The variable, fractional-order discrete-time PD controller in the IISv1.3 robot arm control

Ostalczyk, Piotr; Brzeziński, Dariusz W.; Duch, Piotr; Łaski, Maciej; Sankowski, Dominik

doi:10.2478/s11534-013-0254-9

Cited by 11 publications

(19 citation statements)

References 17 publications

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“…System (3) can be approximated, with the discretization step The D-type variable-order derivative and its discrete approximation is given, respectively, by The E -type variable-order derivative and its discrete approximation is given, respectively, by The main motivation of considering the above definitions of fractional variable order derivatives is a fact, that they are widely presented in literature and can be applied in physical systems. In [22], the A -type of fractional variable order derivative was successfully used to design the variable order PD controller in robot arm control. In [23], the heat transfer process in specific grid-holes media whose geometry is changed in time was modeled by a new D-type definition.…”

Section: (T) = [A I J (T)] ∈ R N×n B(t) = [B Ir (T)] ∈ R N×m C(t)mentioning

confidence: 99%

“…In [22], the A -typ derivative was successfully use PD controller in robot arm con fer process in specific grid-hol changed in time was modeled Moreover, these definitions pos described in [24], which can be variable order differential equati , mation is given, respectively…”

Section: Fractional Variable Ordermentioning

confidence: 99%

“…otivation of considering the above definitions riable order derivatives is a fact, that they are ed in literature and can be applied in physi- [22], the A -type of fractional variable order successfully used to design the variable order in robot arm control. In [23], the heat transspecific grid-holes media whose geometry is e was modeled by a new D-type definition.…”

Section: Time-variant Control Systemmentioning

confidence: 99%

“…In [22], the A -type of fractional variable order ivative was successfully used to design the variable order controller in robot arm control. In [23], the heat transprocess in specific grid-holes media whose geometry is nged in time was modeled by a new D-type definition.…”

Section: Time-variant Control Systemmentioning

confidence: 99%

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Numerical solution of fractional variable order linear control system in state-space form

Malesza

Macias

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The aim of this paper is to introduce a matrix approach for approximate solving of non-commensurate fractional variable order linear control systems in state-space form. The approach is based on switching schemes that realize variable order derivatives. The obtained numerical solution is compared with simulation and analog model results. In our paper, a method of finding a numerical solution of fractional variable order control system in a state-space form is introduced, both for time-invariant and time-variant case. Moreover, the obtained results are also valid for system of differential equations with different types of variable order derivatives. To validate our approach the fractional variable order state-space system was physically built and the experimental results were compared with numerical implementations.The paper is organized as follows. At the beginning, in Section 2, the few types of fractional variable order derivatives are recalled, together with their discrete approximations and matrix forms. In Section 3 the solution of linear control system in statespace form for time-variant and time-invariant non-commensurate fractional variable order system is presented. An analog model of particular type of fractional variable order state-space system is introduced in Section 4. The experimental and numerical results are presented in Section 5. Finally, Section 6 summarizes the main results. Fractional variable order operatorsBelow, we recall the already known different types of fractional constant and variable order derivatives and differences. In our paper, a method of finding a numerical solution of actional variable order control system in a state-space form introduced, both for time-invariant as well as time-variant der state-space system was physically build and the experimental results were compared with numerical implementations. The paper is organized as follows. At the beginning, in Sect. 2, the few types of fractional variable order derivatives are recalled, together with their discrete approximations and matrix forms. In Sect. 3 the solution of linear control system in state-space form for time-variant and time-invariant noncommensurate fractional variable order system is presented. An analog model of particular type of fractional variable order state-space system is introduced in Sect. 4. The experimental and numerical results are collected in Sect. 5. Finally, Sect. 6 summarizes the main results. Fractional variable order operatorsBelow, we recall the already known different types of fractional constant and variable order derivatives and differences. Definitions of variable order operatorsThe following fractional constant order difference of Grünwald-Letnikov type will be used as a base of generalization onto variable orderwhere α ∈ R, l = 0, . . . , k, and h > 0 is a sample time. We will consider the following four types of fractional variable order derivatives and their discrete approximations (differences). We admit the order is changing in time, i.e., α(t) ∈ R for t > 0; and in ...

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Section: (T) = [A I J (T)] ∈ R N×n B(t) = [B Ir (T)] ∈ R N×m C(t)mentioning

confidence: 99%

Section: Fractional Variable Ordermentioning

confidence: 99%

Section: Time-variant Control Systemmentioning

confidence: 99%

Section: Time-variant Control Systemmentioning

confidence: 99%

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Numerical solution of fractional variable order linear control system in state-space form

Malesza

Macias

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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“…In order to reduce the amount of historical data (‗the growing calcu lation tail' and finite microprocessor memo ry [19,29]), imp rove the accuracy of the nu merical solution and derive the recursive control algorith m, a Simp lified and Opt imal analytical Form ‗structure and parameters' o f the Fractional-order Feedback (SOF-FoF) model of the fractional-order controller (12) is proposed. The fract ional feedback state control (12) is defined in its incremental form by using the GL defin ition given by Eq.…”

Section: Elaboration Of a Simplified Form Of Foc Algorithmmentioning

confidence: 99%

Controlling and Synchronizing of Fractional- Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

Soukkou¹,

Leulmi²

2016

IJISA

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In this paper, a simp le and optimal fo rm of fractional-order feedback approach assigned for the control and synchronization of a class of fract ional-order chaotic systems is proposed. The proposed control law can be viewed as a distributed network of linear regulators wherein each node is modeled by a PI controller with moderate gains. The mu ltiobject ive genetic algorithm with chaotic mutation, adopted in this work, can be visualized as a combination of structural and parametric genes of a controller o rchestrated in a hierarchical fashion. Then, it is applied to select an optimal knowledge base, which characterizes the developed controller, and satisfies various design specifications. The proposed design and optimizat ion of the developed controller represents a simp le powerful approach to provide a reasonable tradeoff between computational overhead, storage space, numerical accuracy and stability criterion in control and synchronization of a class of fractional-order chaotic systems. Simu lation results show the satisfactory performance of the proposed approach.

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On the trajectory tracking control for an SCARA robot manipulator in a fractional model driven by induction motors with PSO tuning

et al. 2017

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The variable, fractional-order discrete-time PD controller in the IISv1.3 robot arm control

Cited by 11 publications

References 17 publications

Numerical solution of fractional variable order linear control system in state-space form

Numerical solution of fractional variable order linear control system in state-space form

Controlling and Synchronizing of Fractional- Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

On the trajectory tracking control for an SCARA robot manipulator in a fractional model driven by induction motors with PSO tuning

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