A digital PID controller based on Grünwald-Letnikov fractional-, variable-order operator

Oziablo, Piotr; Mozyrska, Dorota; Wyrwas, Małgorzata

doi:10.1109/mmar.2019.8864688

Cited by 5 publications

(3 citation statements)

References 14 publications

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“…The most important part in our investigations plays the definition of fractional, variable-order h -difference of Grünwald–Letnikov type. In some papers, e.g., [ 14 , 18 , 19 ], this operator is referred as the type

. In the definition, there is a sequence

of coefficients used depending on a given variable-order function.…”

Section: Methodsmentioning

confidence: 99%

“…It means that both orders are changed during the control process. An introduction to variable-, fractional-order differences can be found in [ 11 , 12 , 13 ], and an example algorithm of finding parameters of FVOPID controllers is presented in [ 14 ]. One can find more about potential applications in modelling in [ 15 , 16 , 17 ], where authors provide a survey of the recent relevant literature and findings in primary definitions, models, numerical methods, and their applications of variable-order fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

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Discrete-Time Fractional, Variable-Order PID Controller for a Plant with Delay

Oziablo

Mozyrska

Wyrwas

2020

Entropy

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In this paper, we discuss the implementation and tuning algorithms of a variable-, fractional-order Proportional–Integral–Derivative (PID) controller based on Grünwald–Letnikov difference definition. All simulations are executed for the third-order plant with a delay. The results of a unit step response for all described implementations are presented in a graphical and tabular form. As the qualitative criteria, we use three different error values, which are the following: a summation of squared error (SSE), a summation of squared time weighted error (SSTE) and a summation of squared time-squared weighted error (SST2E). Besides three types of error values, obtained results are additionally evaluated on the basis of an overshoot and a rise time of the output signals achieved by systems with the designed controllers.

show abstract

. In the definition, there is a sequence

of coefficients used depending on a given variable-order function.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discrete-Time Fractional, Variable-Order PID Controller for a Plant with Delay

Oziablo

Mozyrska

Wyrwas

2020

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…It means that integral and derivative orders are in this case changed during the control process and can depend on e.g. time, or the current control error value as shown in [14][15][16]. An introduction to FVOPID controllers theory can be found in [17].…”

Section: Introductionmentioning

confidence: 99%