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

Abstract. This paper deals with the stability problem of two types of inverted pendulum controlled by a fractional order PD controller. Rotational inverted pendulum and cart inverted pendulum are under-actuated mechanical systems with two degrees of freedom and one control input. Detailed mathematical models of both pendulums are derived using the Rodriguez method. Fractional order PD controller is introduced for inverted pendulum stabilization. Stability regions in control parameters space are calculated using the D-decomposition approach, based on which tuning of the fractional order controller can be carried out. Numerical simulations and experimental realization are given to demonstrate the effectiveness of the proposed method.

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“…a 11 ¼ a 11 u ð Þ; a 12 ¼ ÀK 3 cosðuÞ; a 22 ¼ K 4 ; C 12;1 ¼ K 2 sinð2uÞ; [6]. In the case of the cart pendulum system in Fig.…”

Section: System Modellingmentioning

confidence: 99%

“…D-decomposition for linear fractional systems is investigated for the case of linear parameters dependence too. Some results of the D-decomposition procedure for inverted pendulum systems are given in [4][5][6]. This technique enables efficient computational method for determining the asymptotic stability region.…”

Section: Introductionmentioning

confidence: 99%

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

Mandić

Lazarević

Šekara

2016

Advances in Intelligent Systems and Computing

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“…The effect of adaptive feedback using the estimates of matrix A that concerns to the stabilization of a double-inverted pendulum is discussed in [16] without exact knowledge of dynamic equations and in the presence of external bounded perturbations. Fractional order controller for stabilization of rotational inverted pendulum and D-decomposition technique for identifying stability regions in the controller parameter space are employed in [17]. It shows the result with respect to impulse response and not step response.…”

Section: Introductionmentioning

confidence: 99%

Kalman Filter and H∞ Filter Based Linear Quadratic Regulator for Furuta Pendulum

Arulmozhi¹,

Victorie²

2022

Computer Systems Science and Engineering

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This paper deals with Furuta Pendulum (FP) or Rotary Inverted Pendulum (RIP), which is an under-actuated non-minimum unstable non-linear process. The process considered along with uncertainties which are unmodelled and analyses the performance of Linear Quadratic Regulator (LQR) with Kalman filter and H ∞ filter as two filter configurations. The LQR is a technique for developing practical feedback, in addition the desired x shows the vector of desirable states and is used as the external input to the closed-loop system. The effectiveness of the two filters in FP or RIP are measured and contrasted with rise time, peak time, settling time and maximum peak overshoot for time domain performance. The filters are also tested with gain margin, phase margin, disk stability margins for frequency domain performance and worst case stability margins for performance due to uncertainties. The H-infinity filter reduces the estimate error to a minimum, making it resilient in the worst case than the standard Kalman filter. Further, when the β restriction value lowers, the H ∞ filter becomes more robust. The worst case gain performance is also focused for the two filter configurations and tested where H ∞ filter is found to outperform towards robust stability and performance. Also the switchover between the two filters is dependent upon a user-specified co-efficient that gives the flexibility in the design of non-linear systems. The non-linear process is tested for set point tracking, disturbance rejection, un-modelled noise dynamics and uncertainties, which records robust performance towards stability.

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“…The fractional calculus which is an extension of the ordinary integer calculus, has been extensively utilized in various scientific areas e.g., biology [1,2], control systems [3,4], electronics [5,6], dynamical system [7][8][9] and image processing [10,11]. Its related differential equation namely fractional differential equation (FDE) which is an extension of the ordinary differential equation (ODE), serves as the foundation for modelling the fractional order system [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A Dimensional Consistency Aware Time Domain Analysis of the Generic Fractional Order Biquadratic System

Banchuin

Chaisricharoen

2022

JMM

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In this research, the time domain analysis of the fractional order biquadratic system with nonzero input and nonzero damping ratio has been performed. Unlike the previous works, the analysis has been generically done with dimensional consistency awareness without referring to any specific physical system where nonzero input and nonzero damping ratio have been allowed. The fractional differential equation of the system has been derived and analytically solved. The physical measurability of the dimensions of the fractional derivative terms which have been defined in Caputo sense, and response with significantly different dynamic from its dimensional consistency ignored counterpart have been obtained due to our dimensional consistency awareness. The resulting solution is applicable to the fractional biquadratic systems of any kind with any physical nature. Based on such solution and numerical simulations, the influence of the fractional order parameter to all major time domain parameters have been studied in detailed. The obtain results provide insight to the fractional order biquadratic system with dimensional consistency awareness in a generic point of view.

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

Cited by 12 publications

References 13 publications

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

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

Kalman Filter and H∞ Filter Based Linear Quadratic Regulator for Furuta Pendulum

A Dimensional Consistency Aware Time Domain Analysis of the Generic Fractional Order Biquadratic System

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