Model reference control of LPV systems

This paper deals with the problem of model reference control for linear parameter varying (LPV) systems. The LPV systems under consideration depend on a set of parameters that are bounded and available online. The main contribution of this paper is to design an LPV model reference control scheme for LPV systems whose state-space matrices depend affinely on a set of time-varying parameters that are bounded and available online. The design problem is divided into two subproblems: the design of the coefficient matrices of the controller and the design of the gain of the state feedback controller for LPV systems. The singular value decomposition is used to obtain the coefficient matrices, while the linear matrix inequality methodology is used to obtain the parameter-dependent state feedback gain of the control scheme. A simple numerical example is used to illustrate the proposed design and a coupled-tank process example is used to demonstrate the usefulness and practicality of the proposed design. Simulation and experimental results indicate that the proposed scheme works well.

[1]  M. Khammash,et al.  Decentralized power system stabilizer design using linear parameter varying approach , 2004, IEEE Transactions on Power Systems.

[2]  Pascal Gahinet,et al.  H/sub /spl infin// design with pole placement constraints: an LMI approach , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[3]  Gary J. Balas,et al.  Quasi-LPV modeling and LPV control of a generic missile , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[4]  A. Packard,et al.  Induced L/sub 2/-norm control for LPV system with bounded parameter variation rates , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[5]  Pierre Apkarian,et al.  Self-scheduled H-infinity control of missile via linear matrix inequalities , 1995 .

[6]  W. Xie.  H2 gain scheduled state feedback for LPV system with new LMI formulation , 2005 .

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

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

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

[10]  Ricardo Salvador Sánchez Peña,et al.  LPV control of a 6-DOF vehicle , 2002, IEEE Trans. Control. Syst. Technol..

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

[12]  J. Bernussou,et al.  On Inexact LPV Control Design of Continuous–Time Polytopic Systems , 2008, IEEE Transactions on Automatic Control.

[13]  T. IWASAKIt,et al.  All Controllers for the General Control Problem : LMI Existence Conditions and State Space Formulas * , 2002 .

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

[15]  Suttipan Limanond,et al.  Model reference adaptive and nonadaptive control of linear time-varying plants , 2000, IEEE Trans. Autom. Control..

[16]  Alessandro Casavola,et al.  Predictive control of constrained nonlinear systems via LPV linear embeddings , 2003 .

[17]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[18]  A. Packard,et al.  Optimal LQG performance of linear uncertain systems using state-feedback , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[19]  Vikram Kapila,et al.  Experimental validation of a nonlinear backstepping liquid level controller for a state coupled two tank system , 2005 .

[20]  A. Packard,et al.  LQG control design for LPV systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[21]  Fernando D. Bianchi,et al.  Gain scheduling control of variable-speed wind energy conversion systems using quasi-LPV models , 2005 .

[22]  Masayoshi Tomizuka,et al.  Linear parameter varying controller for automated lane guidance: experimental study on tractor-trailers , 2002, IEEE Trans. Control. Syst. Technol..

[23]  Shui-Shong Lu,et al.  A fuzzy cell mapping method for a sub-optimal control implementation , 1994 .

[24]  Jonathan P. How,et al.  Modeling and H∞ control for switched linear parameter-varying missile autopilot , 2003, IEEE Trans. Control. Syst. Technol..

[25]  Ricardo C. L. F. Oliveira,et al.  I guaranteed cost computation by means of parameter-dependent Lyapunov functions , 2004, Autom..

[26]  Fen Wu,et al.  Extended anti-windup control schemes for LTI and LFT systems with actuator saturations , 2004 .

[27]  Junmin Wang,et al.  Air fraction estimation for multiple combustion mode diesel engines with dual-loop EGR systems , 2007, 2007 46th IEEE Conference on Decision and Control.

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

[29]  Qian Wang,et al.  Modeling and Control Design for Performance Management of Web Servers Via an LPV Approach , 2007, IEEE Transactions on Control Systems Technology.

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

[31]  Pierre Apkarian,et al.  Parameterized linear matrix inequality techniques in fuzzy control system design , 2001, IEEE Trans. Fuzzy Syst..

[32]  Pierre Apkarian,et al.  New fuzzy control model and dynamic output feedback parallel distributed compensation , 2004, IEEE Transactions on Fuzzy Systems.

[33]  James E. Steck,et al.  Adaptive Feedback Control by Constrained Approximate Dynamic Programming , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[34]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[35]  Pascale Bendotti,et al.  Linear parameter‐varying versus linear time‐invariant control design for a pressurized water reactor , 1999 .

[36]  Gabriel Abba,et al.  Modeling and robust control of winding systems for elastic webs , 2002, IEEE Trans. Control. Syst. Technol..

[37]  J. Daafouz,et al.  Parameter-dependent control with /spl gamma/-performance for affine LPV systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[38]  Gary J. Balas,et al.  Linear, parameter‐varying control and its application to a turbofan engine , 2002 .

[39]  Sophie Tarbouriech,et al.  Output feedback robust stabilization of uncertain linear systems with saturating controls: an LMI approach , 1999, IEEE Trans. Autom. Control..

[40]  J. Daafouz,et al.  Parameter-dependent state observer design for affine LPV systems , 2001 .

[41]  Edoardo Mosca,et al.  An ellipsoidal off-line MPC scheme for uncertain polytopic discrete-time systems , 2008, Autom..

[42]  Myung Jin Chung,et al.  Gain-scheduled state feedback control design technique for flight vehicles , 2001 .

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

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

[45]  S. Bittanti,et al.  Affine Parameter-Dependent Lyapunov Functions and Real Parametric Uncertainty , 1996 .

[46]  D. Dawson,et al.  Model reference robust control of a class of SISO systems , 1994, IEEE Trans. Autom. Control..

[47]  Michael A. Malcolm,et al.  Computer methods for mathematical computations , 1977 .

[48]  Okko H. Bosgra,et al.  LPV control for a wafer stage: beyond the theoretical solution , 2005 .

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

[50]  Masayuki Fujita,et al.  A scheduled controller design of congestion control considering network resource constraints , 2004 .

[51]  Karolos M. Grigoriadis,et al.  Anti-windup controller design using linear parameter-varying control methods , 2000 .

[52]  Michael Athans,et al.  Guaranteed properties of gain scheduled control for linear parameter-varying plants , 1991, Autom..

[53]  Jeff S. Shamma,et al.  Trajectory scheduled missile autopilot design , 1992, [Proceedings 1992] The First IEEE Conference on Control Applications.

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

[55]  Jeff S. Shamma,et al.  Analysis and design of gain scheduled control systems , 1988 .

[56]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..

[57]  Bin He,et al.  Robust LPV control of diesel auxiliary power unit for series hybrid electric vehicles , 2006, IEEE Transactions on Power Electronics.

[58]  C. de Souza,et al.  Gain‐scheduled ℋ︁2 controller synthesis for linear parameter varying systems via parameter‐dependent Lyapunov functions , 2006 .

[59]  Ricardo C. L. F. Oliveira,et al.  2 guaranteed cost computation by means of parameter dependent Lyapunov functions , 2004, Int. J. Syst. Sci..

[60]  F. Kratz,et al.  Advanced gain scheduling techniques for the design of parameter-dependent observers , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[61]  Jeff S. Shamma,et al.  Gain-scheduled bank-to-turn autopilot design using linear parameter varying transformations , 1996 .

[62]  W. Q. Liu,et al.  Robust Model Reference Control for Multivariable Linear Systems: A Parametric Approach , 2000 .

[63]  Liu Hsu,et al.  Output-feedback model-reference sliding mode control of uncertain multivariable systems , 2003, IEEE Trans. Autom. Control..

[64]  Pramod P. Khargonekar,et al.  On the control of linear systems whose coefficients are functions of parameters , 1984 .