Linear parameter-varying descriptions of nonlinear systems

2004 ◽  
Author(s):  
F. Bruzelius ◽  
S. Pettersson ◽  
C. Breitholtz
Keyword(s):  
Nonlinear Systems ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying

scholarly journals Real Time Stabilization of Lipschitz Nonlinear Systems with Nonlinear Output

2020 ◽  
Vol 53 (4) ◽  
pp. 493-498
Author(s):  
Assem Thabet ◽  
Ghazi Bel Haj Frej ◽  
Noussaiba Gasmi ◽  
Brahim Metoui
Keyword(s):  
Nonlinear Systems ◽  
Real Time ◽  
Nonlinear Function ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Linear Matrix ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Lipschitz Nonlinear Systems ◽  
Parameter Varying

This brief discusses a simple stabilization strategy for a class of Lipschitz nonlinear systems based on the transformation of nonlinear function to Linear Parameter Varying system. Due to the introduction of the Differential Mean Value Theorem (DMVT), the dynamic and output nonlinear functions are transformed into Linear Parameter Varying (LPV) functions. This allows to increase the number of decision variables in the constraint to be resolved and, then, get less conservative and more general Linear Matrix Inequality (LMI) conditions. The established sufficient stability conditions are in the form of LMI with the introduction of a cost control to ensure closed-loop stability. Finally, Real Time Implementation (RTI) using a DSP device (ARDUINO UNO R3) to a typical robot is given to illustrate the performances of the proposed method with a comparison to some existing results.

Embedding of Nonlinear Systems in a Linear Parameter-Varying Representation

2014 ◽  
Vol 47 (3) ◽  
pp. 6907-6913 ◽  
Author(s):  
Hossam S. Abbas ◽  
Roland Tóth ◽  
Mihály Petreczky ◽  
Nader Meskin ◽  
Javad Mohammadpour
Keyword(s):  
Nonlinear Systems ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying

Design of Linear Parameter-Varying Based Sliding Mode Regulator for Limit Protection of Aero-Engines

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Shu-Bo Yang ◽  
Xi Wang ◽  
Peng-Hui Sun
Keyword(s):  
Nonlinear Systems ◽  
Linear Models ◽  
Sliding Mode ◽  
Aircraft Engine ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying ◽  
Limit Protection ◽  
Aero Engines ◽  
Linear Regulators

Abstract In aircraft engine control, replacing linear regulators by sliding mode control (SMC) regulators is considered as an effective approach to reducing the conservatism in the traditional treatment for limit protection. However, most of the relevant studies are based on linear descriptions, which cannot represent the nonlinear systems directly due to their limited valid range. Even if gain scheduling techniques are employed, the stability of the nonlinear systems cannot be theoretically guaranteed. In this paper, a sliding mode strategy for a class of uncertain linear parameter varying (LPV) systems is studied. LPV descriptions are applied to extend the valid range of the linear models covering the entire operation envelope with guaranteed performance and stability. The mismatch between LPV and the real systems is considered as uncertainties. With a sliding surface defined by the tracking errors, system properties on the surface are proved to be satisfactory. After that, a reaching law is designed to ensure global invariance of SMC. Based on a reliable model turbofan, simulation results show that the SMC method can fully exploit the limit margin and, compared to the traditional proportional-integral-derivative (PID) control, has a faster response. In addition, stability and effectiveness of the proposed method are verified in a temperature protection case.

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