Algebraic bound for the phase–frequency response of the commande robuste d'ordre non-entier approximation of fractional differentiators and its applications in control systems analysis

2021 ◽  
pp. 107754632098776
Author(s):  
Khashayar Neshat ◽  
Mohammad Saleh Tavazoei
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Control Systems ◽  
Fractional Order ◽  
Upper Bound ◽  
Systems Analysis ◽  
Sufficient Conditions ◽  
Approximation Process ◽  
Positive Realness

This article deals with analyzing the phase–frequency response of commande robuste d'ordre non-entier approximations of fractional-order differentiators. More precisely, an algebraic tight upper bound is derived for the phase of the approximations obtained from the commande robuste d'ordre non-entier method. Then, some applications for this achievement are discussed in the viewpoint of control systems analysis. These applications include usefulness of the obtained upper bound in stability preservation analysis during the commande robuste d'ordre non-entier–based approximation process and applicability of such a bound in finding necessary or sufficient conditions for test of positive realness/negative imaginariness of a fractional-order transfer function.

A Method of Model Reduction

1986 ◽  
Vol 108 (4) ◽  
pp. 368-371 ◽  
Author(s):  
Jium-Ming Lin ◽  
Kuang-Wei Han
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Model Reduction ◽  
Control Systems ◽  
Response Curve ◽  
Nonlinear Control Systems ◽  
Frequency Response Curve ◽  
Stability Boundaries ◽  
Parameter Variations ◽  
The Stability

In this brief note, the effects of model reduction on the stability boundaries of control systems with parameter variations, and the limit-cycle characteristics of nonlinear control systems are investigated. In order to reduce these effects, a method of model reduction is used which can approximate the original transfer function at S=0, S=∞, and also match some selected points on the frequency response curve of the original transfer function. Examples are given, and comparisons with the methods given in current literature are made.

Simultaneous Compensation of the Gain, Phase, and Phase-Slope

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Vahid Badri ◽  
Mohammad Saleh Tavazoei
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Phase Margin ◽  
Phase Plot ◽  
Phase Slope ◽  
Loop Transfer Function ◽  
Sample Application ◽  
Arbitrary Frequency ◽  
Necessary And Sufficient

This paper deals with the problem of simultaneous compensation of the gain, phase, and phase-slope at an arbitrary frequency by using a fractional-order lead/lag compensator. The necessary and sufficient conditions for feasibility of the problem are derived. Also, the number of existing solutions (i.e., the number of distinct fractional-order lead/lag compensators satisfying the considered compensation requirements) is analytically found. Moreover, as a sample application, it is shown that the obtained results for the considered compensation problem are helpful in tuning fractional-order lead/lag compensators for simultaneously achieving desired phase margin, desired gain cross frequency, and flatness of the Bode phase plot of the loop transfer function at this frequency.

scholarly journals Fractional hold circuits versus positive realness of discrete transfer functions

2005 ◽  
Vol 2005 (3) ◽  
pp. 373-378 ◽  
Author(s):  
M. de la Sen ◽  
A. Bilbao-Guillerna
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Transfer Functions ◽  
Input Output ◽  
Appropriate Use ◽  
First Order ◽  
Positive Realness ◽  
Direct Input

The appropriate use of fractional-order holds (β-FROH) of correcting gainsβ∈[−1,1]as an alternative to the classical zero-and first-order holds (ZOHs, FOHs) is discussed related to the positive realness of the associate discrete transfer functions obtained from a given continuous transfer function. It is proved that the minimum direct input/output gain (i.e., the quotient of the leading coefficients of the numerator and denominator of the transfer function) needed for discrete positive realness may be reduced by the choice ofβcompared to that required for discretization via ZOH.

scholarly journals A New Fractional Order Hold and Its Capability in Frequency Response and Zero Placement

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Farzad Hashemzadeh ◽  
Amin Rezaei Pish-Robat ◽  
Parviz Jabehdar-Maralani
Keyword(s):  
Frequency Response ◽  
Control Systems ◽  
Fractional Order ◽  
Sampling Period ◽  
Zero Order ◽  
Digital Control Systems ◽  
Simulation Results ◽  
The Stability ◽  
Performance Results ◽  
Better Than

This paper introduces a new holder with application on digital control systems. This holder is a combination of fractional order hold (FROH) and zero-order hold (ZOH) that has the capability of both holders and a frequency response better than both of ZOH and FROH. For the stability of zeros of the sampled system two theorems are stated and proved with the assumption that the sampling period is very small. Also simulation results are studied to show the effectiveness of the proposed holder and better performance results in comparison with ZOH and FROH.

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