Gain‐Scheduled H∞ Control for Tensor Product Type Polytopic Plants

A tensor product (TP) model transformation is a recently proposed technique for transforming a given linear parameter‐varying (LPV) model into polytopic model form, for which there are many methods that can be used for controller design. This paper proposes an alternative approach to the design of a gain‐scheduled output feedback H∞ controller with guaranteed L2‐gain parameter‐dependent performance for a class of TP type polytopic models using parameter‐dependent Lyapunov functions where the linear matrix inequalities (LMIs) need only to be evaluated at all vertices of the system state‐space model matrices and the variation rate of the scheduled parameters. In addition, a construction technique of the intermediate controller variables is also proposed as a matrix‐valued function in the polytopic coordinates of the scheduled parameters. The performance of the proposed approach is tested on a missile autopilot design problem. Furthermore, nonlinear simulation results show the effectiveness of these proposed techniques.

[1]  A. Packard,et al.  A collection of robust control problems leading to LMIs , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[2]  Jeff S. Shamma,et al.  Gain-Scheduled Missile Autopilot Design Using Linear Parameter Varying Transformations , 1993 .

[3]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[4]  Fen Wu,et al.  Induced L2‐norm control for LPV systems with bounded parameter variation rates , 1996 .

[5]  Gary J. Balas,et al.  LPV control design for pitch-axis missile autopilots , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

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

[7]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions and real parametric uncertainty , 1996, IEEE Trans. Autom. Control..

[8]  Pascal Gahinet,et al.  Explicit controller formulas for LMI-based H∞ synthesis , 1996, Autom..

[9]  Pierre Apkarian.  On the discretization of LMI-synthesized linear parameter-varying controllers , 1997, Autom..

[10]  M. Spillman,et al.  A parameter-dependent performance criterion for linear parameter-varying systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[11]  Pierre Apkarian,et al.  Advanced gain-scheduling techniques for uncertain systems , 1998, IEEE Trans. Control. Syst. Technol..

[12]  Jong-Yeob Shin,et al.  Blending Methodology of Linear Parameter Varying Control Synthesis of F-16 Aircraft System , 2002 .

[13]  Gary J. Balas,et al.  Systematic Gain-Scheduling Control Design: A Missile Autopilot Example , 2008 .

[14]  Fan Wang,et al.  Improved stability analysis and gain-scheduled controller synthesis for parameter-dependent systems , 2002, IEEE Trans. Autom. Control..

[15]  Pierre Apkarian,et al.  MISSILE AUTOPILOT DESIGN VIA A MULTI-CHANNEL LFT/LPV CONTROL METHOD , 2002 .

[16]  Péter Baranyi,et al.  TP model transformation as a way to LMI-based controller design , 2004, IEEE Transactions on Industrial Electronics.

[17]  József K. Tar,et al.  Approximation capability of TP model forms , 2004, Aust. J. Intell. Inf. Process. Syst..

[18]  Yeung Yam,et al.  Definition of the HOSVD based canonical form of polytopic dynamic models , 2006, 2006 IEEE International Conference on Mechatronics.

[19]  Eugene A. Morelli,et al.  Aircraft system identification : theory and practice , 2006 .

[20]  Yeung Yam,et al.  Case study of the TP-model transformation in the control of a complex dynamic model with structural nonlinearity , 2006, IEEE Transactions on Industrial Electronics.

[21]  Peter Baranyi,et al.  Tensor-product model-based control of two-dimensional aeroelastic system , 2006 .

[22]  Fen Wu,et al.  Switching LPV control of an F-16 aircraft via controller state reset , 2006, IEEE Transactions on Control Systems Technology.

[23]  P. Baranyi,et al.  Numerical Reconstruction of the HOSVD Based Canonical Form of Polytopic Dynamic Models , 2007, 2006 International Conference on Intelligent Engineering Systems.

[24]  R. Patton,et al.  APPROXIMATION PROPERTIES OF TP MODEL FORMS AND ITS CONSEQUENCES TO TPDC DESIGN FRAMEWORK , 2007 .

[25]  Guido Herrmann,et al.  Mathematical Methods for Robust and Nonlinear Control , 2007 .

[26]  I. Postlethwaite,et al.  Linear Matrix Inequalities in Control , 2007 .

[27]  Ian Postlethwaite,et al.  Robust LPV Control of UAV with Parameter Dependent Performance , 2008 .

[28]  James F. Whidborne,et al.  LPV Autopilot Design of a Jindivik UAV , 2009 .

[29]  Péter Várlaki,et al.  HOSVD Based Canonical Form for Polytopic Models of Dynamic Systems , 2009, J. Adv. Comput. Intell. Intell. Informatics.

[30]  Sunan Chumalee.  Robust gain-scheduled H∞ control for unmanned aerial vehicles , 2010 .

[31]  Peter Korondi,et al.  Convex hull manipulation based control performance optimisation , 2010 .

[32]  James F. Whidborne,et al.  Unmanned aerial vehicle aerodynamic model identification from a racetrack manoeuvre , 2010 .

[33]  Peter Galambos,et al.  Representing the model of impedance controlled robot interaction with feedback delay in polytopic LPV form: TP model transformation based approach , 2013 .

[34]  Peter Baranyi,et al.  Tensor-Product-Model-Based Control of a Three Degrees-of-Freedom Aeroelastic Model , 2013 .

[35]  Y. Yam,et al.  Tensor Product Model Transformation in Polytopic Model-Based Control , 2013 .

[36]  James F. Whidborne,et al.  Gain-scheduled H∞ control via parameter-dependent Lyapunov functions , 2015, Int. J. Syst. Sci..