Stabilization of Inverted Pendulum by Fractional Order PD Controller with Experimental Validation: D-decomposition Approach

2016 ◽  
pp. 29-37 ◽  
Author(s):  
Petar D. Mandić ◽  
Mihailo P. Lazarević ◽  
Tomislav B. Šekara
Keyword(s):  
Fractional Order ◽  
Experimental Validation ◽  
Inverted Pendulum ◽  
Pd Controller ◽  
Decomposition Approach

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.

scholarly journals Intelligent control for nonlinear inverted pendulum based on interval type-2 fuzzy PD controller

2014 ◽  
Vol 53 (1) ◽  
pp. 23-32 ◽  
Author(s):  
Ahmad M. El-Nagar ◽  
Mohammad El-Bardini ◽  
Nabila M. EL-Rabaie
Keyword(s):  
Intelligent Control ◽  
Inverted Pendulum ◽  
Pd Controller ◽  
Interval Type ◽  
Fuzzy Pd

Modified PD Control of Rotary Inverted Pendulum

2009 ◽  
Author(s):  
Naserodin Sepehry ◽  
Mahnaz Shamshirsaz
Keyword(s):  
Feedback Control ◽  
Inverted Pendulum ◽  
Break Point ◽  
State Feedback Control ◽  
Pd Controller ◽  
Loop Transfer Function ◽  
Full State ◽  
Full State Feedback ◽  
Rotary Inverted Pendulum ◽  
Space Method

The inverted pendulum, a classical mechatronic application, exists in many different forms. In despite that many works have been done to balance the pendulum link on end of this device using feedback control but few studies have been developed to control this rotary inverted pendulum using PD controller. In classical methods, using PD, PI or PID control, difficulties appear due to one of the coefficients becomes zero in closed loop transfer function denominator and consequently the system becomes unstable. In this study, an arbitrary pole is placed in order to create a break point in root locus, so by this way a PD controller can be designed for this new system. Also, disturbance rejection has been investigated by state space method in this paper. The results of this modified PD controller are compared with full state feedback control and optimal control, so the method used in this study has been validated.

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