Fractional Order [PD] Controller Synthesis for Position Systems

2012 ◽  
pp. 113-131
Keyword(s):  
Fractional Order ◽  
Controller Synthesis ◽  
Pd Controller

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

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Piotr Ostalczyk ◽  
Dariusz Brzezinski ◽  
Piotr Duch ◽  
Maciej Łaski ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Output Signal ◽  
Closed Loop ◽  
Loop System ◽  
Robot Arm ◽  
Pd Controller ◽  
Closed Loop System ◽  
Loop Control ◽  
Robot Arm Control

AbstractIn this paper, the discrete differentiation order functions of the variable, fractional-order PD controller (VFOPD) are considered. In the proposed VFOPD controller, a variable, fractional-order backward difference is applied to perform closed-loop, system error, discrete-time differentiation. The controller orders functions which may be related to the controller input or output signal or an input and output signal. An example of the VFOPD controller is applied to the robot arm closed-loop control due to system changes in moment of inertia. The close-loop system step responses are presented.

scholarly journals D-decomposition technique for stabilization of Furuta pendulum: fractional approach

2016 ◽  
Vol 64 (1) ◽  
pp. 189-196 ◽  
Author(s):  
P.D. Mandić ◽  
M.P. Lazarević ◽  
T.B. Šekara
Keyword(s):  
Fractional Order ◽  
Closed Loop ◽  
Inverted Pendulum ◽  
Parameter Dependence ◽  
Pd Controller ◽  
Closed Loop System ◽  
Decomposition Approach ◽  
Stability Regions ◽  
The Stability ◽  
Made In

Abstract In this paper, the stability problem of Furuta pendulum controlled by the fractional order PD controller is presented. A mathematical model of rotational inverted pendulum is derived and the fractional order PD controller is introduced in order to stabilize the same. The problem of asymptotic stability of a closed loop system is solved using the D-decomposition approach. On the basis of this method, analytical forms expressing the boundaries of stability regions in the parameters space have been determined. The D-decomposition method is investigated for linear fractional order systems and for the case of linear parameter dependence. In addition, some results for the case of nonlinear parameter dependence are presented. An example is given and tests are made in order to confirm that stability domains have been well calculated. When the stability regions have been determined, tuning of the fractional order PD controller can be carried out.

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