Identification with non-quadratic Lyapunov function and new adaptive laws

1999 ◽  
Vol 35 (2) ◽  
pp. 175 ◽  
Author(s):  
M.P.R.V. Rao ◽  
I. Watters
Keyword(s):  
Lyapunov Function ◽  
Quadratic Lyapunov Function ◽  
Adaptive Laws

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.

Stability of Wind Turbine Switching Control in an Integrated Wind Turbine and Rechargeable Battery System: A Common Quadratic Lyapunov Function Approach

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Dushyant Palejiya ◽  
John Hall ◽  
Christine Mecklenborg ◽  
Dongmei Chen
Keyword(s):  
Wind Speed ◽  
Lyapunov Function ◽  
Wind Turbine ◽  
Rechargeable Batteries ◽  
System Stability ◽  
Control Mode ◽  
Rechargeable Battery ◽  
Quadratic Lyapunov Function ◽  
Battery System ◽  
Single Output

The power generated by wind turbines varies due to variations in the wind speed. A pack of rechargeable batteries could be used as a reserve power source to alleviate the intermittency in the wind turbine power. An integrated wind turbine and battery storage system is constructed where the wind turbine is electrically connected to a rechargeable battery system. Such a system can operate in two modes depending on the wind speed, power demand, and battery limit. The switching conditions for the wind turbine to operate in multi-input, single-output and single-input, single-output control mode are discussed. Linearized approximations of the closed loop wind turbine system are derived in order to analyze the switching stability between control modes. Common quadratic Lyapunov function (CQLF) is established for both control modes to prove the system stability. Simulation results demonstrating system stability are also presented.

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