Journal articles: 'Inverted pendulum'

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Mesa, F., R. Ospina Ospina, and D. M. Devia-Narvaez. "Methodology of robust inverted pendulum controllers on a vehicle." Journal of Physics: Conference Series 2102, no. 1 (November 1, 2021): 012012. http://dx.doi.org/10.1088/1742-6596/2102/1/012012.

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Abstract In the theory of controllers, the simple and inverted pendulum play an important role due to the equations that result from them, which imply non-linearities and perturbations, thus, in this article, a brief classification of inverted pendulums is presented: inverted pendulum, inverted double pendulum, inverted rotary pendulum (Furuta pendulum). Subsequently, a mathematical model of the inverted pendulum is described through the deduction of the equations of motion that represent the dynamics of the system. Robust control is presented that allows expanding the richness of the mathematical equations, for this case, a control with output feedback is presented and applied to the inverted pendulum to control the unstable dynamics of this model. The results are compared with a post placement control and a robust control using a norm that analyses the characteristics of the system.

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Nasim, Shahzad, M. Javeed, M. Shafiq, Faraz Liaquat, and Zain Anwar Ali. "Self-Erected Inverted Pendulum." Advanced Materials Research 816-817 (September 2013): 415–19. http://dx.doi.org/10.4028/www.scientific.net/amr.816-817.415.

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The basic theme of this research paper is self-erecting the inverted pendulum by via ARDUINO controller and stabilizes the system through PID algorithm of linear control system. ARDUINO controller acquires the data from the sensors in terms of position and angle of the pendulum and commands the motor through PWM signal after that swing the pendulum from rest position to get and balance the inverted position. Controller read the pendulums angular position through potentiometer then calculates and removes errors via PID algorithm. MATLAB-Simulink and LABVIEW sent and receives runtime information from controller.

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Fahmizal, Geonoky, and Hari Maghfiroh. "Rotary Inverted Pendulum Control with Pole Placement." Journal of Fuzzy Systems and Control 1, no. 3 (December 27, 2023): 90–96. http://dx.doi.org/10.59247/jfsc.v1i3.152.

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The inverted pendulums are multivariable and highly unstable dynamic systems. The inverted pendulum has been used to answer many modern control and control system designs because it has several problems relating to the system model of nonlinearity, difficulty, and inactivity. In this research, the main topic is the rotatory inverted pendulum. Circular path to eliminate the path that is on the pendulum that is traversed by the transversal path. In this paper, the Inverted Rotatory Pendulum is analyzed by state feedback which is adjusted by pole placement. The result of design selection in the system is very important to pay attention to the area where the pendulum will reach the point of agreement.

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PAGANO, DANIEL, LUIS PIZARRO, and JAVIER ARACIL. "LOCAL BIFURCATION ANALYSIS IN THE FURUTA PENDULUM VIA NORMAL FORMS." International Journal of Bifurcation and Chaos 10, no. 05 (May 2000): 981–95. http://dx.doi.org/10.1142/s0218127400000700.

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Inverted pendulums are very suitable to illustrate many ideas in automatic control of nonlinear systems. The rotational inverted pendulum is a novel design that has some interesting dynamics features that are not present in inverted pendulums with linear motion of the pivot. In this paper the dynamics of a rotational inverted pendulum has been studied applying well-known results of bifurcation theory. Two classes of local bifurcations are analyzed by means of the center manifold theorem and the normal form theory — first, a pitchfork bifurcation that appears for the open-loop controlled system; second, a Hopf bifurcation, and its possible degeneracies, of the equilibrium point at the upright pendulum position, that is present for the controlled closed-loop system. Some numerical results are also presented in order to verify the validity of our analysis.

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Wang, Yujue, Weining Mao, Qing Wang, and Bin Xin. "Fuzzy Cooperative Control for the Stabilization of the Rotating Inverted Pendulum System." Journal of Advanced Computational Intelligence and Intelligent Informatics 27, no. 3 (May 20, 2023): 360–71. http://dx.doi.org/10.20965/jaciii.2023.p0360.

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The rotating inverted pendulum is a nonlinear, multivariate, strongly coupled unstable system, and studying it can effectively reflect many typical control problems. In this paper, a parameter self-tuning fuzzy controller is proposed to perform the balance control of a single rotating inverted pendulum. Particle swarm optimization is used to adjust its control parameters, and simulation experiments are performed to show that the system can achieve stability with the designed parametric self-tuning fuzzy controller, with control performance better than that of the conventional fuzzy controller. Furthermore, the leader-follower control strategy is used to realize the cooperative control of multiple rotating inverted pendulums. Two QUBE-Servo 2 rotating inverted pendulums are used for a cooperative pendulum swing-up experiment and stabilization experiment, and the effectiveness of the proposed cooperative control strategy is verified.

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Sultan, Ghassan A., and Ziyad K. Farej. "Design and Performance Analysis of LQR Controller for Stabilizing Double Inverted Pendulum System." Circulation in Computer Science 2, no. 9 (October 20, 2017): 1–5. http://dx.doi.org/10.22632/ccs-2017-252-45.

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Double inverted pendulum (DIP) is a nonlinear, multivariable and unstable system. The inverted pendulum which continually moves toward an uncontrolled state represents a challenging control problem. The problem is to balance the pendulum vertically upward on a mobile platform that can move in only two directions (left or right) when it is offset from zero stat. The aim is to determine the control strategy that deliver better performance with respect to pendulum's angles and cart's position. A Linear-Quadratic-Regulator (LQR) technique for controlling the linearized system of double inverted pendulum model is presented. Simulation studies conducted in MATLAB environment show that the LQR controller are capable of controlling the multi output double inverted pendulum system. Also better performance results are obtained for controlling heavy driven part DIP system.

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7

Pippard, A. B. "The inverted pendulum." European Journal of Physics 8, no. 3 (July 1, 1987): 203–6. http://dx.doi.org/10.1088/0143-0807/8/3/012.

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Luca, Roberto De, Marco Di Mauro, and Adele Naddeo. "The inverted pendulum." European Journal of Physics 39, no. 5 (August 3, 2018): 055008. http://dx.doi.org/10.1088/1361-6404/aad3d6.

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Yi, Jianqiang, Naoyoshi Yubazaki, and Kaoru Hirota. "A New Fuzzy Controller for Stabilizing Inverted Pendulums Based on Single Input Rule Modules Dynamically Connected Fuzzy Inference Model." Journal of Advanced Computational Intelligence and Intelligent Informatics 5, no. 1 (January 20, 2001): 58–70. http://dx.doi.org/10.20965/jaciii.2001.p0058.

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A fuzzy controller is presented based on the Single Input Rule Modules (SIRMs) dynamically connected fuzzy inference model for stabilization control of inverted pendulums. The angle and angular velocity of the pendulum and the position and velocity of the cart are selected as input items and the driving force as the output item. By using SIRMs and dynamic importance degrees, the fuzzy controller realizes angular control of the pendulum and position control of the cart in parallel with totally only 24 fuzzy rules. Switching between angular control of the pendulum and position control of the cart is smoothly performed by automatically adjusting dynamic importance degrees according to control situations. For any inverted pendulums, of which the pendulum length is among [0.5m, 2.2m], simulation results show that the proposed fuzzy controller has a high generalization ability to stabilize the pendulum systems completely in about 6.0 seconds when the initial angle of the pendulum is among [-30.0°, +30.0°], or the initial position of the cart is among [-2.1m, +2.1m].

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10

Wang, Hong Qi. "Dynamics Modeling of the Planar Double Inverted Pendulum." Applied Mechanics and Materials 195-196 (August 2012): 17–22. http://dx.doi.org/10.4028/www.scientific.net/amm.195-196.17.

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planar double inverted pendulum is a strong coupling, uncertain and complex nonlinear system, and the dynamics model of which is the basis of control, simulation and analysis. In the paper coordinate systems of the planar double inverted pendulum were first defined, and then the dynamics model of which was built up based on screw theory and the Lagrange principle. The modeling method used being systematic and standardized, it is easy to extend to dynamics modeling of higher order planar inverted pendulums or other multi-body systems.

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Bindu, B., Srikanth N, Haris Raja V, Barath Kumar JK, and Dharmendra R. "Comparative analysis of inverted pendulum control." Scientific Temper 14, no. 02 (June 6, 2023): 516–20. http://dx.doi.org/10.58414/scientifictemper.2023.14.2.44.

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The main motive of this paper is to balance the inverted pendulum system (non-linear model) using controllers and to compare the results obtained from using different controllers. The aim is to determine which controller provides best results with respect to cart’s position and pendulum’s angle. The controllers used in this paper are PI, PD, PID. The inverted pendulum model is modeled using Simscape and the simulation results are obtained using MATLAB

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Abdul Kareem, Ali Fawzi, and Ahmed Abdul Hussein Ali. "Robust Stability Control of Inverted Pendulum Model for Bipedal Walking Robot." Al-Nahrain Journal for Engineering Sciences 23, no. 1 (March 20, 2020): 81–88. http://dx.doi.org/10.29194/njes.23010081.

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This paper proposes robust control for three models of the linear inverted pendulum (one mass linear inverted pendulum model, two masses linear inverted pendulum model and three masses linear inverted pendulum model) which represents the upper, middle and lower body of a bipedal walking robot. The bipedal walking robot is built of light-weight and hard Aluminum sheets with 2 mm thickness. The minimum phase system and non-minimum phase system are studied and investigated for inverted pendulum models. The bipedal walking robot is programmed by Arduino microcontroller UNO. A MATLAB Simulink system is built to embrace the theoretical work. The results showed that one linear inverted pendulum is the worst performance, worst noise rejection and the worst set point tracking to the zero moment point. But two masses linear inverted pendulum models and three masses linear inverted pendulum model have a better performance, a better high-frequency noise rejection characteristic and better set-point tracking to the zero moment point.

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Samiee, Ahmad. "Optimal Control Comparisons on a Flywheel Based Inverted Pendulum." Mapta Journal of Mechanical and Industrial Engineering (MJMIE) 3, no. 1 (April 20, 2019): 18–26. http://dx.doi.org/10.33544/mjmie.v3i1.108.

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This paper introduces a comparison between two optimal controllers on a flywheel-based inverted pendulum. Inverted pendulums have an essential place in developing under-actuation nonlinear control schemes due to their nonlinear structure. This system is a basic structure for many advanced systems such as biped and mobile wheeled robots. Optimal controllers addressed in this paper consist of State-Dependent Riccati Equation (SDRE) and Linear Quadratic Regulator (LQR). A Proportional–Integral–Derivative controller (PID) is also designed and tested in the simulation. One axis self-balancing flywheel based inverted pendulum system is designed to validate the controllers' performance on an experimental setup.

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14

Voevoda, Aleksandr, and Vladislav Filiushov. "Feedback linearization: inverted pendulum." Transaction of Scientific Papers of the Novosibirsk State Technical University, no. 3 (October 13, 2016): 49–60. http://dx.doi.org/10.17212/2307-6879-2016-3-49-60.

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Voevoda, Aleksandr, and Vladislav Filiushov. "Feedback linearization: inverted pendulum." Transaction of Scientific Papers of the Novosibirsk State Technical University, no. 4 (December 16, 2016): 62–71. http://dx.doi.org/10.17212/2307-6879-2016-4-62-71.

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Lastomo, Dwi, Herlambang Setiadi, and Muhammad Ruswandi Djalal. "Design Controller of Pendulum System using Imperialist Competitive Algorithm." INTEK: Jurnal Penelitian 4, no. 1 (May 3, 2017): 53. http://dx.doi.org/10.31963/intek.v4i1.94.

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Due to development of technology in recent years, complexity and nonlinearity of mechanical and electrical system are increasing significantly. Inverted pendulum is nonlinear system that has become popular in recent years. However, inverted pendulum is nonlinear and unstable system. Therefore appropriate design controller of inverted pendulum system is crucial. Hence, this paper proposed, design of inverted pendulum system based on imperialist competitive algorithm (ICA). In order to design the controller, dynamic model of inverted pendulum system is used. Time domain simulation is used to address the controller performance. From the simulation result, it is found that imperialist competitive algorithm can be used to design inverted pendulum system controller.

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17

Shi, Xiang, Zhe Xu, Ka Tian, and Qing Yi He. "Optimal Control for Wheeled Inverted Pendulum Based on Collaborative Simulation." Applied Mechanics and Materials 556-562 (May 2014): 2444–47. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.2444.

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To control wheeled inverted pendulum is a good way to test all kinds of theories of control. The optimal control based on MATLAB is used to control wheeled inverted pendulum, and the control law is designed, and its feasibility is verified. However the mathematical model of the wheeled inverted pendulum is linearized and inverted pendulum is a high-order nonlinear system, both of them exist errors. Then the collaborative simulation of MATLAB and ADAMS is also used to control wheeled inverted pendulum, in which wheeled inverted pendulum is built up to virtual prototype model in ADAMS based on virtual prototype technology, and the control law designed from simulation of MATLAB is consulted. At last the results of simulation demonstrate the correctness of optimal control of wheeled inverted pendulum, and it also indicates the way is worth advocating in the study.

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Kumagai, Masaaki, and Takaya Ochiai. "Development of a Robot Balanced on a Ball - First Report, Implementation of the Robot and Basic Control -." Journal of Robotics and Mechatronics 22, no. 3 (June 20, 2010): 348–55. http://dx.doi.org/10.20965/jrm.2010.p0348.

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This paper proposes the implementation and control scheme of a robot balanced on a ball. Unlike a twowheeled inverted pendulum, such as the Segway Human Transporter, an inverted pendulum using a ball moves in any direction without changing orientation, enabling isotropic movement and stabilization. The robot on the ball can be used in place of the twowheeled robots. Our robot has three omnidirectional wheels with stepping motors that drive the ball and two sets of rate gyroscopes and accelerometers as attitude sensors. It can keep station, traverse in any direction, and turn around its vertical axis. Inverted pendulum control is applied to two axes to maintain attitude. Ball acceleration is used as control input of the system, unlike most of inverted pendulums which use torque or force as input. This acceleration input makes the robot robust against change of inertia parameters, as confirmed by Nyquist diagrams. The mechanism of the robot, the control method, and the experimental results are described in this paper.

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Öksüz, Mehmet, and Recep Halicioğlu. "Alternative Controller Design for Rotary Inverted Pendulum." Tehnički glasnik 12, no. 3 (September 25, 2018): 139–45. http://dx.doi.org/10.31803/tg-20180208152214.

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The inverted pendulum has been considered a classical control problem. Two designs of inverted pendulum are planar and rotary with a nonlinear unstable system characteristic. Inverted pendulum systems are nonlinear. They can be used for testing and studying various observers and controllers. Control of a rotary inverted pendulum is studied here. This paper proposes stabilization of the rotary inverted pendulum at its upright position by using full-state controller. Full-state controllers are designed by using different damping ratios. MATLAB simulation results and the experimental results are taken for 10 degrees step for 5 seconds. The best controller is chosen for SRV02-Rotary inverted pendulum by looking at the simulation and experimental results.

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Al Juboori, Ameen M., Mustafa Turki Hussein, and Ali Sadiq Gafer Qanber. "Swing-up control of double-inverted pendulum systems." Mechanical Sciences 15, no. 1 (January 29, 2024): 47–54. http://dx.doi.org/10.5194/ms-15-47-2024.

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Abstract. This article deals with presenting a new swing-up control approach of a double-inverted pendulum on a trolley. The dynamic model of the double-inverted pendulum is derived and linearized. Two different linearization approaches are used: first, the traditional Taylor's series approach and, second, using partial linearization. A state feedback control algorithm has been implemented based on the linearized model from Taylor's series. Furthermore, a method for swinging up the pendulum to the inversion position from rest (swing-up) has been presented. The design and implementation of the swing-up function of the pendulum are implemented using the partial linearized model. The swing-up control procedure depends on using the feedforward–feedback controllers' combination to transfer the pendulums from the downward to the upward position. The time-variant controller gain is used for the sake of the swing-up control procedure. The performances of these algorithms are shown in this paper through simulations.

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Li, Wen Ping, and Li Qiang Wu. "Synthesized ADRC for One-Level Inverted Pendulum System through Combination of Separating and Assembling." Applied Mechanics and Materials 490-491 (January 2014): 794–97. http://dx.doi.org/10.4028/www.scientific.net/amm.490-491.794.

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Inverted pendulum system is the ideal study object of nonlinear system. The ADRC has good estimate for disturbances, strong robustness and using static decoupling instead of dynamical decoupling. The one-level inverted pendulum system can be regarded as composing of the pendulum angel system and the cart position system. The former is faster and the later is slower. The synthesized ADRC for one-level inverted pendulum system is built through combination of separating and assembling to reduce difficulty in optimizing ADRC parameters of the inverted pendulum system. The synthesized controller is simulated by Matlab under different parameters of the inverted pendulum. Simulation results show that the pendulum angle and the cart position are well controlled.

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Medrano-Cerda, G. A., E. E. Eldukhri, and M. Cetin. "Balancing and Attitude Control of Double and Triple Inverted Pendulums." Transactions of the Institute of Measurement and Control 17, no. 3 (August 1995): 143–54. http://dx.doi.org/10.1177/014233129501700306.

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The design of robust computer control systems for balancing and attitude control of double and triple inverted pendulums is considered in this paper. For the double inverted pendulum, a DC motor mounted at the upper hinge is used to balance and control attitude of the upper link. For the triple inverted pendulum a DC motor mounted at the middle hinge is used to control the middle link, whereas proportional position control applied to a motor at the upper hinge is utilised to maintain the upper link in alignment with the middle link. In both cases the lower hinge is left free to rotate. The controller designs are based on linearised discrete-time models of the inverted pendulums. Each controller utilises state feedback implemented via reduced-order state observers. The relative stability properties of the control systems are evaluated using Nyquist plots of suitably defined functions. The controllers are designed using Matlab and implemented in a PC using C language. Experimental results showed satisfactory performance.

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Kao, Sho-Tsung, and Ming-Tzu Ho. "Balance Control of a Configurable Inverted Pendulum on an Omni-Directional Wheeled Mobile Robot." Applied Sciences 12, no. 20 (October 13, 2022): 10307. http://dx.doi.org/10.3390/app122010307.

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This paper considers the balance control problems of a configurable inverted pendulum with an omni-directional wheeled mobile robot. The system consists of two parts. One is an inverted pendulum, and another one is an omni-directional wheeled mobile robot. The system can be configured as a rotary inverted pendulum or a spherical inverted pendulum. The objective is to control the omni-directional wheeled mobile robot to provide translational force on the plane to balance the spherical inverted pendulum and to provide the moment to balance the rotary inverted pendulum. Detailed dynamic models of these two systems are derived for the control strategy design and simulation studies. Stabilizing controllers based on the second-order sliding mode control are designed for both systems. The closed-loop stability is proved based on the passivity properties. The proposed control schemes can guarantee semi-globally asymptotical stability over the upper-half plane. In addition, the conventional sliding mode controllers proposed in our previous work and Linear-Quadratic Regulator (LQR) controllers based on the linearized system models about its upright equilibrium point are also used for performance comparison. The effectiveness of the control strategies is investigated and verified using simulation and experimental studies. In the simulation studies, different sources of uncertainty and disturbance are investigated. It is shown that the second-order sliding mode control outperforms the conventional sliding mode control and LQR control without any uncertainty and disturbance. For robustness to the matched disturbance, the simulation results show that the second-order sliding mode controller has a less significant steady-state oscillation in the pendulum’s angular displacement than other controllers. The simulation results also show that only the second-order sliding mode controller can stabilize the system with a significant initial deviation from the pendulum’s upright position. Finally, the experimental results demonstrate that second-order sliding mode control outperforms conventional sliding mode control and LQR control.

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Xu, Tu, and Cui Fang Zhang. "Multi-Level Linear Flexible Inverted Pendulum Modeling." Applied Mechanics and Materials 518 (February 2014): 290–96. http://dx.doi.org/10.4028/www.scientific.net/amm.518.290.

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Linear flexible inverted pendulum is a very good platform for testing control algorithm. A new algorithm will usually be used to control linear inverted pendulum in order to detect its control performance. Before that, you need to know the exact mathematical model of the inverted pendulum. Known modeling of multi-level linear flexible inverted pendulum used Newton's second law, in the case of ignoring the mass obtained, therefore, there are imprecise situation. Here the use of Lagrange equations with dissipation function, consider the quality of the mass of the multi-level linear flexible inverted pendulum modeling to obtain a more accurate mathematical model.

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Zhang, Jiao Long, and Wei Zhang. "Adaptive Fuzzy Sliding Mode Control for Uncertain Inverted Pendulum System." Applied Mechanics and Materials 273 (January 2013): 683–88. http://dx.doi.org/10.4028/www.scientific.net/amm.273.683.

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Firstly, the mathematical model of inverted pendulum system is created. Taking into account the uncertainty of inverted pendulum system external disturbances, adaptive fuzzy sliding mode controller is proposed with sliding mode control (SMC) theory and fuzzy logic theory. This controller can weaken the impact of uncertainty through fuzzification of the switching gain, Owing to Fuzzy approximation of the inverted pendulum system equations for an inverted pendulum with unknown parameters, this system achieve the adaptive control and optimize the control action. Secondly, inverted pendulum system has the features which SMC can keep invariance to the external disturbance and parameter perturbation. Lyapunov function is used to prove the stability of the controller. Simulation results also show that this controller can ensure inverted pendulum system fast response and robustness in the SIMULINK conditions.

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Li, Yongsheng, Jiahui Feng, Ruei-Yuan Wang, Ho-Sheng Chen, and Yongzhen Gong. "Study on Control of Inverted Pendulum System Based on Simulink Simulation." International Journal of Advanced Engineering Research and Science 10, no. 12 (2023): 01–09. http://dx.doi.org/10.22161/ijaers.1012.1.

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This study aims to conduct control research on an inverted pendulum system using the Simulink simulation platform. The inverted pendulum system is a classic nonlinear dynamic system with important theoretical and practical applications. Firstly, establish a mathematical model of the inverted pendulum system, including the dynamic equation of the pendulum rod and the sensor measurement model. Subsequently, the PID (proportional integral differential) controller design method based on the inverted pendulum system and the fuzzy PID controller design methods were verified through simulation experiments. The ultimate goal is for the designed fuzzy PID controller to effectively stabilize the inverted pendulum system in the vertical position and achieve fast tracking of the target position. Simulation and experimental results show that compared to traditional PID controllers, fuzzy PID controllers can quickly stabilize the pendulum in the target position and have good practicality, stability, speed, and accuracy. Future research can further explore the application of other advanced control strategies in inverted pendulum systems, as well as their potential applications in practical engineering.

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Sun, Qian Lai, and Zhi Yi Sun. "A Simple Control Strategy to Stabilize an Inverted Pendulum System." Advanced Materials Research 433-440 (January 2012): 3997–4002. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.3997.

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A simple control strategy is presented to control An inverted pendulum. The control strategy is obtained via mathematical derivation based on the dynamical model of the inverted pendulum system. That control law is simple and independent of the model of the controlled plant. It is applicable for the multi input single output systems similar to inverted pendulum systems. A controller based on that method was designed to control an inverted pendulum. The structure of the controller is simple. And the parameter adjusting is relatively easy. Then the simulation study was realized. The simulation result shows that control law is valid for the inverted pendulum system.

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Ou, Qun Yong. "The Design of Real-Time Control System Based on Single-Inverted Pendulum." Advanced Materials Research 850-851 (December 2013): 553–56. http://dx.doi.org/10.4028/www.scientific.net/amr.850-851.553.

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An inverted pendulum is a classic control problem and is widely used as a benchmark for testing various control algorithms. First, this paper analyse the dynamic and non-linear model of the inverted pendulum, then focus on the real-time control of the inverted pendulum, we developed real-time control software for the single-stage inverted pendulum by using Visual C++ 2010, its mainly operate API functions to control board and implement various control algorithms.

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Stojanovic, Nikola, and Vladan Vuckovic. "Real-Time 3D Visualisation for inverted pendulum." Facta universitatis - series: Electronics and Energetics 23, no. 3 (2010): 299–309. http://dx.doi.org/10.2298/fuee1003299s.

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Real-Time 3D Visualisation for Inverted Pendulum is developed by the authors, as the result of some advanced research and real-time 3D simulation of an inverted pendulum. Nowadays, there are some practical applications and robots, controlled mostly using the microprocessor fuzzy controllers, generating the new interest for these machines. Our application has intention to simulate the movements of the inverted pendulum in real time and could interact with user during the generating process. It includes Inverted Pendulum Generator (written in Delphi) and 3d Pendulum Viewer. The application is standalone.

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Kishida, Yoshiyuki, Sigeru Omatu, and Michifumi Yoshioka. "Self-Tuning Neuro-PID for Stabilization of Double Inverted Pendulum." Journal of Robotics and Mechatronics 10, no. 5 (October 20, 1998): 439–44. http://dx.doi.org/10.20965/jrm.1998.p0439.

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This paper covers a new self-tuning neuro-PID control architecture and its application to stabilization of single and double inverted pendulums. Single-Input multioutput controls the inverted pendulum using the PID controller. PID gains are tuned using two types of neural networks. Simulation results demonstrate the effectiveness of the proposed approach.

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Cong, Linxiao, Jiabin Wang, Jianfei Long, Jianchao Mu, Haoye Deng, and Congfeng Qiao. "Microgravity Decoupling in Torsion Pendulum for Enhanced Micro-Newton Thrust Measurement." Applied Sciences 14, no. 1 (December 21, 2023): 91. http://dx.doi.org/10.3390/app14010091.

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To enhance the accuracy of micro-Newton thrust measurements via a torsion pendulum, addressing microgravity coupling effects caused by platform tilt and pendulum mass eccentricity is crucial. This study focuses on analyzing and minimizing these effects by alleviating reference surface tilt and calibrating the center of mass during thrust measurements. The study introduced analysis techniques and compensation measures. It first examined the impact of reference tilt and center of mass eccentricity on the stiffness and compliance of the torsion pendulum by reconstructing its dynamic model. Simscape Multibody was initially employed for numerical analysis to assess the dynamic coupling effects of the tilted pendulum. The results showed the influence of reference tilt on the stiffness and compliance of the torsion pendulum through simulation. An inverted pendulum was developed to amplify the platform’s tilt angle for microgravity drag-free control. Center of mass calibration can identify the gravity coupling caused by the center of mass position. Based on the displacement signal from the capacitive sensor located at the end of the inverted pendulum, which represents the platform’s tilt angle, the pendulum’s vibration at 0.1 mHz was reduced from 5.7 μm/Hz1/2 to 0.28 μm/Hz1/2 by adjusting the voltage of piezoelectric actuator. Finally, a new two-stage torsion pendulum structure was proposed to decouple the tilt coupling buried in both pitch and roll angle. The study utilized theoretical models, numerical analysis, and experimental testing to validate the analysis methods and compensation measures for microgravity coupling effects in torsion pendulums. This led to a reduction in low-frequency noise caused by ground vibrations and thermal strains, ultimately improving the micro-Newton thrust measurement accuracy of the torsion pendulum through the platform’s drag-free control.

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Siradjuddin, Indrazno, Zakiyah Amalia, Erfan Rohadi, Budhy Setiawan, Awan Setiawan, Ratna Ika Putri, and Erni Yudaningtyas. "State-feedback control with a full-state estimator for a cart-inverted pendulum system." International Journal of Engineering & Technology 7, no. 4.44 (December 1, 2018): 203. http://dx.doi.org/10.14419/ijet.v7i4.44.26985.

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A Cart Inverted Pendulum System is an unstable, nonlinear and underactuated system. This makes a cart inverted pendulum system used as a benchmark for testing many control method. A cart must occupy the desired position and the angle of the pendulum must be in an equilibrium point. System modeling of a cart inverted pendulum is important for controlling this system, but modeling using assumptions from state-feedback control is not completely valid. To minimize unmeasured state variables, state estimators need to be designed. In this paper, the state estimator is designed to complete the state-feedback control to control the cart inverted pendulum system. The mathematical model of the cart inverted pendulum system is obtained by using the Lagrange equation which is then changed in the state space form. Mathematical models of motors and mechanical transmissions are also included in the cart inverted pendulum system modeling so that it can reduce errors in a real-time application. The state gain control parameter is obtained by selecting the weighting matrix in the Linear Quadratic Regulator (LQR) method, then added with the Leuenberger observer gain that obtained by the pole placement method on the state estimator. Simulation is done to determine the system performance. The simulation results show that the proposed method can stabilize the cart inverted pendulum system on the cart position and the desired pendulum angle.

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Anh, N. D., and N. X. Nguyen. "A global-local approach to the design of dynamic vibration absorber for damped inverted pendulum structures." Vietnam Journal of Mechanics 37, no. 1 (February 27, 2015): 57–70. http://dx.doi.org/10.15625/0866-7136/37/1/5865.

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In practice, an inverted pendulum can be used to model many real structures as the arms of robots, soil structures, or fluid structures. However, the study on the design of dynamic vibration absorber for inverted pendulum structures is very limited in the literature. To the best knowledge of the authors, however, there has been no study on the dynamic vibration absorber when the primary inverted pendulum structure is damped. This paper deals with the optimization problem of dynamic vibration absorber for inverted pendulum structures. Two novel findings of the present study are summarized as follows. First, the optimal parameters of dynamic vibration absorber for undamped inverted pendulum structures are given by using \(H_{\infty }\) optimization. Second, the authors suggest a so-called global-local approach to determine approximate expressions for optimal parameters of a pendulum type absorber attached to a damped inverted pendulum structure. Finally, a numerical simulation is done for an example of the articulated tower in the ocean to validate the effectiveness of the results obtained in this work.

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Monir, Md. "Analyzing and Designing Control System for an Inverted Pendulum on a Cart." European Scientific Journal, ESJ 14, no. 6 (February 28, 2018): 387. http://dx.doi.org/10.19044/esj.2018.v14n6p387.

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It is a collection of MATLAB functions and scripts, and SIMULINK models, useful for analyzing Inverted Pendulum System and designing Control System for it. Automatic control is a growing field of study in the field of Mechanical Engineering. This covers the proportional, integral and derivative (PID). The principal reason for its popularity is its nonlinear and unstable control. The reports begin with an outline of research into inverted pendulum design system and along with mathematical model formation. This will present introduction and review of the system. Here one dimensional inverted pendulum is analyzed for simulating in MATLAB environment. Control of Inverted Pendulum is a Control Engineering project based on the flight simulation of rocket or missile during the initial stages of flight. The aim of this study is to stabilize the Inverted Pendulum such that the position of the carriage on the track is controlled quickly and accurately so that the pendulum is always erected in its inverted position during such movements.

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Li, Ai Lian, Hong Yu Qi, and Li Liang. "Based on T-S Fuzzy Classification of the Double Inverted Pendulum Multi Mode Adaptive Control." Advanced Materials Research 902 (February 2014): 300–305. http://dx.doi.org/10.4028/www.scientific.net/amr.902.300.

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Double Inverted pendulum as an important object of study on robotics and aviation field, is also a major platform for teaching and scientific research.Usually double Inverted pendulum modeling is usually will be linearized processing system, ignoring the effect of the angle of system. But the realization of double inverted pendulum is a nonlinear system, the angle affect the stability control. From the actual situation of double Inverted pendulum motion, double Inverted pendulum system of the input space is divided into 9 sub-space, by T-S fuzzy and feedback gain matrix to select the corresponding state equation, making the system more close to its dynamic performance. The multi mode adaptive control and T-S fuzzy method of combining the successful implementation of double inverted pendulum system simulation and real-time control.The number of rules they use far less than Mamdani fuzzy, but also successfully resolved the fuzzy control algorithm due to the presence of multiple variables and the resulting "rule explosion problem".

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Fitria, Trisonia, Wipsar Sunu Brams Dwandaru, Warsono, R. Yosi Aprian Sari, Dian Puspita Eka Putri, and Adiella Zakky Juneid. "Application Of Inverted Pendulum in Laplace Transformation of Mathematics Physics." Jurnal Penelitian Pendidikan IPA 9, no. 7 (July 25, 2023): 5446–52. http://dx.doi.org/10.29303/jppipa.v9i7.2953.

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The Laplace transform is a technique used to convert differential equations into algebra, it is often used for the analysis of dynamic systems and inverted pendulum systems. An inverted pendulum is a mechanism that moves objects from one place to another and shows the function of its activity while walking. This system is widely used in various fields, for example in the fields of robotics, industry, technology and organics. In an inverted pendulum there is an inverted pendulum dynamic system with a reading and driving force. The results of the study show that using the Laplace transform can make it easier to find solutions regarding the inverted pendulum system for a variety of conditions, both in the initial conditions and when given an additional force or load. The application of the Laplace transform is useful for understanding how an inverted pendulum system will react to various forces, loads and initial conditions, which can be used to predict how the system will operate in the real world

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Cao, Xu, Nian Feng Li, and Hua Xun Zhang. "Robust Controller Design for Inverted Pendulum System." Advanced Materials Research 631-632 (January 2013): 1342–47. http://dx.doi.org/10.4028/www.scientific.net/amr.631-632.1342.

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For the high order, unstable, multivariable, nonlinear and strong coupling characteristics, robust stability is an important indicator of inverted pendulum system. In this paper an LQR robust controller of inverter pendulum system is designed. The simulation and the experimental results showed that the stability of the robust LQR controller is better than the original LQR controller. When the system departure counterpoise for all kinds of reasons, it get back equilibrium state without depleting any energy, and approach state of equilibrium of all state component.

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Bajrami, Xhevahir, Arbnor Pajaziti, Ramë Likaj, Ahmet Shala, Rinor Berisha, and Mirlind Bruqi. "Control Theory Application for Swing Up and Stabilisation of Rotating Inverted Pendulum." Symmetry 13, no. 8 (August 13, 2021): 1491. http://dx.doi.org/10.3390/sym13081491.

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This paper introduces a new scheme for sliding mode control using symmetry principles for a rotating inverted pendulum, with the possibility of extension of this control scheme to other dynamic systems. This was proven for swing up and stabilisation control problems via the new sliding mode control scheme using both simulations and experiments of rotary inverted pendulum (RIP) underactuated systems. According to the Lyapunov theory, a section of the pendulum was compensated with a scale error in the upright position, as the desired trajectory was followed by the pendulum arm section. As the RIP’s dynamic equations were nonlinearly complex and coupled, the complex internal dynamics made the task of controller design difficult. The system control for the pathway of the reference model of the rotational actuator with the application of the sliding mode technique for moving back and forth up the inverted pendulum’s structure, till the arm to reach the linear range round the vertical upright position, was created and tested in an existent device. The stabilisation scheme was switched on in the sliding mode as soon as the arm reached the linear range. A comparison of the stabilisation performance for the same rotating inverted pendulum as discussed by other authors revealed that the proposed controller was more flexible and reliable in terms of the swing up and stabilisation time.

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Gao, Qiang, and Yi Li. "Generalized Predictive Control for Rotary Inverted Pendulum System." Applied Mechanics and Materials 130-134 (October 2011): 4256–60. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.4256.

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Inverted pendulum system is a complex, multivariable, nonlinear, strong-coupling, unstable system of high order. Compared with the straight-line inverted pendulum, rotary inverted pendulum is more complicated and unstable. In this paper, the mathematic model of a rotary inverted pendulum system is analyzed and deduced detailedly by applying the Lagrange method; the control properties and characteristics of generalized predictive control are researched with matlab simulation. Finally, the results of the experiment prove the system controlled by GPC has a better stability and quickness.

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Zhai, Xiao Hua, Shu Xia Yao, and Zhi Hui Xu. "Research on Fuzzy Control of Inverted Pendulum in the MATLAB Environment." Applied Mechanics and Materials 182-183 (June 2012): 1211–14. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1211.

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Inverted Pendulum is a typical system with multivariate, nonlinear system. Research on inverted pendulum can be attributed to research on nonlinear multivariate absolutely unstable system. Its control methods and ideas have an extensive usage. In this paper, a fuzzy controller is introduced to control single inverted pendulum system, and the performance characteristic of this system is also introduced. The control result of the inverted pendulum is good, the oscillation is small. Research result indicated that the control performance of fuzzy control is to select good membership function and discourse domain.

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Sun, Jian Zhong, Jian Kang Lu, Bin Yang, and Jun Li Li. "Sliding Mode Variable Structural Control of Nonlinear Inverted Pendulum." Advanced Materials Research 433-440 (January 2012): 74–80. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.74.

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In this paper, the multi-input linear and nonlinear mathematical differential equations of inverted pendulum system were established based on the traditional single-input linear inverted pendulum. Aiming at multi-input nonlinear model, nonlinear state transformation are carried through on the basis of the test of distribution involution and the calculation of integral manifold, then, the multi-input nonlinear inverted pendulum system was transformed into two single-input nonlinear inverted pendulum system to study. In the end, make use of related nonlinear system control theory of the sliding mode variable structure, designed the controller structure.

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Cao, Rong Min, Hui Xing Zhou, and Rong Hua Ma. "Experiment Platform Design cSPACE-Based for a Permanent Magnet Linear Synchronous Motor Driven Inverted Pendulum." Applied Mechanics and Materials 84-85 (August 2011): 452–56. http://dx.doi.org/10.4028/www.scientific.net/amm.84-85.452.

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Permanent magnet linear synchronous motor (PMLSM) driven inverted pendulum is a new member of present similar devices, various unexpected disturbances such as lag effect of a belt attached to a cart and errors caused by a rotary encoder while detecting the position of a cart can be eliminated or reduced to a small range.In this paper, ironless permanent magnet synchronous linear motor driven inverted pendulum experiment platform is developed. The plant is hardware in the loop real time simulation control development system (Hardware-in-Loop, HIL)based on TMS320F2812DSP and MATLAB, it can use simple and efficient way to achieve linear motor driven inverted pendulum real-time control. Long design time for programming and debugging difficulty are avoided for traditional programming language. Control algorithm can be investigated directly on MATLAB/Simulink, and can be generated automatically control code to control single and double -stage inverted pendulum system. The real performance of the driven inverted pendulum is researched in this paper, the results showed that the controllability of the driven inverted pendulum is fine.

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Ouyang, Lijun, TingTing Li, Bin Zhen, and Lei Wei. "Dynamics of a Pedestrian’s Walking Motion Based on the Inverted Pendulum Model." International Journal of Structural Stability and Dynamics 18, no. 11 (October 22, 2018): 1850145. http://dx.doi.org/10.1142/s0219455418501456.

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In this paper, the inverted pendulum model is proposed to describe a pedestrian’s walking motion by considering that the pivot point vibrates periodically up and down. The stability, periodic solutions and oscillations of the inverted pendulum are theoretically investigated, the correctness of which is illustrated by numerical simulations. According to frequency spectrum analysis, the inverted pendulum can exhibit periodically or quasi-periodically stable oscillations. However, we demonstrate that the inverted pendulum will maintain the ratio between the lateral and vertical vibration frequencies near [Formula: see text] as an optimizing selection of stability. The theoretical result agrees with the measurement result for a normal pedestrian such that the lateral step frequency is always half the vertical step frequency, which means that it is feasible and reasonable to describe a pedestrian’s walking motion using the inverted pendulum with the pivot vibrating harmonically in the vertical direction. The inverted pendulum model suggested in this paper could contribute to the study of pedestrian–footbridge interaction, which overcomes the difficulty of directly determining the expression of the lateral force induced by pedestrians.

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Antonio-Cruz, Mayra, Victor Manuel Hernandez-Guzman, and Ramon Silva-Ortigoza. "Limit Cycle Elimination in Inverted Pendulums: Furuta Pendulum and Pendubot." IEEE Access 6 (2018): 30317–32. http://dx.doi.org/10.1109/access.2018.2839642.

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Barton, Taylor W. "Stabilizing the dual inverted pendulum." IFAC Proceedings Volumes 42, no. 24 (2010): 113–18. http://dx.doi.org/10.3182/20091021-3-jp-2009.00022.

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Lundberg, Kent H., and Taylor W. Barton. "History of Inverted-Pendulum Systems." IFAC Proceedings Volumes 42, no. 24 (2010): 131–35. http://dx.doi.org/10.3182/20091021-3-jp-2009.00025.

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HAYASE, Toshiyuki, and Yoshikazu SUEMATSU. "Control of flexible inverted pendulum." Journal of the Robotics Society of Japan 9, no. 2 (1991): 162–68. http://dx.doi.org/10.7210/jrsj.9.162.

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Grasser, F., A. D'Arrigo, S. Colombi, and A. C. Rufer. "JOE: a mobile, inverted pendulum." IEEE Transactions on Industrial Electronics 49, no. 1 (2002): 107–14. http://dx.doi.org/10.1109/41.982254.

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BISHOP, S. R., and D. J. SUDOR. "THE "NOT QUITE" INVERTED PENDULUM." International Journal of Bifurcation and Chaos 09, no. 01 (January 1999): 273–85. http://dx.doi.org/10.1142/s0218127499000158.

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The planar pendulum has been used as an example of a simple oscillator for over 300 years with notable historical contributions by Galileo and Huygens. Initially interest was focused on small displacements from the stable hanging position specifically to determine the period of oscillation. More recently attention has switched to larger amplitude and chaotic motions as a consequence of periodic forcing to the pivot point. To explain experimentally observed behavior, we investigate here the existence of stable inverted solutions of a pendulum sinusoidally driven, in the first instance by a purely vertical force and then by an almost vertical force by giving a small tilt to the system. An effective potential function is considered to provide analytical justification of the numerical simulations.

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Ma, Yan, Dengguo Xu, Jiashun Huang, and Yahui Li. "Robust Control of An Inverted Pendulum System Based on Policy Iteration in Reinforcement Learning." Applied Sciences 13, no. 24 (December 12, 2023): 13181. http://dx.doi.org/10.3390/app132413181.

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This paper is primarily focused on the robust control of an inverted pendulum system based on policy iteration in reinforcement learning. First, a mathematical model of the single inverted pendulum system is established through a force analysis of the pendulum and trolley. Second, based on the theory of robust optimal control, the robust control of the uncertain linear inverted pendulum system is transformed into an optimal control problem with an appropriate performance index. Moreover, for the uncertain linear and nonlinear systems, two reinforcement-learning control algorithms are proposed using the policy iteration method. Finally, two numerical examples are provided to validate the reinforcement learning algorithms for the robust control of the inverted pendulum systems.

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Journal articles on the topic 'Inverted pendulum'

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