Robust Stabilization of Multi Input Plants With Saturating Actuators

This technical note proposes the use of a time-varying sliding surface for stabilizing linear, possibly unstable, Multi-Input plants subject to saturating actuators, in the presence of bounded matched uncertainties. The present work generalizes our previous contributions in several different directions. First, the constructive procedure is generalized, and a result about asymptotical stabilization is given, under the usual assumption of the saturation threshold being larger than the bound on uncertainties. Another goal of the technical note is to widen the set of plants considered including linear Multi-Input systems. Simulation results show both the effectiveness of the control technique and the low computational burden required.

[1]  Tong Heng Lee,et al.  Composite nonlinear feedback control for linear systems with input saturation: theory and an application , 2003, IEEE Trans. Autom. Control..

[2]  Zongli Lin.  H∞-almost disturbance decoupling with internal stability for linear systems subject to input saturation , 1997, IEEE Trans. Autom. Control..

[3]  Luca Zaccarian,et al.  Linear LMI-based external anti-windup augmentation for stable linear systems , 2004, Autom..

[4]  H. Sussmann,et al.  On the stabilizability of multiple integrators by means of bounded feedback controls , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[5]  R. Schwarzenberger.  ORDINARY DIFFERENTIAL EQUATIONS , 1982 .

[6]  D. Bernstein,et al.  A chronological bibliography on saturating actuators , 1995 .

[7]  S. Tarbouriech,et al.  Control design for linear systems with saturating actuators and /spl Lscr//sub 2/-bounded disturbances , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[8]  Zongli Lin,et al.  Semi-global exponential stabilization of linear systems subject to “input saturation” via linear feedbacks , 1993 .

[9]  Andrew R. Teel,et al.  Control of linear systems with saturating actuators , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[10]  Maria Letizia Corradini,et al.  Linear unstable plants with saturating actuators: Robust stabilization by a time varying sliding surface , 2007, Autom..

[11]  Ali Saberi,et al.  Semi-global exponential stabilization of linear discrete-time systems subject to input saturation via linear feedbacks , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[12]  Eduardo Sontag,et al.  A general result on the stabilization of linear systems using bounded controls , 1994, IEEE Trans. Autom. Control..

[13]  W. Rugh.  Linear System Theory , 1992 .

[14]  J. J. Slotine,et al.  Tracking control of non-linear systems using sliding surfaces with application to robot manipulators , 1983, 1983 American Control Conference.

[15]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[16]  Zongli Lin.  Global Control of Linear Systems with Saturating Actuators , 1998, Autom..

[17]  Semyon M. Meerkov,et al.  An LQR/LQG theory for systems with saturating actuators , 2001, IEEE Trans. Autom. Control..

[18]  Zongli Lin,et al.  Global practical stabilization of planar linear systems in the presence of actuator saturation and input additive disturbance , 2006, IEEE Transactions on Automatic Control.

[19]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[20]  A. Teel.  Global stabilization and restricted tracking for multiple integrators with bounded controls , 1992 .

[21]  Tingshu Hu,et al.  Stabilization of exponentially unstable linear systems with saturating actuators , 2001, IEEE Trans. Autom. Control..

[22]  A. Teel.  Anti-windup for exponentially unstable linear systems , 1999 .

[23]  Giorgio Bartolini,et al.  Global stabilization for nonlinear uncertain systems with unmodeled actuator dynamics , 2001, IEEE Trans. Autom. Control..

[24]  Jan C. Willems,et al.  Almost disturbance decoupling with internal stability , 1989 .

[25]  Y. Hurmuzlu,et al.  Eliminating the Reaching Phase From Variable Structure Control , 2000 .

[26]  Peter Hippe,et al.  Systematic closed-loop design in the presence of input saturations , 1999, Autom..

[27]  Eduardo Sontag.  An algebraic approach to bounded controllability of linear systems , 1984 .

[28]  Panos J. Antsaklis,et al.  Linear Systems , 1997 .

[29]  A. Fuller.  In-the-large stability of relay and saturating control systems with linear controllers , 1969 .

[30]  V. Utkin,et al.  Integral sliding mode in systems operating under uncertainty conditions , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[31]  Eduardo Sontag,et al.  Nonlinear output feedback design for linear systems with saturating controls , 1990, 29th IEEE Conference on Decision and Control.

[32]  Sergey K. Korovin,et al.  Variable-Structure Control Systems: Discrete and Digital , 1995 .