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fractional-order-system
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Adaptive asymptotic tracking control of uncertain fractional-order nonlinear systems with unknown quantized input and control directions subject to actuator failures
, Article JVC/Journal of Vibration and Control ; Volume 28, Issue 19-20 , 2022 , Pages 2625-2641 ; 10775463 (ISSN) ; Shahrokhi, M ; Moradvandi, A ; Sharif University of Technology
SAGE Publications Inc
2022
Abstract
This article addresses an adaptive backstepping control design for uncertain fractional-order nonlinear systems in the strict-feedback form subject to unknown input quantization, unknown state-dependent control directions, and unknown actuator failure. The system order can be commensurate or noncommensurate. The total number of failures is allowed to be infinite. The Nussbaum function is used to deal with the problem of unknown control directions. Compared with the existing results, the control gains can be functions of states and the knowledge of quantization parameters and characteristics of the actuator failure are unknown. By applying the backstepping control approach based on the...
Reducing conservatism in robust stability analysis of fractional-order-polytopic systems
, Article ISA Transactions ; Volume 119 , 2022 , Pages 106-117 ; 00190578 (ISSN) ; Dehghani, M ; Tavazoei, M. S ; Sharif University of Technology
ISA - Instrumentation, Systems, and Automation Society
2022
Abstract
This paper studies the robust stability of the fractional-order (FO) LTI systems with polytopic uncertainty. Generally, the characteristic polynomial of the system dynamic matrix is not an affine function of the uncertain parameters. Consequently, the robust stability of the uncertain system cannot be evaluated by well-known approaches including LMIs or exposed edges theorem. Here, an over-parameterization technique is developed to convert the main characteristic polynomial into a set of local over-parameterized characteristic polynomials (LOPCPs). It is proved that the robust stability of LOPCPs implies the robust stability of the uncertain system. Then, an algorithm is proposed to explore...
On robust stability of linear time invariant fractional-order systems with real parametric uncertainties
, Article ISA Transactions ; Volume 48, Issue 4 , 2009 , Pages 484-490 ; 00190578 (ISSN) ; Haeri, M ; Sharif University of Technology
2009
Abstract
In this paper, the robust bounded-input bounded-output stability of a large class of linear time invariant fractional order families of systems with real parametric uncertainties is analyzed. The transfer functions contain polynomials in fractional powers of the Laplace variable s, possibly in combination with exponentials of fractional powers of s. Using the concept of the value set and a generalization of the zero exclusion condition theorem, a theorem to check the robust bounded-input bounded-output stability of these families of systems is presented. An upper cutoff frequency for drawing the value sets is provided as well. Finally, two numerical examples are given to illustrate results...
Robust Stability Analysis of a Family of Fractional Order Systems with Structured Real Parametric Uncertainties
, Ph.D. Dissertation Sharif University of Technology ; Haeri, Mohammad (Supervisor)
Abstract
Transfer functions of some important classes of infinite-dimensional LTI systems contain semi-polynomials in fractional powers of Laplace variable , possibly in combination with delay terms or exponentials of fractional powers of . They can be observed in many systems and subjects such as biological systems, distributed parameter systems and heat flowing phenomena. Some appropriate theorems relevant to the subject of BIBO-stability are available for a large class of such systems, though many difficulties arise in applying them analytically. In this work, some parameters of the transfer functions of such systems (e.g., the coefficients of the numerators and denominators) are considered as...
Observer-Based Controller Design for Nonlinear Fractional Order Systems
, M.Sc. Thesis Sharif University of Technology ; Shahrokhi, Mohammad (Supervisor)
Abstract
In this study, an adaptive controller design for nonlinear fractional order systems in the strict-feedback form has been investigated. The system is subject to unknown dynamics, unmeasured state variables, quantized input and output, and input nonlinearity. A linear observer is used to solve the problem of unmeasured state variables. The fuzzy logic system is used to estimate the unknown functions, and instead of updating all the regressor weights, only the upper bound of their norms is updated, which significantly reduces the computational load. In the controller design, limitations due to the bandwidth of data transmission have been considered by applying quantizers in the input and output...
Design of fractional order proportional-integral-derivative controller based on moment matching and characteristic ratio assignment method
, Article Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering ; Volume 225, Issue 8 , December , 2011 , Pages 1040-1053 ; 09596518 (ISSN) ; Haeri, M ; Sharif University of Technology
2011
Abstract
This paper presents a new analytical method to design fractional-order proportional- integral-derivative (PID) controllers. The control parameters are calculated so that the closedloop system approximates a desired transfer function with transient response requirements. This function is determined based on the characteristic ratio assignment method. The control parameters are calculated by matching the first three moments of the closed-loop transfer function with the corresponding values of the desired system. Furthermore, to ensure closed-loop stability the proposed method is improved by using the shifted moments around the crossover frequency. Illustrative examples are given to show the...
Stabilization of fractional order systems using a finite number of state feedback laws
, Article Nonlinear Dynamics ; Volume 66, Issue 1-2 , 2011 , Pages 141-152 ; 0924090X (ISSN) ; Sedigh, A. K ; Haeri, M ; Sharif University of Technology
Abstract
In this paper, the stabilization of linear time-invariant systems with fractional derivatives using a limited number of available state feedback gains, none of which is individually capable of system stabilization, is studied. In order to solve this problem in fractional order systems, the linear matrix inequality (LMI) approach has been used for fractional order systems. A shadow integer order system for each fractional order system is defined, which has a behavior similar to the fractional order system only from the stabilization point of view. This facilitates the use of Lyapunov function and convex analysis in systems with fractional order 1
Stable regions in the parameter space of delays for LTI fractional-order systems with two delays
, Article Signal Processing ; Volume 107 , February , 2015 , Pages 415-424 ; 01651684 (ISSN) ; Haeri, M ; Sharif University of Technology
Elsevier
2015
Abstract
This paper studies fractional-order systems of retarded type with two independent delays, and determines the stability regions in spaces of delays. In this approach, an auxiliary polynomial is employed to calculate all purely imaginary roots of the characteristic equation of the system on the imaginary axis. Since roots of the characteristic equation are continuous with respect to delays, these purely imaginary roots determine the stability regions in delay space. Also, the necessary and sufficient condition for stability independent of delays is developed for the systems. Furthermore, a simple inequality constraint is established to obtain pure imaginary poles of the scalar systems....
Characteristic ratio assignment in fractional order systems
, Article ISA Transactions ; Volume 49, Issue 4 , October , 2010 , Pages 470-478 ; 00190578 (ISSN) ; Haeri, M ; Sharif University of Technology
2010
Abstract
In this paper the characteristic ratios and generalized time constant are defined for all-pole commensurate fractional order systems. The sufficient condition for stability of these systems in terms of their characteristic ratios is obtained. Also an analytical approach for characteristic ratio assignment (CRA) to have a non-overshooting fast closed loop step response is introduced. The proposed CRA method is then employed to design a fractional order controller. Computer simulation results are presented to illustrate the performance of the CRA based designed fractional order controllers
Generalization of order distribution concept use in the fractional order system identification
, Article Signal Processing ; Volume 90, Issue 7 , July , 2010 , Pages 2243-2252 ; 01651684 (ISSN) ; Haeri, M ; Sharif University of Technology
2010
Abstract
In this paper, the order distribution concept in the frequency domain identification has been extended to include fractional order systems having poles and zeros simultaneously. The existing nonlinear optimization problem appeared when both poles and zeros, is are changed to a quadratic problem that can be solved using least squares algorithms. To collect the required data, system is excited by a multi sine input signal with appropriately selected frequencies. Then a nonparametric identification in frequency domain is accomplished to calculate the empirical transfer function estimate (ETFE). This estimate is then used to implement the frequency domain identification on all defined members of...
Some analytical results on tuning fractional-order [proportional-integral] controllers for fractional-order systems
, Article IEEE Transactions on Control Systems Technology ; Volume 24, Issue 3 , 2016 , Pages 1059-1066 ; 10636536 (ISSN) ; Tavazoei, M. S ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2016
Abstract
The first objective of this brief is to discover the solution existence conditions in the methods recently proposed for tuning fractional-order [proportional-integral] (FO-[PI]) controllers. The FO-[PI] controller tuned by these methods can simultaneously ensure the desired phase margin, the desired gain crossover frequency, and the flatness of the phase Bode plot at such a frequency. In this brief, the achievable performance region of these tuning methods is also found in the gain crossover frequency-phase margin plane. Moreover, some results on the shape of this region and the uniqueness of the controller resulting from the considered tuning methods are given. By combining the presented...
An efficient numerical algorithm for stability testing of fractional-delay systems
, Article ISA Transactions ; Volume 48, Issue 1 , 2009 , Pages 32-37 ; 00190578 (ISSN) ; Karimi Ghartemani, M ; Sharif University of Technology
2009
Abstract
This paper presents a numerical algorithm for BIBO stability testing of a certain class of the so-called fractional-delay systems. The characteristic function of the systems under consideration is a multi-valued function of the Laplace variable s which is defined on a Riemann surface with finite number of Riemann sheets where the origin is a branch point. The stability analysis of such systems is not straightforward because there is no universally applicable analytical method to find the roots of the characteristic equation on the right half-plane of the first Riemann sheet. The proposed method is based on the Rouche's theorem which provides the number of the zeros of a given function in a...