Relevant bibliographies by topics / Inverted Pendulum on a Cart

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
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  6. Reports

Academic literature on the topic 'Inverted Pendulum on a Cart'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Inverted Pendulum on a Cart"

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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 (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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Siradjuddin, Indrazno, Zakiyah Amalia, Erfan Rohadi, et al. "State-feedback control with a full-state estimator for a cart-inverted pendulum system." International Journal of Engineering & Technology 7, no. 4.44 (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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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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Antonio-Cruz, Mayra, Victor Manuel Hernández-Guzmán, Ramón Silva-Ortigoza, and Gilberto Silva-Ortigoza. "Implementation of a Controller to Eliminate the Limit Cycle in the Inverted Pendulum on a Cart." Complexity 2019 (February 4, 2019): 1–13. http://dx.doi.org/10.1155/2019/8271584.

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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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Monir, Md. "Analyzing and Designing Control System for an Inverted Pendulum on a Cart." European Scientific Journal, ESJ 14, no. 6 (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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Siradjuddin, Indrazno, Zakiyah Amalia, Budhy Setiawan, et al. "Stabilising a cart inverted pendulum with an augmented PID control scheme." MATEC Web of Conferences 197 (2018): 11013. http://dx.doi.org/10.1051/matecconf/201819711013.

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A cart inverted pendulum is an under actuated system that highly unstable and nonlinear. Therefore, it makes a good problem example which attracts control engineers to validate the developed control algorithms. In this paper, an augmented PID control algorithm is proposed to stabilise a cart inverted pendulum at the desired state. The derivation of a mathematical model of the cart inverted pendulum using Lagrange's equation is discussed in detail. The system dynamics is illustrated to understand better the behaviour of the system. A simulation program has been developed to verify the performance of the proposed control algorithm. The system dynamic behaviours with respect to the variation of the controller parameters are analysed and discussed. Controllers parameters are expressed into two PID gain sets which associated with 2 dynamic states: the cart position (ϰ) and the pendulum angle (θ). It can be concluded from the simulation result that the proposed control algorithm can perform well where acceptable steady errors can be achieved. The best response from the cart inverted pendulum system has been obtained with the value of kPX 190, kDX 50, kIX 5, kPθ 140, kDθ 5, and kIθ 25.
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Colombo, Federico, Luigi Mazza, Giuseppe Pepe, Terenziano Raparelli, and Andrea Trivella. "Stability analysis of a pneumatically actuated inverted pendulum." E3S Web of Conferences 197 (2020): 07008. http://dx.doi.org/10.1051/e3sconf/202019707008.

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This paper deals with the stabilization of an inverted pendulum on cart; the latter is pneumatically actuated by a double acting cylinder controlled by low cost proportional valves. In particular, a numerical model of whole system is developed in order to find the ability of the pneumatic actuation in stabilizing the pendulum and evaluate its bandwidth. A cascade of two control loops (the inner one for the pendulum angle, the outer one for the cart displacement) are analyzed and proper compensators are defined. The possibility of introducing an additional loop to control the force exerted by the actuator on the cart is evaluated.
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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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Liu, Xuan, Xiang Shi, Zhe Xu, and Ka Tian. "Mathematical Modelling for Wheeled Inverted Pendulum." Applied Mechanics and Materials 543-547 (March 2014): 1365–68. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1365.

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To control wheeled inverted pendulum is a good way to test all kinds of theories of control, On the basis of Newtonian mechanics and dynamic characteristics, the dynamical equation of DC motor, cart and pendulum is studied. Then the approximate linear model of wheeled inverted pendulum is concluded, which is based on the way of linearization of small Angle.
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BAKHTIAR, T. "MASALAH GALAT PENJEJAKAN MINIMUM PADA SISTEM PENDULUM TERBALIK." Journal of Mathematics and Its Applications 9, no. 1 (2010): 15. http://dx.doi.org/10.29244/jmap.9.1.15-22.

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This paper studies the optimal tracking error control problem on an inverted pendulum model. We characterize the optimal tracking error in term of pendulum’s parameters. Particularly, we derive the closed form expression for the pendulum length which gives minimum error. It is shown that the minimum error can always be accomplished as long as the ratio between the mass of the pendulum and that of the cart satisfies a certain constancy, regardless the type of material we use for the pendulum.
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Dissertations / Theses on the topic "Inverted Pendulum on a Cart"

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Ingram, Stephen D. "Visual Feedback Stabilisation of a Cart Inverted Pendulum A." Thesis, University of Bradford, 2016. http://hdl.handle.net/10454/17375.

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Vision-based object stabilisation is an exciting and challenging area of research, and is one that promises great technical advancements in the field of computer vision. As humans, we are capable of a tremendous array of skilful interactions, particularly when balancing unstable objects that have complex, non-linear dynamics. These complex dynamics impose a difficult control problem, since the object must be stabilised through collaboration between applied forces and vision-based feedback. To coordinate our actions and facilitate delivery of precise amounts of muscle torque, we primarily use our eyes to provide feedback in a closed-loop control scheme. This ability to control an inherently unstable object by vision-only feedback demonstrates an exceptionally high degree of voluntary motor skill. Despite the pervasiveness of vision-based stabilisation in humans and animals, relatively little is known about the neural strategies used to achieve this task. In the last few decades, with advancements in technology, we have tried to impart the skill of vision-based object stabilisation to machines, with varying degrees of success. Within the context of this research, we continue this pursuit by employing the classic Cart Inverted Pendulum; an inherently unstable, non-linear system to investigate dynamic object balancing by vision-only feedback. The Inverted Pendulum is considered to be one of the most fundamental benchmark systems in control theory; as a platform, it provides us with a strong, well established test bed for this research. We seek to discover what strategies are used to stabilise the Cart Inverted Pendulum, and to determine if these strategies can be deployed in Real-Time, using cost-effective solutions. The thesis confronts, and overcomes the problems imposed by low-bandwidth USB cameras; such as poor colour-balance, image noise and low frame rates etc., to successfully achieve vision-based stabilisation. The thesis presents a comprehensive vision-based control system that is capable of balancing an inverted pendulum with a resting oscillation of approximately ±1º. We employ a novel, segment-based location and tracking algorithm, which was found to have excellent noise immunity and enhanced robustness. We successfully demonstrate the resilience of the tracking and pose estimation algorithm against visual disturbances in Real-Time, and with minimal recovery delay. The algorithm was evaluated against peer reviewed research; in terms of processing time, amplitude of oscillation, measurement accuracy and resting oscillation. For each key performance indicator, our system was found to be superior in many cases to that found in the literature. The thesis also delivers a complete test software environment, where vision-based algorithms can be evaluated. This environment includes a flexible tracking model generator to allow customisation of visual markers used by the system. We conclude by successfully performing off-line optimization of our method by means of Artificial Neural Networks, to achieve a significant improvement in angle measurement accuracy.<br>Goodrich Engine Control Systems and Balfour Beatty Rail Technologies
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Li, Bo. "Rotational Double Inverted Pendulum." University of Dayton / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1375188910.

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Houchin, Scott J. "Pendulum : controlling an inverted pendulum using fuzzy logic /." Online version of thesis, 1991. http://hdl.handle.net/1850/11294.

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Lundberg, Kent Howard. "Linear dual inverted pendulum control." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/10767.

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Stenbeck, Filip, and Aron Nygren. "Controller Analysis with Inverted Pendulum." Thesis, KTH, Maskinkonstruktion (Inst.), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-184515.

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The aim of this thesis is to examine if feedback of the angle from an inverted pendulum is sufficient to control its angle at an unstable equilibrium with statics and force impulses, and through different approaches and choice of controller find the most suitable one for these types of applications. The controllers that were tested was, the PID regulator and the state space regulator. The results would show that the mathematical approach to find a controller is difficult and time consuming, and it is often better to use a trial and error approach to find a regulator if repeated test on the system is possible. The core of the thesis lies in the mathematical approximations of the mechanical and electrical system, the analysis of the controller and the choice and usage of components. Analysis of the combined electrical and mechanical systems were made in Simulink and Matlab and was then generated to mechanical code to an micro controller controlling the voltage to a dc-motor. The system is non linear but can be linearised around the equilibrium point that we want to maintain, which is a good approximation for small angles. This thesis describes the electrical and mechanical components used to build a rotary inverted pendulum and how to produce an effective controller in detail.<br>Målet med examensarbetet är att utvärdera om återkoppling av vinkeln frånen inverterad pendel är tillräcklig för att kontrollera denna kring en instabil jämviktspunkt med störningar samt pålagda kraftimpulser, och genom val av olika tillvägagångssätt och regulatorer finna den mest lämpliga för dessa typer av tillämpningar. De regulatorer som användes i projektet var PID-regulatorn samt state space regulatorn. Resultaten kom att visa att ett matematisk tillvägagångsätt att skapa en regulator är svårt och tidskrävande, och det är ofta mer effektivt att testa sig fram till en regulator om systemet tillåter. Kärnan i arbetet ligger i de matematiska approximationerna av de mekaniska och elektriska system, analysen av kontrollern och valet samt tillämpningen av komponenter. Analysen av det kombinerade elektriska och mekaniska systemen gjordes i Simulink och Matlab och var därefter genererad till mekanisk kod till en mikro-kontroller för att regulera spänningen till en likströmsmotor. Den inverterade pendeln är ett olinjärt system men kan med god approximation och litet fel linjariseras runt dess instabila jämnviktspunkt. Detta examensarbete kommer i huvudsak handla om hur man konstruerar en regulator genom simulering samt analys av systemet. Alla komponenter såväl elektriska som mekaniska kommer att beskrivas i detalj.
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Kirchner, Tomáš. "Návrh a řízení modelu laboratorního dvojitého kyvadla." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-417786.

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Improvement of the current double inverted pendulum model on a cart as well as a new LQG control and swing-up realization are the main goal of this thesis. Movement of the cart is driven by DC motor and gear belt mechanism. At first the control algorithms were simulated in Simulink program and then also implemented into the real system with MF624 card.
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Lei, Kam Kin. "Fuzzy control on double inverted pendulum." Thesis, University of Macau, 2005. http://umaclib3.umac.mo/record=b1445842.

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Cox, Bruce. "Feedback Stabilization of Inverted Pendulum Models." VCU Scholars Compass, 2005. http://scholarscompass.vcu.edu/etd/1174.

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Many mechanical systems exhibit nonlinear movement and are subject to perturbations from a desired equilibrium state. These perturbations can greatly reduce the efficiency of the systems. It is therefore desirous to analyze the asymptotic stabilizability of an equilibrium solution of nonlinear systems; an excellent method of performing these analyses is through study of Jacobian linearization's and their properties. Two enlightening examples of nonlinear mechanical systems are the Simple Inverted Pendulum and the Inverted Pendulum on a Cart (PoC). These examples provide insight into both the feasibility and usability of Jacobian linearizations of nonlinear systems, as well as demonstrate the concepts of local stability, observability, controllability and detectability of linearized systems under varying parameters. Some examples of constant disturbances and effects are considered. The ultimate goal is to examine stabilizability, through both static and dynamic feedback controllers, of mechanical systems
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Ni, Jie. "Control of the spatial double inverted pendulum." Thesis, McGill University, 2011. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=104855.

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The stabilization of a hip-actuated spatial double inverted pendulum can be considered as a problem of postural control of a humanoid robot. Based on an existing model of this underactuated mechanical system with four degrees of freedom, the ultimate objective is to design a suitable controller to achieve global stabilization around the unstable upright equilibrium position. This thesis presents a number of control algorithms and simulation results that provide either local stabilization or semi-global swing-up. For the effort of local stabilization in the vicinity of the upright equilibrium position, both an lqr controller and three types of linearization-based sliding mode control algorithms are presented. The region of convergence of the lqr controller is investigated. System performance and robustness against disturbances are compared for all controllers.In order to realize semi-global swing-up, two types of nonlinear sliding mode control approaches are explored for the swing up of the system in an attempt to bring the system into the region of convergence of the local linear controllers. The hybrid approach is proposed to switch from the swing-up controller to a local linear controller under certain conditions in the vicinity of the upright equilibrium to complete the stabilization effort. However, despite extensive tuning of the controllers, it has not been possible to achieve global stabilization with such an approach. Further investigation is needed in order to resolve this issue. The main contribution of this thesis is a successful extension of existing 2-dimensional sliding mode control algorithms into 3-D for the control of the spatial double inverted pendulum. The linearization-based sliding mode controllers serve as alternatives to lqr for local stabilization. The nonlinear sliding mode controllers are able bring the system from a configuration far from the upright equilibrium to the vicinity of the unstable upright equilibrium in semi-global swing-up.<br>La stabilisation d'un double pendule spatiale inversé actionné à la hanche peut-être considérée comme un problème de contrôle de la posture d'un robot humanoïde. Basé sur un modèle existant de ce système mécanique sous-actionné avec quatre degrés de liberté, l'ultime objectif est de concevoir un régulateur approprié pour obtenir une stabilisation globale autour de l'instable position d'équilibre debout. Cette thèse présente un certain nombre d'algorithmes de contrôle et les résultats de simulation qui permettent une stabilisation locale ou semi-globale pivoter-vers-le-haut. Pour l'effort de stabilisation locale dans le voisinage de la position d'équilibre en position verticale, à la fois un contrôleur lqr et trois types de linéarisation basée sur des algorithmes de contrôle de mode glissant sont présentés. La région de la convergence du contrôleur lqr est étudiée. La performance et la robustesse du système sont comparées pour tous les contrôleurs. Afin de réaliser la strateǵie semi-globale pivoter-vers-le-haut, deux types d'approches de commande non linéaire de mode glissant sont explorés pour le balancement du système dans un essai pour amener le système dans la région de convergence locale des contrôleurs linéaires. L'approche hybride est proposée pour passer du contrôleur pour pivoter-vers-le-haut à un contrôleur linéaire local sous certaines conditions dans le voisinage de l'équilibre en position verticale afin de compléter l'effort de stabilisation. Toutefois, malgré des ajustements des contrôleurs, il n'a pas été possible de parvenir à une stabilisation globale avec une telle approche. Une enquête plus profonde est nécessaire pour résoudre ce problème. La contribution principale de cette thèse est la réussite une d'extension d'algorithmes de commande de 2-dimensions de mode glissant qui existent pour le cas de 3-D pour le contrôle du double pendule inversé spatial. Les contrôleurs de mode glissant basés sur un modèle du système linéarisé servent comme alternatives au contrôleur lqr pour la stabilisation locale. Les contrôleurs de mode glissant non-linéaires sont capables, à partir d'une configuration loin de l'équilibre de mettre le système dans la proximité de l'équilibre debout vertical utilisant le principe semi-global pivoter-vers-le-haut.
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Xinjilefu, Xinjilefu. "Stabilization of the spatial double inverted pendulum." Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=95109.

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The stabilization of a double inverted pendulum moving in a three dimensional space may be considered to be a model of a human - and of other animals - postural control. In this thesis, we focus on modelling the spatial double inverted pendulum, and applying different control strategies to stabilize it. In modelling, we introduce three algorithms: the Natural Orthogonal Complement, the Composite Rigid Body Algorithm, and the Articulated Body Algorithm, all in the framework of Plucker coordinates. The main contribution of this thesis is we show that postural control is possible by minimization of the system Lagrangian. An stochastic programming procedure proves to be able to find oscillatory inputs that bring the system close to the unstable upright equilibrium position. In conclusion, our study demonstrates that steering complex mechanical systems may in certain cases be actually be simpler than expected.<br>La stabilisation d'un double pendule inversé se déplaçant dans un espace à trois dimensions peut être considéré comme un modèle de la posture humaine ou animale. Dans cette thèse, nous nous concentrons sur la modélisation du pendule et sur l'application de différentes stratégies de contrôle pour le stabiliser. Dans la modélisation, nous introduisons trois algorithmes : le Complément Orthogonal Naturel, l'Algorithme du Corps Rigide Composé et l'Algorithme du Corps Articulé. Tous utilisent les coordonnées pluckeriennes. La principale contribution de cette thèse vient de la démonstration que le contrôle de la posture est possible par la minimisation du Lagrangien du sytème. Une procédure de programmation stochastique est capable de trouver la stimulation oscillatoire en entrée qui ammène le système près de la position droite en équilibre instable. En conclusion, notre étude démontre que la direction de systèmes mécaniques complexes peut, dans certains cas, s'avérer plus simple que l'on pourrait s'y attendre.
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Books on the topic "Inverted Pendulum on a Cart"

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Li, Zhijun. Advanced Control of Wheeled Inverted Pendulum Systems. Springer London, 2013.

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Li, Zhijun, Chenguang Yang, and Liping Fan. Advanced Control of Wheeled Inverted Pendulum Systems. Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-2963-9.

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King, S. P. Digital control of an inverted pendulum using an H-infinity design. UMIST, 1994.

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Loram, Ian David. Mechanisms for human balancing of an inverted pendulum using the ankle strategy. University of Birmingham, 2002.

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Inverted Pendulum [Working Title]. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.80106.

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Advanced Control Of Wheeled Inverted Pendulum Systems. Springer, 2012.

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Li, Zhijun, Chenguang Yang, and Liping Fan. Advanced Control of Wheeled Inverted Pendulum Systems. Springer, 2014.

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Holzapfel, Frank G. Fuzzy logic control of an inverted pendulum with vision feedback. 1994.

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Barrett, Spencer Brown. Predictive control using feedback-: A case study of an inverted pendulum. 1995.

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Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator is studied using an example by Trefethen et al. The integrable models (KdV, Hasimoto’s vortex soliton) and their hamiltonian formalism are studied. Delving into deeper mathematics, geodesics on Lie groups are studied: first using the Lie algebra and then using Milnor’s approach to the curvature of the Lie group. Arnold’s deep idea that Euler’s equations are the geodesic equations on the diffeomorphism group is then explained and its curvature calculated. The next three chapters are an introduction to numerical methods: spectral methods based on Chebychev functions for ODEs, their application by Orszag to solve the Orr–Sommerfeld equation, finite difference methods for elementary PDEs, the Magnus formula and its application to geometric integrators for ODEs. Two appendices give an introduction to dynamical systems: Arnold’s cat map, homoclinic points, Smale’s horse shoe, Hausdorff dimension of the invariant set, Aref ’s example of chaotic advection. The last appendix introduces renormalization: Ising model on a Cayley tree and Feigenbaum’s theory of period doubling.
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Book chapters on the topic "Inverted Pendulum on a Cart"

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Mokhtari, Mohand, and Michel Marie. "Cart with inverted pendulum." In Engineering Applications of MATLAB® 5.3 and SIMULINK® 3. Springer London, 2000. http://dx.doi.org/10.1007/978-1-4471-0741-5_8.

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Colombo, F., L. Mazza, G. Pepe, T. Raparelli, and A. Trivella. "Inverted Pendulum on a Cart Pneumatically Actuated by Means of Digital Valves." In Advances in Service and Industrial Robotics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00232-9_46.

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Sharma, Bharat, and Barjeev Tyagi. "LQR-Based TS-Fuzzy Logic Controller Design for Inverted Pendulum-Coupled Cart System." In Lecture Notes in Electrical Engineering. Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2141-8_18.

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Herrera, Marco, Xavier Aguas, Oscar Gonzales, and Oscar Camacho. "Optimal-Robust Controller Applied to an Inverted Pendulum-Cart System: A Graphic Performance Analysis." In Communications in Computer and Information Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42531-9_21.

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Sain, D., S. K. Swain, and S. K. Mishra. "Design of Two-Loop PID Controller for Inverted Cart-Pendulum System Using Modified Genetic Algorithm." In Advances in Intelligent Systems and Computing. Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2525-9_11.

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Sidana, Amanvir Singh, Akarsh Kumar, Akshit Kanda, Vineet Kumar, and K. P. S. Rana. "Grey Predictor Assisted Fuzzy and Fractional Order Fuzzy Control of a Moving Cart Inverted Pendulum." In Fractional Order Control and Synchronization of Chaotic Systems. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50249-6_3.

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Mohd Salleh, Mohd Fakhrurrazi, and Mohamad Amir Shamsudin. "Mathematical Modelling and Quadratic Optimal Tuning Based PID Scheme for an Inverted Pendulum-Cart System." In Communications in Computer and Information Science. Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6502-6_17.

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Telles Ribeiro, José Geraldo, Julio Cesar de Castro Basilio, Americo Cunha, and Tiago Roux Oliveira. "On the Classical and Fractional Control of a Nonlinear Inverted Cart-Pendulum System: A Comparative Analysis." In Mechanisms and Machine Science. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-60694-7_26.

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Salicone, Simona, and Marco Prioli. "The Inverted Pendulum." In Measuring Uncertainty within the Theory of Evidence. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74139-0_24.

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Xin, Xin, and Yannian Liu. "Double Pendulum on Cart." In Control Design and Analysis for Underactuated Robotic Systems. Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6251-3_14.

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Conference papers on the topic "Inverted Pendulum on a Cart"

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Lare, Constance, and Warren N. White. "Continuum of Motion Equations and Control Laws for the Inverted Pendulum Cart and Rotary Pendulum." In ASME 2020 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/dscc2020-3298.

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Abstract This paper questions whether the controller properties for a given rigid body mechanical system still apply as the given system is changed. As a first attempt in this investigation, the controller for the underactuated rotary pendulum is investigated as the system morphs into an underactuated inverted pendulum cart. As the limiting condition of the inverted pendulum cart is approached, the investigation allows the controller to also morph. The authors show that, as the pendulum base radius grows, the rotary pendulum equations of motion morph into the inverted pendulum cart dynamics. The paper presents necessary conditions for the successful morphing of the dynamic equations. The morphing process for the controller tests the idea whether the control law also satisfies the same continuum basis as the motion equations. The paper presents a framework for the class of controllers investigated for providing insight into when the controller morphing may be successful. This paper presents dimensionless quantities that render the equations of motion and controller for the inverted pendulum cart and rotary pendulum into dimensionless form. These dimensionless quantities allow comparison of controllers and systems that are not possible through simple inspection. This comparison ability is especially useful for quantifying the nonlinearities of a given system and controller compared to another system and controller having different parameter sizes, a comparison rarely seen in the control literature.
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Mondal, Reetam, Jayati Dey, Suman Halder та Arindam Chakraborty. "Stabilization of the cart-inverted pendulum system using PIλDμcontroller". У 2017 4th IEEE Uttar Pradesh Section International Conference on Electrical, Computer and Electronics (UPCON). IEEE, 2017. http://dx.doi.org/10.1109/upcon.2017.8251060.

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Basin, Michael, Pablo Rodriguez-Ramirez, Steven X. Ding, Tim Daszenies, and Yuri Shtessel. "Continuous fixed-time control for cart inverted pendulum stabilization." In 2016 IEEE 55th Conference on Decision and Control (CDC). IEEE, 2016. http://dx.doi.org/10.1109/cdc.2016.7799260.

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Konigsmarkova, Jana, and Milos Schlegel. "Identification of n-link inverted pendulum on a cart." In 2017 21st International Conference on Process Control (PC). IEEE, 2017. http://dx.doi.org/10.1109/pc.2017.7976186.

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Wang, Haoping, Afzal Chamroo, Christian Vasseur, and Vladan Koncar. "Hybrid control for vision based Cart-Inverted Pendulum system." In 2008 American Control Conference (ACC '08). IEEE, 2008. http://dx.doi.org/10.1109/acc.2008.4587093.

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Bdirina, El Khansa, Mohamed Seghir Boucherit, Ramdane Hadjar, and Madni Zineb. "State constrained predictive control of cart with inverted pendulum." In 2015 3rd International Conference on Control, Engineering & Information Technology (CEIT). IEEE, 2015. http://dx.doi.org/10.1109/ceit.2015.7233021.

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Maity, Sayani, and Greg R. Luecke. "Simulation Study of a Spherical Inverted Pendulum on an Omnidirectional Cart With Holonomic Constraints." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-9102.

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In this paper we develop the control and stabilization of a spherical jointed inverted pendulum balanced on an omnidirectional cart. The system consists of an omnidirectional cart with mecanum wheels equipped with a spherical inverted pendulum attached at the center of the platform. The inverted pendulum is free to fall in any direction perpendicular to the horizontal plane. The omnidirectional cart has the special ability to move in any direction without changing orientation. It can also rotate around its vertical axis. This balancing platform provides a base with holonomic motion to support and balance the pendulum. In this work, the system has been decoupled into two separate subsystems in the x-z and y-z plane. We develop the system dynamic equations in both vertical planes and design a LQR controller to stabilize the system. Using one-dimensional pendulum experimental data, we validate our controller and extend the approach to stabilize the spherical pendulum in both vertical directions. Simulation results are presented to show the effectiveness of the decoupled system LQR controller in stabilizing the spherical pendulum.
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Balkan, Tuna, and Mehmet Emin Ari. "Fuzzy Control of an Inverted Pendulum." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/cie-1441.

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Abstract An inverted pendulum system has been designed and constructed as a physical model of inherently unstable mechanical systems. The vertical upright position of a pendulum is controlled by changing the horizontal position of a cart to which the pendulum is hinged. The stability of the system has been investigated when a fuzzy controller is used to produce the control signal, while making a single measurement. It has been shown that by using simple fuzzy rules to allow real time computation with a single angular position measurement, the system can not be made absolutely stable. However, the stability and performance of the system have been considerably improved by shrinking the membership functions of angular position, computed angular velocity and control signal when inverted pendulum is very close to the vertical upright position.
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Dabiri, Arman, Morad Nazari, and Eric A. Butcher. "Linguistic Fuzzy Logic Control of a Double Inverted Pendulum With Destabilizing Fractional Dampers." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-67979.

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In this paper, a fuzzy controller is designed for a mechanical system with fractional damping without a priori knowledge of the system dynamics. Because of the constitutive equation of the damping, equations of motion of the system consist of fractional order terms. In the process of developing the fuzzy controller, the fuzzy rules are selected based on the human brain functions. The controller is first implemented for the case of a single inverted pendulum with destabilizing fractional dampings mounted on a cart, i.e. a two degree of freedom (DOF) system, where the functions of human brain in balancing a stick on a fingertip are used to train the fuzzy rules. Then, by extending the linguistic rules, the controller is applied to a double inverted pendulum with destabilizing fractional dampings mounted on a cart, i.e. a three DOF system. Since the linguistic rules are based on qualitative motion of the pendulums, the controller is capable bringing the system to rest at the unstable equilibrium point despite the fractional destabilizing damping in the system. Finally, the numerical results of the both examples are discussed.
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Gandhi, Prasanna, and Jaish Meena. "Chaos in Inverted Flexible Pendulum With Tip Mass." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38500.

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Flexible link systems are increasingly being used in the robotic and other applications. The dynamics of distributed parameter single flexible link system, especially in the vertical planes, is known to demonstrate chaotic behavior upon harmonic excitation. However, to the best of authors knowledge, chaotic dynamics of ultra-large deflection flexible systems with distributed and lumped parameters considered together has not been considered in the literature so far. Dynamics of a representative case, an inverted flexible pendulum with tip mass on cart system, is analysed in this paper. Experimental results on a custom built system consisting of link having 1. ultra large deformation (300 times thickness) as compared to thickness, 2. a tip mass, and 3. base fixed to a cart, under harmonic excitation under several frequencies were obtained. Poincaré maps with large set of data show successive progression with a small cluster of points to start with splitting into two clusters finally leading to butterfly figure of chaotic vibrations. Effect of variation of the excitation amplitude is also explored leading to interesting change in the patterns of Poincaré maps observed.
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Reports on the topic "Inverted Pendulum on a Cart"

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Altendorfer, Richard, Uluc Saranli, Haldun Komsuoglu, et al. Evidence for Spring Loaded Inverted Pendulum Running in a Hexapod Robot. Defense Technical Information Center, 2001. http://dx.doi.org/10.21236/ada438810.

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Petrov, Plamen. Dynamics and Adaptive Motion Control of a Two-wheeled Inverted Pendulum Robot. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2018. http://dx.doi.org/10.7546/crabs.2018.07.11.

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Seto, Danbing, and Lui Sha. A Case Study on Analytical Analysis of the Inverted Pendulum Real-Time Control System. Defense Technical Information Center, 1999. http://dx.doi.org/10.21236/ada373286.

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