Stabilisation of unstable FOPDT processes with a single zero by fractional-order controllers

Kheirizad, Iraj; Jalali, Ahvand; Khandani, Khosro

doi:10.1080/00207721.2012.659696

Cited by 6 publications

(3 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Meanwhile, it has been also shown that fractional-order controllers can achieve better robustness and performance than the integer-order counterparts [4,5]. Hence, many innovative design methods of fractional-order controllers have been proposed in this literature [6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Stabilizing region of fractional‐order proportional integral derivative controllers for interval delayed fractional‐order plants

Ghorbani

Tepljakov

Petlenkov

2022

Asian Journal of Control

View full text Add to dashboard Cite

This paper concentrates on computing the stabilizing region of fractional‐order proportional integral derivative (FOPID) controllers for interval delayed fractional‐order plants. An interval delayed fractional‐order plant is defined as a fractional‐order transfer function with a time delay whose denominator and numerator coefficients are all uncertain and lie in specified intervals. In the present study, first, a theorem is proven to analyze the robust stability of the given closed‐loop. Then, a method is proposed to solve the problem of robustly stabilizing interval delayed fractional‐order plants by using FOPID controllers. Moreover, two auxiliary functions are presented to fulfill the additional specifications of design, ensuring better performance of the controlled system with respect to the disturbance and noise. Finally, two examples are provided to illustrate the design procedure.

show abstract

Section: Introductionmentioning

confidence: 99%

Stabilizing region of fractional‐order proportional integral derivative controllers for interval delayed fractional‐order plants

Ghorbani

Tepljakov

Petlenkov

2022

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…Stabilization and control of fractional-order systems have also been widely investigated [1,2]. Moreover, fractional-order controllers have been successfully utilized for improving the responses of dynamical systems [3][4][5]. In order to obtain a desirable response from a fractional-order closed-loop system, state feedback is a very effective method.…”

Section: Introductionmentioning

confidence: 99%

An H_∞non‐fragile observer‐based adaptive sliding mode controller design for uncertain fractional‐order nonlinear systems with time delay and input nonlinearity

Parvizian

Khandani

Majd

2019

Asian Journal of Control

Self Cite

View full text Add to dashboard Cite

In this paper the problem of non‐fragile adaptive sliding mode observer design is addressed for a class of nonlinear fractional‐order time‐delay systems with uncertainties, external disturbance, exogenous noise, and input nonlinearity. An H∞ observer‐based adaptive sliding mode control considering the non‐fragility of the observer is proposed for this system. The sufficient asymptotic stability conditions are derived in the form of linear matrix inequalities. It is proven that the sliding surface is reachable in finite time. An illustrative example is provided which corroborates the effectiveness of the theoretical results.

show abstract

“…Stability analysis performed for FOS and CCOS is similar to those used for conventional integer-order control system because of their skew-symmetric frequency response phases (Kheirizad et al, 2013). In other words, inverse Laplace transforms of the FOS and CCOS transfer functions are real-valued functions of time and hence, their stability analysis can be conducted by investigating only half of their frequency response associated with positive frequencies.…”

Section: Introductionmentioning

confidence: 99%

From fractional-order to complex-order integrator loop gain: Robust control design and its stability analysis

Rahmani

Jalali

2019

Transactions of the Institute of Measurement and Control

Self Cite

View full text Add to dashboard Cite

Complex-order differintegral (COD) is the extended version of fractional-order one in which the differintegral order can be a complex number rather than a real number. In comparison with fractional-order differintegral (FOD), the distinguishing feature of the COD is that the phase slope of its Bode diagram is a function of imaginary part of the complex order of the COD. In this paper, by the use of this property of the COD, a robust control system is proposed. The design procedure and the realization of the proposed COD-based closed-loop control system are discussed. Since the phase of COD’s frequency response is a nonsymmetric function of frequency, stability analysis of the proposed control system is considered a problematic task. It is proven that for the stability of the control system, it is essential that the COD be applied in a limited frequency band that is derived by the use of the Nyquist stability criterion. Finally, some numerical examples are given to demonstrate the validity and superiority of the proposed complex-order control system.

show abstract

Stabilisation of unstable FOPDT processes with a single zero by fractional-order controllers

Cited by 6 publications

References 31 publications

Stabilizing region of fractional‐order proportional integral derivative controllers for interval delayed fractional‐order plants

Stabilizing region of fractional‐order proportional integral derivative controllers for interval delayed fractional‐order plants

An H_∞non‐fragile observer‐based adaptive sliding mode controller design for uncertain fractional‐order nonlinear systems with time delay and input nonlinearity

From fractional-order to complex-order integrator loop gain: Robust control design and its stability analysis

Contact Info

Product

Resources

About

Stabilisation of unstable FOPDT processes with a single zero by fractional-order controllers

Cited by 6 publications

References 31 publications

Stabilizing region of fractional‐order proportional integral derivative controllers for interval delayed fractional‐order plants

Stabilizing region of fractional‐order proportional integral derivative controllers for interval delayed fractional‐order plants

An H∞non‐fragile observer‐based adaptive sliding mode controller design for uncertain fractional‐order nonlinear systems with time delay and input nonlinearity

From fractional-order to complex-order integrator loop gain: Robust control design and its stability analysis

Contact Info

Product

Resources

About

An H_∞non‐fragile observer‐based adaptive sliding mode controller design for uncertain fractional‐order nonlinear systems with time delay and input nonlinearity