Limit Cycle Elimination in Inverted Pendulums: Furuta Pendulum and Pendubot

Antonio-Cruz, Mayra; Hernández-Guzmán, Victor Manuel; Silva‐Ortigoza, Ramón

doi:10.1109/access.2018.2839642

Cited by 21 publications

(36 citation statements)

References 42 publications

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“…The experimental results are reported as follows. On the one hand, in Figures 5 and 6, the results associated with the hierarchical controller, that is, Equations (32) and (33), correspond to υ h , i h , u 1av h , ω h , i a h , and u 2av h . The results related to the passive controller, that is, Equations (36) and (37), are υ p , i p , u 1av p , ω p , i a p , and u 2av p .…”

Section: Resultsmentioning

confidence: 99%

“…Motivated by the obtained experimental results, related to the robustness of the proposed controller for the DC/DC Buck-Boost converter-inverter-DC motor system, applications in mobile robotics [2][3][4]34] and underactuated mechanical systems [32,33] are considered as future work.…”

Section: Discussionmentioning

confidence: 99%

“…• Controllers. In this block, the synthesis and programming of the hierarchical controller Equations (32) and (33) and the passive controller Equations (36) and 37is carried-out via Matlab-Simulink. The corresponding program is shown in Figure 3, where the following four stages are observed: (i) Signals acquisition, (ii) Reference variables, (iii) Hierarchical controller, and (iv) Passive controller.…”

Section: Experimental Testbedmentioning

confidence: 99%

“…It is worth noting that industrial and mechatronic applications would be limited if [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] were only considered compared with [6,[25][26][27][28][29][30][31]. For example, in mobile robots [2][3][4], and underactuated mechanical systems [32,33], among others.…”

Section: Introductionmentioning

confidence: 99%

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Robust Tracking Controller for a DC/DC Buck-Boost Converter–Inverter–DC Motor System

et al. 2018

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This paper has two aims. The first is to develop a robust hierarchical tracking controller for the DC/DC Buck-Boost–inverter–DC motor system. This controller considers a high level control for the inverter–DC motor subsystems and a low level control for the DC/DC Buck-Boost converter subsystem. Such controls solve the tracking task associated with the angular velocity of the motor shaft and the output voltage of the converter, respectively, via the differential flatness approach. The second aim is to present a comparison of the robust hierarchical controller to a passive controller. This, with the purpose of showing that performance achieved with the hierarchical controller proposed in this paper, is better than the one achieved with the passive controller. Both controllers are experimentally implemented on a prototype of the DC/DC Buck-Boost–inverter–DC motor system by using Matlab-Simulink along with the DS1104 board from dSPACE. According to experimental results, the proposal in the present paper achieves a better performance than the passive controller.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Experimental Testbedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Tracking Controller for a DC/DC Buck-Boost Converter–Inverter–DC Motor System

et al. 2018

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“…On the other hand, underactuated mechanical systems, and in particular inverted pendulums, have attracted the attention of several researchers because they are an excellent benchmark to study position control, limit cycles, and system stability [18]. Motivated by this scenario and by [19,20], this paper deals with the elimination of limit cycles generated by a friction-induced dead-zone nonlinearity when regulating the inverted pendulum on a cart.…”

Section: Introductionmentioning

confidence: 99%

Implementation of a Controller to Eliminate the Limit Cycle in the Inverted Pendulum on a Cart

et al. 2019

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A frequency response-based linear controller is implemented to regulate the inverted pendulum on a cart at the inverted position. The objective is to improve the performance of the control system by eliminating the limit cycle generated by the dead-zone, induced by static friction, at the actuator of the mechanism. This control strategy has been recently introduced and applied by the authors to eliminate the limit cycle in the Furuta pendulum and the pendubot systems. Hence, the main aim of the present paper is to study the applicability of the control strategy to eliminate the limit cycle in the inverted pendulum on a cart. The successful results that are obtained in experiments corroborate that the approach introduced by the authors to eliminate the limit cycle in the Furuta pendulum and pendubot is also valid for the inverted pendulum on a cart.

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Stability analysis of dynamic interval type‐2 fuzzy control systems in frequency domain

Namadchian

Zare

2020

Asian Journal of Control

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The present paper aims to analyze the stability of dynamic Interval Type-2 fuzzy control systems (IT2 FCSs) with adjustable parameters by investigating the existence of limit cycles based on the describing function (DF) method. To simplify the stability analysis, the following structured procedure is described. First, to avoid complex computation, a simple architecture of the IT2 FCS using two embedded Type-1 fuzzy control systems (T1 FCSs) is proposed. Then, the DF of IT2 FCS is obtained based on the DFs of embedded T1FCSs. Subsequently, integrating the stability equation and parameter plane approaches provides a solution to identify the limit cycle and the asymptotically stability regions. Moreover, particle swarm optimization (PSO) technique is utilized to minimize the limit cycle region. Other focus of this paper is on the stability margins analysis for robust design. For this purpose, a gain-phase margin tester is applied to determine the minimum Gain Margin (GM min ) and Phase Margin (PM min ) when limit cycles can arise. Finally, two simulation examples are given to verify the effectiveness of the proposed approach.

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Limit Cycle Elimination in Inverted Pendulums: Furuta Pendulum and Pendubot

Cited by 21 publications

References 42 publications

Robust Tracking Controller for a DC/DC Buck-Boost Converter–Inverter–DC Motor System

Robust Tracking Controller for a DC/DC Buck-Boost Converter–Inverter–DC Motor System

Implementation of a Controller to Eliminate the Limit Cycle in the Inverted Pendulum on a Cart

Stability analysis of dynamic interval type‐2 fuzzy control systems in frequency domain

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