Fractional Order Universal Adaptive Stabilizer for Fractional Order Systems

2009 ◽  
Author(s):  
Yan Li ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Order System ◽  
Adaptive Stabilization ◽  
Space System ◽  
Control Effort ◽  
Finite Control ◽  
State Space System ◽  
Adaptive Stabilizer ◽  
Fractional Controller ◽  
Order State

In this paper, the fractional order universal adaptive stabilization of fractional order SISO system is discussed. The fractional universal adaptive stabilizer is u(t) = −k(t)sgn{CB}y(t), where 0Dtβk(t) = ‖y(t)‖p, which guarantees the asymptotic stability of the equilibrium point of fractional order state space system with finite control effort. Moreover, the fractional order system with order α ∈ (0, 1/(1+p)) can be stabilized by the fractional controller but not for the integer order controller. Simulation results are provided as the proof of concepts.

A FRACTIONAL ORDER UNIVERSAL HIGH GAIN ADAPTIVE STABILIZER

2012 ◽  
Vol 22 (04) ◽  
pp. 1250081 ◽  
Author(s):  
YAN LI ◽  
YANGQUAN CHEN
Keyword(s):  
Fractional Order ◽  
Mimo Systems ◽  
Adaptive Strategy ◽  
High Gain ◽  
Control Effort ◽  
Single Output ◽  
Control Gain ◽  
Multiple Input ◽  
Finite Control ◽  
Adaptive Stabilizer

In this paper, a fractional order universal high gain adaptive stabilizer is proposed which guarantees the Lp stability of fractional order multiple–input and multiple–output (MIMO) systems with finite control effort. The boundedness of the control gain for the fractional order universal adaptive strategy is discussed for fractional order MIMO systems, and an upper bound of the control gain is presented for fractional order single-input and single-output (SISO) systems. Some advantages of the discussed fractional order universal adaptive stabilizer are demonstrated in numerical simulations, such as the overshoots of system outputs can be efficiently reduced by decreasing the fractional order of the universal adaptive stabilizer without significantly increasing the system gains.

scholarly journals Extracting second-order system matrices from state space system

2006 ◽  
Vol 220 (8) ◽  
pp. 1147-1149 ◽  
Author(s):  
P R Houlston
Keyword(s):  
Technical Note ◽  
Second Order ◽  
Order System ◽  
System Modelling ◽  
Direct Control ◽  
Space System ◽  
First Order ◽  
The Reformation ◽  
State Space System ◽  
Second Order Systems

This technical note concerns the reformation of a second-order system from an arbitrary first-order system. At present, the majority of control literature is concerned with controlling systems within the first-order linearization of a system. The author is part of a growing community looking to expand the direct control of second-order systems and the benefits associated in doing so. However, there are potential stages of system modelling that may result in it being necessary to form the first-order form of the system, such as model reduction. This may have the effect of destroying the second-order notion of the system. The purpose of this note is to regain the structure of the second-order system and thus enable the benefits of direct second-order control to be realized. Although the problem itself has been previously resolved, the author proposes the virtue of a simpler method.

scholarly journals Adaptive Stabilization of a Fractional-Order System with Unknown Disturbance and Nonlinear Input via a Backstepping Control Technique

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 55
Author(s):  
Xiaomin Tian ◽  
Zhong Yang
Keyword(s):  
Fractional Order ◽  
Dead Zone ◽  
External Disturbance ◽  
Lyapunov Theory ◽  
Fractional Order System ◽  
Control Technique ◽  
Order System ◽  
Distributed Model ◽  
Adaptive Stabilization ◽  
Unknown Parameters

In this paper, a new backstepping-based adaptive stabilization of a fractional-order system with unknown parameters is investigated. We assume that the controlled system is perturbed by external disturbance, the bound of external disturbance to be unknown in advance. Moreover, the effects of sector and dead-zone nonlinear inputs both are taken into account. A fractional-order auxiliary system is established to generate the necessary signals for compensation the nonlinear inputs. Meantime, in order to deal with these unknown parameters, some fractional-order adaption laws are given. The frequency-distributed model is used so that the indirect Lyapunov theory is available in designing controllers. Finally, simulation results are presented to verify the effectiveness and robustness of the proposed control strategy.

scholarly journals CHAOS CONTROL AND SYNCHRONIZATION USING SYNERGETIC CONTROLLER WITH FRACTIONAL AND LINEAR EXTENDED MANIFOLD

2016 ◽  
Vol 17 (1) ◽  
pp. 115-126
Author(s):  
Morteza Pourmehdi ◽  
Abolfazl Ranjbar Noei ◽  
Jalil Sadati
Keyword(s):  
Fractional Order ◽  
Chaos Control ◽  
Order System ◽  
State Variables ◽  
System Quality ◽  
Control Effort ◽  
Lower Amplitude ◽  
The Stability ◽  
Fractional Order Controller ◽  
Control And Synchronization

In this manuscript, for the first time, a fractional-order manifold in a synergetic approach using a fractional order controller is introduced. Furtheremore, in the synergetic theory a macro variable is expended into a linear combination of state variables. An aim is to increase the convergence rate as well as time response of the whole closed loop system. Quality of the proposed controller is investigated to control and synchronize a nonlinear chaotic Coullet system in comparison with an integer order manifold synergetic controller. The stability of the proposed controller is proven using the Lyapunov method. In this regard stabilizing control effort is yielded. Simulation result confirm convergence of states towards zero. This is achieved through a control effort with fewer oscillations and lower amplitude of signls which confirm feasibility of the control effort in practice.KEYWORDS:  synergetic control theory; fractional order system; synchronization; nonlinear chaotic Coullet system; chaos control

Heat transfer modeling and identification using fractional order state space models

2008 ◽  
Vol 42 (6-8) ◽  
pp. 939-951 ◽  
Author(s):  
Tounsia Jamah ◽  
Rachid Mansouri ◽  
Saïd Djennoune ◽  
Maâmar Bettayeb
Keyword(s):  
Heat Transfer ◽  
State Space ◽  
Fractional Order ◽  
State Space Models ◽  
Heat Transfer Modeling ◽  
Order State
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