Microbial pathogenesis.