Non-quadratic Lyapunov function and adaptive laws for model reference adaptive control

1998 ◽  
Vol 34 (23) ◽  
pp. 2278 ◽  
Author(s):  
M.P.R.V. Rao
Keyword(s):  
Adaptive Control ◽  
Lyapunov Function ◽  
Model Reference Adaptive Control ◽  
Quadratic Lyapunov Function ◽  
Model Reference ◽  
Adaptive Laws ◽  
Model Reference Adaptive

Novel model reference adaptive control with application to wing rock example

2021 ◽  
pp. 095441002098704
Author(s):  
Jafar Roshanian ◽  
Ehssan Rahimzadeh
Keyword(s):  
Adaptive Control ◽  
Lyapunov Function ◽  
Closed Loop ◽  
Tracking Error ◽  
Model Reference Adaptive Control ◽  
Closed Loop System ◽  
Quadratic Lyapunov Function ◽  
Adaptive Laws ◽  
State Tracking ◽  
Model Reference Adaptive

In this study, we propose new adaptive laws for adjusting the controller parameters of the model reference adaptive control (MRAC) and MRAC with integral feedback schemes. The innovation presented in this study is considering a new form for the Lyapunov function candidate to prove the stability of the closed-loop system. In general, a Lyapunov function candidate contains two sets of quadratic expressions. The first set contains the state tracking error variable, while the second one consists of the controller parameter estimation errors. We prove that by choosing the tracking error quadratic expressions in the form of the exponential function, new adaptive laws that contain the tracking error quadratic expressions are obtained. The difference between the standard MRAC adaptive laws and the proposed new adaptive laws is the state tracking error exponential quadratic expression appears in the adaptive laws. It is shown that the adaptive laws obtained by the exponential quadratic Lyapunov function are similar to those obtained by the quadratic Lyapunov function except that the adaptive gains are variable with time. The advantage of using these new adaptive laws is improving the tracking performance of the closed-loop system, which has been proven analytically and verified by numerical simulations. Also, the robustness analysis of the proposed MRAC controller in the presence of the exogenous disturbance is studied. We consider the single degree of freedom of the wing rock example to evaluate the performance of the designed controllers.

scholarly journals Robust Model Reference Adaptive Control for Tail-Sitter VTOL Aircraft

Actuators ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 162
Author(s):  
Ahmed R. Ajel ◽  
Amjad J. Humaidi ◽  
Ibraheem Kasim Ibraheem ◽  
Ahmad Taher Azar
Keyword(s):  
Adaptive Control ◽  
Stability Analysis ◽  
Dead Zone ◽  
Tracking Error ◽  
Model Reference Adaptive Control ◽  
Roll Motion ◽  
Wind Disturbance ◽  
Model Reference ◽  
Adaptive Laws ◽  
Model Reference Adaptive

This study presents a control design of roll motion for a vertical take-off and landing unmanned air vehicle (VTOL-UAV) design based on the Model Reference Adaptive Control (MRAC) scheme in the hovering flight phase. The adaptive laws are developed for the UAV system under nonparametric uncertainty (gust and wind disturbance). Lyapunov-based stability analysis of the adaptive controlled UAV system under roll motion has been conducted and the adaptive laws have been accordingly developed. The Uniform Ultimate Boundness (UUB) of tracking error has been proven and the stability analysis showed that the incorporation of dead-zone modification in adaptive laws could guarantee the uniform boundness of all signals. The computer simulation has been conducted based on a proposed controller for tracking control of the roll motion. The results show that the drift, which appears in estimated gain behaviors due to the application of gust and wind disturbance, could be stopped by introducing dead-zone modification in adaptive laws, which leads to better robustness characteristics of the adaptive controller.

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