On Fractional PI? Controllers: Some Tuning Rules for Robustness to Plant Uncertainties

Monje, Concepción A.; Martín, Antonio; Vinagre, Blas M.; Chen, YangQuan; Feliú, V.

doi:10.1007/s11071-004-3767-3

Cited by 223 publications

(121 citation statements)

References 7 publications

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“…The equation in (17) can be seen to be nonlinear in nature. Thus, a simple Bisection method can be used to numerically solve for its peak time T P > 0.…”

Section: The Class Of Two-term Fractional-order Systems Will Always Rmentioning

confidence: 99%

“…Consider for example the system described by the transfer function P( ) = 1 1 6 + 1 (17) in which the step-response is shown in Fig. 5.…”

Section: Half-cycle Posicast Control For the Classmentioning

confidence: 99%

“…Moreover, many types of fractional-order controllers are possible and the most common models are based on the PID family such as, but not limited to: fractional PI [15][16][17][18], fractional PD [19][20][21][22][23], fractional PID [24][25][26][27][28] controllers, fractional lead-lag networks [29,30], and other special types of fractional-order controllers, e.g. [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

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Posicast control of a class of fractional-order processes

et al. 2013

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Abstract:The number of studies on the control of fractional-order processesprocesses having dynamics described by differential equations of arbitrary orderhas been increasing in the past two decades and it is now ubiquitous. Various methods have emerged and have been proven to effectively control such processes usually resulting in fractional-order controllers similar to their conventional integer-order counterparts, which include, but are not limited to fractional PID and fractional lead-lag controllers. However, such methods require a lot of computational effort and fractional-order controllers could be challenging when it comes to their synthesis and implementation. In this paper, we propose a simple yet effective delay-based controller with the use of the Posicast control methodology in controlling the overshoot of a fractional-order process of the class : {P( ) = 1/( α + )} having orders 1 < α < 2. Such controllers have proven to be easy to implement because they only require delays and summers. In this paper, the Posicast control methodology introduced in the past few years is modified to minimize the overshoot of the processes step response to a level that is acceptable in control engineering and automation practices. Furthermore, proof of the existence of overshoot for such class of processes, as well as the determination of the peak-time of the open-loop response of a fractional-order process of the class is presented. Validation through numerical simulations for a class of fractional-order processes are presented in this paper.

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“…The equation in (17) can be seen to be nonlinear in nature. Thus, a simple Bisection method can be used to numerically solve for its peak time T P > 0.…”

Section: The Class Of Two-term Fractional-order Systems Will Always Rmentioning

confidence: 99%

“…Consider for example the system described by the transfer function P( ) = 1 1 6 + 1 (17) in which the step-response is shown in Fig. 5.…”

Section: Half-cycle Posicast Control For the Classmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Posicast control of a class of fractional-order processes

et al. 2013

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“…The performance criteria are frequently specified in terms of gain crossover frequency, phase crossover frequency, phase margin, gain margin, and robustness to openloop gain variations [15], [16].…”

Section: Introductionmentioning

confidence: 99%

Fractional order control of a DC motor with load changes

Copot

Muresan

Ionescu

et al. 2014

2014 International Conference on Optimization of Electrical and Electronic Equipment (OPTIM)

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Abstract-This paper investigates the robustness of a fractional-order controller against the load changes of a DC motor. The gains and time constants of the DC motor are modified by means of a change in the brake. Two different setups of a DC motor, one with 25% brake and the other with 50% brake are considered in the experimental evaluation. The closed-loop performances of the fractional-order controller are compared with integer-order controller using the same performance criteria and the same tuning algorithm. Both controllers were designed based on time domain specifications. The experimental results show that the fractional-order controller outperforms the classical controller under nominal conditions as well as under gain variations situation.

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“…The fractional order PIDs have two supplementary parameters compared to the traditional PIDs. It is for this reason, that the fractional order PIDs have the potential to meet more design specifications than the traditional PIDs and hence to increase the performance and robustness of closed loop systems [1][2][3][4]. A couple of interesting methods have been proposed for tuning such FO-PIDs with the great majority centered upon Matlab's fminsearch or graphical approaches [1,[5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Simplified Optimization Routine for Tuning Robust Fractional Order Controllers

Muresan¹

2013

AJCM

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Fractional order controllers have been used intensively over the last decades in controlling different types of processes. The main methods for tuning such controllers are based on a frequency domain approach followed by optimization routine, generally in the form of the Matlab fminsearch, but also evolving to more complex routines, such as the genetic algorithms. An alternative to these time consuming optimization routines, a simple graphical method has been proposed. However, these graphical methods are not suitable for all combinations of the imposed performance specifications. To preserve their simplicity, but also to make these graphical methods generally applicable, a modified graphical method using a very straightforward and simple optimization routine is proposed within the paper. Two case studies are presented, for tuning fractional order PI and PD controllers.

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On Fractional PI? Controllers: Some Tuning Rules for Robustness to Plant Uncertainties

Cited by 223 publications

References 7 publications

Posicast control of a class of fractional-order processes

Posicast control of a class of fractional-order processes

Fractional order control of a DC motor with load changes

Simplified Optimization Routine for Tuning Robust Fractional Order Controllers

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