PCA-Based Parameter Set Mappings for LPV Models With Fewer Parameters and Less Overbounding

This brief presents a method for an automated generation of improved representations of linear parameter varying (LPV) systems, which is based on principal component analysis applied to typical scheduling trajectories. The procedure can help to reduce the conservatism in controller design by finding tighter regions in the space of scheduling parameters that contain the set of given trajectories. In addition, this method allows to determine approximations of LPV models with a reduced number of parameters and facilitates a systematic tradeoff between the number of parameters and the desired accuracy of the model. The proposed technique is illustrated by the application to a model of a two-link robot. Performance achieved with the controller designed using the reduced model is compared with those obtained by a robust control approach.

[1]  Herbert Werner,et al.  Linear parameter varying PID controller design for charge control of a spark-ignited engine , 2009 .

[2]  Z. Szabo,et al.  The Design of an Integrated Control System in Heavy Vehicles Based on an LPV Method , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[3]  Herbert Werner,et al.  ROBUST H2 CONTROLLER DESIGN AND TUNING FOR THE ACC BENCHMARK PROBLEM AND A REAL-TIME APPLICATION , 2002 .

[4]  Andreas Varga,et al.  Symbolic techniques for low order LFT-modelling , 2005 .

[5]  P. Gahinet,et al.  A convex characterization of gain-scheduled H∞ controllers , 1995, IEEE Trans. Autom. Control..

[6]  P. Gahinet,et al.  A convex characterization of gain-scheduled H∞ controllers , 1995, IEEE Trans. Autom. Control..

[7]  P. Apkarian,et al.  LPV techniques for control of an inverted pendulum , 1999, IEEE Control Systems.

[8]  J. Edward Jackson,et al.  A User's Guide to Principal Components: Jackson/User's Guide to Principal Components , 2004 .

[9]  Peng-Yung Woo,et al.  Polytopic gain scheduled H[infty infinity] control for robotic manipulators , 2003, Robotica.

[10]  Claes Breitholtz,et al.  LPV-based gain scheduling technique applied to a turbo fan engine model , 2002, Proceedings of the International Conference on Control Applications.

[11]  Pierre Apkarian,et al.  Self-scheduled H∞ control of linear parameter-varying systems: a design example , 1995, Autom..

[12]  M. Schultalbers,et al.  LPV controller synthesis for charge control of a car engine - A hybrid evolutionary algebraic approach , 2007, 2007 European Control Conference (ECC).

[13]  Herbert Werner,et al.  Less conservative polytopic LPV models for charge control by combining parameter set mapping and set intersection , 2007, 2007 46th IEEE Conference on Decision and Control.

[14]  H. Werner,et al.  Automated Generation and Assessment of Affine LPV Models , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[15]  Herbert Werner,et al.  Robust tuning of power system stabilizers using LMI-techniques , 2003, IEEE Trans. Control. Syst. Technol..

[16]  Andras Varga,et al.  Enhanced LFR-toolbox for MATLAB , 2004 .

[17]  A. Kwiatkowski,et al.  LPV Control of a 2-DOF Robot Using Parameter Reduction , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[18]  Pierre Apkarian,et al.  Parameterized LMIs in Control Theory , 2000, SIAM J. Control. Optim..

[19]  K. Uchida,et al.  A New LMI Approach to Analysis of Linear Systems Depending on Scheduling Parameter in Polynomial Forms , 2000 .

[20]  Ian Postlethwaite,et al.  A MULTIVARIATE POLYNOMIAL MATRIX ORDER-REDUCTION ALGORITHM FOR LINEAR FRACTIONAL TRANSFORMATION MODELLING , 2005 .

[21]  Keith Glover,et al.  Calibratable linear parameter-varying control of a turbocharged diesel engine , 2006, IEEE Transactions on Control Systems Technology.

[22]  M. Schultalbers,et al.  Application of LPV gain scheduling to charge control of a SI engine , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[23]  Feng Zhang,et al.  Linear Parameter-Varying Lean Burn Air-Fuel Ratio Control , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[24]  Peng-Yung Woo,et al.  Gain Scheduled LPV H∞ Control Based on LMI Approach for a Robotic Manipulator , 2002, J. Field Robotics.