Non-smooth predictive control for mechanical transmission systems with backlash-like hysteresis

This paper proposes a non-smooth predictive control approach for mechanical transmission systems described by dynamic models with preceded backlash-like hysteresis. In this type of system, the work platform is driven by a DC motor through a gearbox. The work platform is represented by a linear dynamic sub-model connected in series with a backlash-like hysteresis inherent in gearbox. Here, backlash-like hysteresis is modeled as a non-smooth function with multi-valued mapping. In this case, the conventional model predictive control for such system cannot be implemented directly since the gradients of the control objective function with respect to control variables do not exist at non-smooth points. In order to solve this problem, a non-smooth receding horizon strategy is proposed. Moreover, the stability of predictive control of such non-smooth dynamic systems is analyzed. Finally, a numerical example and a simulation study on a mechanical transmission system are presented for validating the proposed method.

[1]  Biao Huang,et al.  Output feedback model predictive control for nonlinear systems represented by Hammerstein-Wiener model , 2007 .

[2]  Guo-Ping Liu,et al.  A Predictive Control-Based Approach to Networked Hammerstein Systems: Design and Stability Analysis , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  David W. Clarke,et al.  Generalized predictive control - Part I. The basic algorithm , 1987, Autom..

[4]  A. Cambini,et al.  Generalized Convexity and Optimization: Theory and Applications , 2008 .

[5]  Jing Zhou,et al.  Robust Adaptive Output Control of Uncertain Nonlinear Plants With Unknown Backlash Nonlinearity , 2007, IEEE Transactions on Automatic Control.

[6]  Bo Egardt,et al.  MODEL PREDICTIVE CONTROL OF AUTOMOTIVE POWERTRAINS WITH BACKLASH , 2005 .

[7]  Igor Škrjanc,et al.  Continuous-Time Wiener-Model Predictive Control of a pH Process , 2007 .

[8]  Yudi Samyudia,et al.  A hybrid formulation and design of model predictive control for systems under actuator saturation and backlash , 2006 .

[9]  M. M. MÄKELÄ,et al.  Comparing Nonsmooth Nonconvex Bundle Methods in Solving Hemivariational Inequalities , 1999, J. Glob. Optim..

[10]  Marko Mäkelä,et al.  Survey of Bundle Methods for Nonsmooth Optimization , 2002, Optim. Methods Softw..

[11]  Manfred Morari,et al.  A hybrid approach to modelling, control and state estimation of mechanical systems with backlash , 2007, Int. J. Control.

[12]  Wolfgang Marquardt,et al.  Nonlinear model predictive control of multivariable processes using block-structured models , 2007 .

[13]  David W. Clarke,et al.  Generalized Predictive Control - Part II Extensions and interpretations , 1987, Autom..

[14]  Yonghong Tan,et al.  Internal Model Control for Dynamic Systems With Preceded Backlash , 2009 .

[15]  I.S. Baruch,et al.  A mechanical system backlash compensation by means of a recurrent neural multi-model , 2004, 2004 2nd International IEEE Conference on 'Intelligent Systems'. Proceedings (IEEE Cat. No.04EX791).

[16]  Chin-Wang Tao.  Fuzzy control for linear plants with uncertain output backlashes , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[17]  Roy S. Smith,et al.  An inexact bundle method for solving large structured linear matrix inequalities , 2001 .

[18]  Guo-Ping Liu,et al.  Networked Predictive Control Systems Based on the Hammerstein Model , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[19]  Mattias Nordin,et al.  Controlling mechanical systems with backlash - a survey , 2002, Autom..

[20]  Yonghong Tan,et al.  Recursive identification for dynamic systems with backlash , 2009 .

[21]  Klaus Janschek,et al.  Nonsmooth Predictive Control for Wiener Systems With Backlash-Like Hysteresis , 2016, IEEE/ASME Transactions on Mechatronics.