Sliding-mode control of discrete-time linear plants with input saturation: application to a twin-rotor system

This paper investigates the stabilisation problem for discrete-time linear controllable systems subject to actuator saturation. In the case of completely known plants, a control design technique based on a time-varying sliding surface is proposed ensuring stabilisation under the assumption of availability of all state measurements. Further, in the presence of matched disturbances with a known constant bound, a discrete-time sliding-mode controller is proposed ensuring plant practical stabilisation, and a conservative estimate of the attraction domain is given. Theoretical results have been validated by experimental data using a twin-rotor system.

[1]  R. Rosenberg,et al.  System Dynamics: Modeling and Simulation of Mechatronic Systems , 2006 .

[2]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[3]  Lisa Werner.  Control Systems With Saturating Inputs Analysis Tools And Advanced Design , 2016 .

[4]  Christopher Edwards,et al.  Sliding mode stabilization of uncertain systems using only output information , 1995 .

[5]  Stephen P. Boyd,et al.  Analysis of linear systems with saturation using convex optimization , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[6]  Katsuhisa Furuta,et al.  VSS type self-tuning control , 1993, IEEE Trans. Ind. Electron..

[7]  Maria Letizia Corradini,et al.  Control Systems with Saturating Inputs , 2012 .

[8]  Tingshu Hu,et al.  Analysis and design for discrete-time linear systems subject to actuator saturation , 2002, Syst. Control. Lett..

[9]  Maria Letizia Corradini,et al.  Robust Stabilization of Multi Input Plants With Saturating Actuators , 2010, IEEE Transactions on Automatic Control.

[10]  Wen-Fang Xie,et al.  Sliding-Mode Observer Based Adaptive Control for Servo Actuator with Friction , 2007, 2007 International Conference on Mechatronics and Automation.

[11]  Zongli Lin,et al.  Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[12]  A. Teel.  Semi-global stabilizability of linear null controllable systems with input nonlinearities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[13]  S. Tarbouriech,et al.  Local stabilization of discrete-time linear systems with saturating controls: an LMI-based approach , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[14]  Roy M. Howard,et al.  Linear System Theory , 1992 .

[15]  Zongli Lin,et al.  Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function , 2003, Autom..

[16]  S. Liberty,et al.  Linear Systems , 2010, Scientific Parallel Computing.

[17]  Sophie Tarbouriech,et al.  Stability regions for linear systems with saturating controls via circle and Popov criteria , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

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

[19]  Okyay Kaynak,et al.  Sliding Mode Neuro-Adaptive Control of Electric Drives , 2007, IEEE Transactions on Industrial Electronics.

[20]  Jinhoon Choi,et al.  On the stabilization of linear discrete time systems subject to input saturation 1 1 This research w , 1999 .

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

[22]  Maria Letizia Corradini,et al.  Stabilization of discrete-time linear systems with saturating actuators using sliding modes: Application to a twin-rotor system , 2011, IEEE Conference on Decision and Control and European Control Conference.

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

[24]  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.

[25]  Maria Letizia Corradini,et al.  Variable structure control of discretized continuous-time systems , 1998, IEEE Trans. Autom. Control..

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

[27]  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.

[28]  Zongli Lin.  Robust semi-global stabilization of linear systems with imperfect actuators , 1997 .

[29]  Asif Sabanoviç,et al.  Sliding-Mode Control for High-Precision Motion of a Piezostage , 2007, IEEE Transactions on Industrial Electronics.

[30]  Weibing Gao,et al.  Discrete-time variable structure control systems , 1995, IEEE Trans. Ind. Electron..

[31]  Vadim I. Utkin,et al.  Adaptive sliding mode control in discrete-time systems , 1995, Autom..