Robust stabilization and control using fractional order integrator

2016 ◽  
Vol 39 (10) ◽  
pp. 1559-1576 ◽  
Author(s):  
Amina Ben Hmed ◽  
Messaoud Amairi ◽  
Mohamed Aoun
Keyword(s):  
Stability Boundary ◽  
Robust Stabilization ◽  
Smith Predictor ◽  
Order System ◽  
Stabilization Problem ◽  
Stabilizing Controller ◽  
First Order ◽  
Analytic Expressions ◽  
The Stability ◽  
And Control

This paper addresses the robust stabilization problem of first-order uncertain systems. To treat the robust stabilization problem, an interval-based stabilization method using stability conditions of the non-commensurate elementary fractional transfer function of the second kind is developed. Some analytic expressions are determined to compute the set of all stabilizing controller parameters and plot the stability boundary. A robust performance control is also developed to fulfil some desired time-domain performances as the iso-overshoot property. The fractional controller can be used combined with the Smith predictor to control a first-order system with time delay and achieve desired specifications. Numerical examples are presented to illustrate the obtained results.

scholarly journals Full Characterization of Act-and-wait Control for First-order Unstable Lag Processes

2010 ◽  
Vol 16 (7-8) ◽  
pp. 1209-1233 ◽  
Author(s):  
T. Insperger ◽  
P. Wahi ◽  
A. Colombo ◽  
G. Stépán ◽  
M. Di Bernardo ◽  
...  
Keyword(s):  
Time Delay ◽  
Feedback Systems ◽  
Periodic Control ◽  
First Order ◽  
Full Characterization ◽  
The Stability ◽  
And Control ◽  
Time Periodic ◽  
Special Case

Act-and-wait control is a special case of time-periodic control for systems with feedback delay, where the control gains are periodically switched on and off in order to stabilize otherwise unstable systems. The stability of feedback systems in the presence of time delay is a challenging problem. In this paper, we show that the act-and-wait type time-periodic control can always provide deadbeat control for first-order unstable lag processes with any (large but) fixed value of the time delay in the feedback loop. A full characterization of this act-and-wait controller with respect to the system and control parameters is given based on performance and robustness against disturbances.

SYNCHRONIZATION OF TIME-DELAYED T–S FUZZY CHAOTIC SYSTEMS VIA SCALAR OUTPUT VARIABLE

2005 ◽  
Vol 15 (08) ◽  
pp. 2593-2601 ◽  
Author(s):  
JAE-HUN KIM ◽  
HYUNSEOK SHIN ◽  
EUNTAI KIM ◽  
MIGNON PARK
Keyword(s):  
Time Delay ◽  
Fuzzy Model ◽  
Order System ◽  
Linear Matrix ◽  
Output Variable ◽  
First Order ◽  
Scalar Output ◽  
The Stability ◽  
Takagi Sugeno ◽  
System With Time Delay

It has been known that very complex chaotic behaviors can be observed in a simple first-order system with time-delay. This paper presents a fuzzy model-based approach for synchronization of time-delayed chaotic system via a scalar output variable. Takagi–Sugeno (T–S) fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive and response system with time-delay. Since only a scalar output variable is available for synchronization, a fuzzy observer based on T–S fuzzy model is designed and applied to chaotic synchronization. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov–Krasovskii theory and derive stability conditions by solving linear matrix inequalities (LMI's) problem. A numerical example is given to demonstrate the validity of the proposed synchronization approach.

scholarly journals Dynamics Analysis and Control of a Five-Term Fractional-Order System

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Li-xin Yang ◽  
Xiao-jun Liu
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Phase Portraits ◽  
Order System ◽  
Bifurcation Diagrams ◽  
Compound Structure ◽  
Dynamical Properties ◽  
The Stability ◽  
And Control

This paper proposes a new fractional-order chaotic system with five terms. Firstly, basic dynamical properties of the fractional-order system are investigated in terms of the stability of equilibrium points, Jacobian matrices theoretically. Furthermore, rich dynamics with interesting characteristics are demonstrated by phase portraits, bifurcation diagrams numerically. Besides, the control problem of the new fractional-order system is discussed via numerical simulations. Our results demonstrate that the new fractional-order system has compound structure.

On the Unsteady Supersonic Cascade With a Subsonic Leading Edge—An Exact First Order Theory—Part 2

1974 ◽  
Vol 96 (1) ◽  
pp. 23-31 ◽  
Author(s):  
M. Kurosaka
Keyword(s):  
Closed Form ◽  
Stability Boundary ◽  
Pressure Rise ◽  
Leading Edge ◽  
Order Theory ◽  
Back Pressure ◽  
First Order ◽  
First Order Theory ◽  
The Stability ◽  
Stagger Angle

Pursuant to Part 1, the analysis of the aerodynamic forces acting on slowly oscillating airfoils in a supersonic cascade with a subsonic leading edge is presented. First the flow field between adjacent airfoils is determined. In the limit of sonic leading edge, the present results for the velocity potential agree with the sonic limit of Lane’s supersonic leading edge analysis. The requirement of the continuity of pressure in the “train” leads to functional equations for the train velocity; their solutions, obtained in closed form, are found to involve arbitrary constants which are related to the back pressure. The effect of the back pressure on the “train” is discussed in detail. For a cascade with zero pressure rise across it, the train velocity is determined completely and the formulas for lift and moment, accurate to the first order of a frequency parameter, are obtained in closed form. Stability criteria for a single-degree-of-freedom motion are examined. A pure bending motion is found to be stable, but a pure torsional motion becomes unstable under certain circumstances. These results are consistent with analogous oscillations of an isolated airfoil. However, the stability boundary for a typical cascade differs significantly from the case of the isolated airfoil, being strongly influenced by such cascade parameters as solidity, blade-to-blade phase difference, and stagger angle.

scholarly journals Generalization of the FOPDT Model for Identification and Control Purposes

Processes ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 682 ◽  
Author(s):  
Cristina I. Muresan ◽  
Clara M. Ionescu
Keyword(s):  
Real Life ◽  
Parameter Design ◽  
Dynamic Feedback ◽  
Discussion Section ◽  
Stability Margins ◽  
Closed Loops ◽  
First Order ◽  
Design Systems ◽  
The Stability ◽  
And Control

This paper proposes a theoretical framework for generalization of the well established first order plus dead time (FOPDT) model for linear systems. The FOPDT model has been broadly used in practice to capture essential dynamic response of real life processes for the purpose of control design systems. Recently, the model has been revisited towards a generalization of its orders, i.e., non-integer Laplace order and fractional order delay. This paper investigates the stability margins as they vary with each generalization step. The relevance of this generalization has great implications in both the identification of dynamic processes as well as in the controller parameter design of dynamic feedback closed loops. The discussion section addresses in detail each of this aspect and points the reader towards the potential unlocked by this contribution.

Improved Statistical Linearization for Analysis and Control of Nonlinear Stochastic Systems: Part I: An Extended Statistical Linearization Technique

1981 ◽  
Vol 103 (1) ◽  
pp. 14-21 ◽  
Author(s):  
J. J. Beaman ◽  
J. Karl Hedrick
Keyword(s):  
Stochastic Systems ◽  
Practical Method ◽  
Order System ◽  
Statistical Linearization ◽  
Linearization Technique ◽  
Expansion Technique ◽  
Mean Square Response ◽  
Simplifying Assumptions ◽  
The Stability ◽  
And Control

A practical method of improving the accuracy of the Gaussian statistical linearization technique is presented. The method uses a series expansion of the unknown probability density function which includes up to fourth order terms. It is shown that by the use of the Gram-Charlier expansion a simple generating function can be derived to evaluate analytically the integrals required. It is also shown how simplifying assumptions can be used to substantially reduce the required extra equations, e.g. symmetric or assymetric and single input nonlinearities. It is also shown that the eigenvalues of the statistically linearized system can be used to estimate the stability and speed of response of the nonlinear system. The reduced expansion technique is applied to first and second order nonlinear systems and the predicted mean square response is compared to the Gaussian statistical linearization and the exact solution. The prediction of the time response of the mean of a nonlinear first order system by the use of the statistically linearized eigenvalues is compared to a 300 run Monte Carlo digital solution.

Completeness on the stability criterion of fractional order LTI systems

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Yiheng Wei ◽  
Yuquan Chen ◽  
Songsong Cheng ◽  
Yong Wang
Keyword(s):  
Fractional Order ◽  
Stability Criterion ◽  
Positive Definite Matrix ◽  
Order System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
The Stability ◽  
Definition Of ◽  
And Control

AbstractThe importance of the concept of stability in fractional order system and control has been recognized for some time now. Recently, it has become evident that many conclusions were drawn, but little consensus was reached. Consequently, there is an urgent need for a much deeper understanding of such a concept. With the definition of fractional order positive definite matrix, a set of equivalent and elegant stability criteria are developed via revisiting a stability criterion we proposed before. All the results are formed in terms of linear matrix inequalities. Afterwards, a series of interesting properties of these criteria are revealed profoundly, including completeness, singularity, conservatism, etc. Eventually, a simulation study is provided to validate the effectiveness of the obtained results.

scholarly journals A New Design Method for PI-PD Control of Unstable Fractional-Order System with Time Delay

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Min Zheng ◽  
Tao Huang ◽  
Guangfeng Zhang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Graphical Method ◽  
Stability Boundary ◽  
Fractional Order System ◽  
Stable Region ◽  
Order System ◽  
Pd Controller ◽  
The Stability ◽  
System With Time Delay

In this paper, a practical PI-PD controller parameter tuning method is proposed, which uses the incenter of the triangle and the Fermat point of the convex polygon to optimize the PI-PD controller. Combined with the stability boundary locus method, the PI-PD controller parameters that can ensure stability for the unstable fractional-order system with time delay are obtained. Firstly, the parameters of the inner-loop PD controller are determined by the centre coordinates of the CSR in the kd−kf plane. Secondly, a new graphical method is used to calculate the parameters of the PI controller, in which Fermat points in the CSR of (kp−ki) plane are selected. Furthermore, the method is extended to uncertain systems, and the PI-PD controller parameters are obtained by using the proposed method through common stable region of all stable regions. The proposed graphical method not only ensures the stability of the closed-loop system but also avoids the complicated optimization calculations. The superior control performance of this method is illustrated by simulation.

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