Composite Model Reference Adaptive Control for a Class of Nonlinear Fractional Order Systems

2015 ◽  
Author(s):  
Yiheng Wei ◽  
Shu Liang ◽  
Yangsheng Hu ◽  
Yong Wang
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Closed Loop ◽  
Tracking Error ◽  
Model Reference Adaptive Control ◽  
Prediction Errors ◽  
Model Reference ◽  
Closed Loop Systems ◽  
The Stability ◽  
Model Reference Adaptive

This article presents a novel model reference adaptive control of fractional order nonlinear systems, which is a generalization of existing method for integer order systems. The formulating adaptive law is in terms of both tracking and prediction errors, whereas existing methods only depends on tracking error. The transient performance of the closed-loop systems with the proposed control strategy improves in the sense of generating smooth system output. The stability and tracking convergence of the resulting closed-loop system are analyzed via the indirect Lyapunov method. Meanwhile, the proposed controller is implemented by employing some fractional order tracking differentiator to generate the required fractional derivatives of a signal. Numerical examples are provided to illustrate the effectiveness of our results.

scholarly journals Fractional-Order Closed-Loop Model Reference Adaptive Control for Anesthesia

Algorithms ◽  
2018 ◽  
Vol 11 (7) ◽  
pp. 106 ◽  
Author(s):  
Gerardo Navarro-Guerrero ◽  
Yu Tang
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Closed Loop ◽  
Adaptive Controller ◽  
Model Reference Adaptive Control ◽  
Loop Model ◽  
Unknown Parameters ◽  
Model Reference ◽  
State Measurement ◽  
Model Reference Adaptive

The design of a fractional-order closed-loop model reference adaptive control (FOCMRAC) for anesthesia based on a fractional-order model (FOM) is proposed in the paper. This proposed model gets around many difficulties, namely, unknown parameters, lack of state measurement, inter and intra-patient variability, and variable time-delay, encountered in controller designs based on the PK/PD model commonly used for control of anesthesia, and allows to design a simple adaptive controller based on the Lyapunov analysis. Simulations illustrate the effectiveness and robustness of the proposed control.

Stability Behavior of Model Reference Adaptive Control Methods in Presence of Aircraft Structural Damage

2007 ◽  
Author(s):  
Pascal Nespeca ◽  
Nesrin Sarigul-Klijn
Keyword(s):  
Adaptive Control ◽  
Numerical Study ◽  
Function Analysis ◽  
Model Reference Adaptive Control ◽  
Approximation Technique ◽  
Control Methods ◽  
Model Reference ◽  
Stability Behavior ◽  
The Stability ◽  
Model Reference Adaptive

Any classical control design starts by first satisfying stability and then looking towards satisfying transient requirements. Similarly, a Model Reference Adaptive Control (MRAC) Method should start with a stability analysis. Lyapunov function analysis is first used to justify the stability of the adaptive scheme. Next, a numerical study is conducted to predict the stability behavior of three different MRAC methods in the presence of large unanticipated changes in the dynamics of an aircraft. The Model reference adaptive control methods studied are: Method:1, an adaptive gain method; Method:2, a Neural Network (NN) approximation technique; and, Method:3, a linear approximation technique. For comparison purposes, the aircraft is assumed to have Linear Time Invariant, LTI dynamics. Each algorithm is given full state feedback, an inaccurate reference model and a poor Linear Quadratic Regulator, LQR design for the true plant. It is seen that when the LQR stabilizes the true plant, the three algorithms all achieve the same steady state error to a step command. Numerical results predict the different types of stability behavior that the algorithms provide. It is seen that the Methods: 2 and 3 can only provide a bounded stability, whereas Method: 1 can provide an asymptotic stability. A robust static controller can satisfy stability, but a robust static controller that accommodates variations in plant dynamics might not always be able to match transient requirements as expected. Although there may be no analytical guarantee from adaptive controllers of transient performance, one might look at anecdotal performances.

The Model Reference Adaptive Control of the DC Electric Drive System

2014 ◽  
Vol 875-877 ◽  
pp. 2030-2035 ◽  
Author(s):  
Marian Gaiceanu ◽  
Cristian Eni ◽  
Mihaita Coman ◽  
Romeo Paduraru
Keyword(s):  
Adaptive Control ◽  
Reference Model ◽  
Sliding Mode ◽  
Tracking Error ◽  
Model Reference Adaptive Control ◽  
Drive System ◽  
Mode Switching ◽  
Sigmoid Function ◽  
Model Reference ◽  
Model Reference Adaptive

Due to the parametric and structural uncertainty of the DC drive system, an adaptive control method is necessary. Therefore, an original model reference adaptive control (MRAC) for DC drives is proposed in this paper. MRAC ensures on-line adjustment of the control parameters with DC machine parameter variation. The proposed adaptive control structure provides regulating advantages: asymptotic cancellation of the tracking error, fast and smooth evolution towards the origin of the phase plan due to a sliding mode switching k-sigmoid function. The reference model can be a real strictly positive function (the tracking error is also the identification error) as its order is relatively higher than one degree. For this reason, the synthesis of the adaptive control will use a different type of error called augmented or enhanced error. The DC machine with separate excitation is fed at a constant flux. This adaptive control law assures robustness to external perturbations and to unmodelled dynamics.

Switched Fractional Order Model Reference Adaptive Control for First Order Plants: a Simulation-Based Study

2021 ◽  
Author(s):  
Norelys Aguila Camacho ◽  
JorgeE García Bustos ◽  
EduardoI Castillo López ◽  
Javier A. Gallego ◽  
JuanC TraviesoTorres
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Reference Model ◽  
Model Reference Adaptive Control ◽  
System Behavior ◽  
Order Model ◽  
Model Reference ◽  
First Order ◽  
Fractional Order Model ◽  
Model Reference Adaptive

Abstract This paper presents the results and analysis of an exhaustive simulation study where Switched Fractional Order Model Reference Adaptive Control (SFOMRAC) is used for first order plants, along with the analytical proof of boundedness and convergence of the scheme. The analysis is focused on the controlled system behavior through the integral of the timed squared control error (ITSE) and on the control energy though the integral of the squared control signal (ISI). Controller parameters such as fractional order, adaptive gain and switching time are varied along the simulation studies, as well as plant parameters and reference models. The results show that SFOMRAC controllers can be found for every plant and reference model used, such that both system behavior and control energy can be improved, compared to equivalent non switched fractional order and integer order control strategies.

Experimental evaluation of a model reference adaptive control for a hydraulic robot: a case study

Robotica ◽  
2003 ◽  
Vol 21 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Ali Kireçci ◽  
Mehmet Topalbekiroglu ◽  
İlyas Eker
Keyword(s):  
Adaptive Control ◽  
Model Reference Adaptive Control ◽  
Computational Time ◽  
Position Tracking ◽  
Control Input ◽  
Model Reference ◽  
Solution Methods ◽  
The Stability ◽  
Classical Control ◽  
Model Reference Adaptive

This paper presents the implementation of an explicit model reference adaptive control (MRAC) for position tracking of a dynamically unknown robot. An auto regressive exogenous (ARX) model is chosen to define the plant model and the control input is optimised in a H2 norm to reduce computational time and to simplify the algorithm. The theory of MRAC falls into a description of the various forms of controllers and parameter estimation techniques, therefore, applications may require very complicated solution methods depending on the selected laws. However, in this study, the proposed MRAC shows that applications may be as easy as classical control methods, such as PID, by guaranteeing the stability and achieving the convergency of the plant parameters. Despite the selected simple control model, simple optimisation method and drawbacks of the robot the experimental results show that MRAC provides an excellent position tracking compared with conventional control (PID). Many experimental implementations have been done on the robot and one of them is included in the paper.

scholarly journals On Fractional Model Reference Adaptive Control

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Bao Shi ◽  
Jian Yuan ◽  
Chao Dong
Keyword(s):  
Adaptive Control ◽  
Reference Model ◽  
Model Reference Adaptive Control ◽  
Lyapunov Theory ◽  
Model Reference ◽  
Fractional Integrator ◽  
The Stability ◽  
Adaptation Law ◽  
Integrator Model ◽  
Model Reference Adaptive

This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapunov theory. Moreover, numerical simulations of both linear and nonlinear systems are performed to exhibit the viability and effectiveness of the proposed methodology.

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