# Adaptive Neuro fuzzy inference system controller design for single stage Inverted Pendulum

VIT University

^{1}20 Apr 2016-pp 472-476

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TL;DR: The architecture and learning procedure underlying ANFIS (adaptive-network-based fuzzy inference system) is presented, which is a fuzzy inference System implemented in the framework of adaptive networks.

Abstract: The architecture and learning procedure underlying ANFIS (adaptive-network-based fuzzy inference system) is presented, which is a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs. In the simulation, the ANFIS architecture is employed to model nonlinear functions, identify nonlinear components on-line in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificial neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. >

13,738 citations

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01 Dec 1994

TL;DR: This chapter discusses Fuzzy Systems Simulation, specifically the development of Membership Functions and the Extension Principle, and some of the methods used to derive these functions.

Abstract: About the Author. Preface to the Third Edition. 1 Introduction. The Case for Imprecision. A Historical Perspective. The Utility of Fuzzy Systems. Limitations of Fuzzy Systems. The Illusion: Ignoring Uncertainty and Accuracy. Uncertainty and Information. The Unknown. Fuzzy Sets and Membership. Chance Versus Fuzziness. Sets as Points in Hypercubes. Summary. References. Problems. 2 Classical Sets and Fuzzy Sets. Classical Sets. Operations on Classical Sets. Properties of Classical (Crisp) Sets. Mapping of Classical Sets to Functions. Fuzzy Sets. Fuzzy Set Operations. Properties of Fuzzy Sets. Alternative Fuzzy Set Operations. Summary. References. Problems. 3 Classical Relations and Fuzzy Relations. Cartesian Product. Crisp Relations. Cardinality of Crisp Relations. Operations on Crisp Relations. Properties of Crisp Relations. Composition. Fuzzy Relations. Cardinality of Fuzzy Relations. Operations on Fuzzy Relations. Properties of Fuzzy Relations. Fuzzy Cartesian Product and Composition. Tolerance and Equivalence Relations. Crisp Equivalence Relation. Crisp Tolerance Relation. Fuzzy Tolerance and Equivalence Relations. Value Assignments. Cosine Amplitude. Max Min Method. Other Similarity Methods. Other Forms of the Composition Operation. Summary. References. Problems. 4 Properties of Membership Functions, Fuzzification, and Defuzzification. Features of the Membership Function. Various Forms. Fuzzification. Defuzzification to Crisp Sets. -Cuts for Fuzzy Relations. Defuzzification to Scalars. Summary. References. Problems. 5 Logic and Fuzzy Systems. Part I Logic. Classical Logic. Proof. Fuzzy Logic. Approximate Reasoning. Other Forms of the Implication Operation. Part II Fuzzy Systems. Natural Language. Linguistic Hedges. Fuzzy (Rule-Based) Systems. Graphical Techniques of Inference. Summary. References. Problems. 6 Development of Membership Functions. Membership Value Assignments. Intuition. Inference. Rank Ordering. Neural Networks. Genetic Algorithms. Inductive Reasoning. Summary. References. Problems. 7 Automated Methods for Fuzzy Systems. Definitions. Batch Least Squares Algorithm. Recursive Least Squares Algorithm. Gradient Method. Clustering Method. Learning From Examples. Modified Learning From Examples. Summary. References. Problems. 8 Fuzzy Systems Simulation. Fuzzy Relational Equations. Nonlinear Simulation Using Fuzzy Systems. Fuzzy Associative Memories (FAMS). Summary. References. Problems. 9 Decision Making with Fuzzy Information. Fuzzy Synthetic Evaluation. Fuzzy Ordering. Nontransitive Ranking. Preference and Consensus. Multiobjective Decision Making. Fuzzy Bayesian Decision Method. Decision Making Under Fuzzy States and Fuzzy Actions. Summary. References. Problems. 10 Fuzzy Classification. Classification by Equivalence Relations. Crisp Relations. Fuzzy Relations. Cluster Analysis. Cluster Validity. c-Means Clustering. Hard c-Means (HCM). Fuzzy c-Means (FCM). Fuzzy c-Means Algorithm. Classification Metric. Hardening the Fuzzy c-Partition. Similarity Relations from Clustering. Summary. References. Problems. 11 Fuzzy Pattern Recognition. Feature Analysis. Partitions of the Feature Space. Single-Sample Identification. Multifeature Pattern Recognition. Image Processing. Summary. References. Problems. 12 Fuzzy Arithmetic and the Extension Principle. Extension Principle. Crisp Functions, Mapping, and Relations. Functions of Fuzzy Sets Extension Principle. Fuzzy Transform (Mapping). Practical Considerations. Fuzzy Arithmetic. Interval Analysis in Arithmetic. Approximate Methods of Extension. Vertex Method. DSW Algorithm. Restricted DSW Algorithm. Comparisons. Summary. References. Problems. 13 Fuzzy Control Systems. Control System Design Problem. Control (Decision) Surface. Assumptions in a Fuzzy Control System Design. Simple Fuzzy Logic Controllers. Examples of Fuzzy Control System Design. Aircraft Landing Control Problem. Fuzzy Engineering Process Control. Classical Feedback Control. Fuzzy Control. Fuzzy Statistical Process Control. Measurement Data Traditional SPC. Attribute Data Traditional SPC. Industrial Applications. Summary. References. Problems. 14 Miscellaneous Topics. Fuzzy Optimization. One-Dimensional Optimization. Fuzzy Cognitive Mapping. Concept Variables and Causal Relations. Fuzzy Cognitive Maps. Agent-Based Models. Summary. References. Problems. 15 Monotone Measures: Belief, Plausibility, Probability, and Possibility. Monotone Measures. Belief and Plausibility. Evidence Theory. Probability Measures. Possibility and Necessity Measures. Possibility Distributions as Fuzzy Sets. Possibility Distributions Derived from Empirical Intervals. Deriving Possibility Distributions from Overlapping Intervals. Redistributing Weight from Nonconsonant to Consonant Intervals. Comparison of Possibility Theory and Probability Theory. Summary. References. Problems. Index.

4,957 citations

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TL;DR: This paper presents the key motivations for the use of that system and explains, in details, the main reflections on how the inverted pendulum benchmark gives an effective and efficient application.

Abstract: For at least fifty years, the inverted pendulum has been the most popular benchmark, among others, for teaching and researches in control theory and robotics. This paper presents the key motivations for the use of that system and explains, in details, the main reflections on how the inverted pendulum benchmark gives an effective and efficient application. Several real experiences, virtual models and web-based remote control laboratories will be presented with emphasis on the practical design implementation of this system. A bibliographical survey of different design control approaches and trendy robotic problems will be presented through applications to the inverted pendulum system. In total, 150 references in the open literature, dating back to 1960, are compiled to provide an overall picture of historical, current and challenging developments based on the stabilization principle of the inverted pendulum.

85 citations

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TL;DR: In this article, an adaptive-network-based fuzzy inference system (ANFIS) model is proposed to compute the characteristic impedances of air-suspended trapezoidal-shaped microshield lines (AS-TSMLs) and AS-RSMLs, and four optimization algorithms, hybrid learning, simulated annealing, genetic, and least squares, are used to determine optimally the design parameters of ANFIS.

Abstract: In this article, adaptive-network-based fuzzy inference system (ANFIS) models are proposed to compute the characteristic impedances of air-suspended trapezoidal-shaped microshield lines (AS-TSMLs) and air-suspended rectangular-shaped microshield lines (AS-RSMLs). The ANFIS is a fuzzy inference system implemented within the architecture and optimization procedure of adaptive networks. Four optimization algorithms, hybrid learning, simulated annealing, genetic, and least-squares, are used to determine optimally the design parameters of ANFIS. The characteristic impedance results of ANFIS models are in very good agreement with the results available in the literature. When the performances of ANFIS models are compared with each other, the best results are obtained from the ANFIS model trained by the hybrid learning algorithm. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 20–24, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24829

39 citations

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TL;DR: A novel selective partial-state feedback control law is made for swing-up control of double inverted pendulum systems that is not at all sensitive to uncertainties such as modelling error and sensor noise, and is both reliable and robust.

Abstract: In Part I a technique for the swing-up control of single inverted pendulum system is presented. The requirement is to swing-up a carriage mounted pendulum system from its natural pendent position to its inverted position. It works for all carriage balancing single inverted pendulum systems as the swing-up control algorithm does not require knowledge of the system parameters. Comparison with previous swing-up controls shows that the proposed swing-up control is simpler, eaiser. more efficient, and more robust. In Part II the technique is extended to the case of the swing-up control of double inverted pendulum systems. Use is made of a novel selective partial-state feedback control law. The nonlinear, open-loop unstable, nonminimum-phase. and interactive MIMO pendulum system is actively linearised and decoupled about a neutrally stable equilibrium by the partial-state feedback control. This technique for swing-up control is not at all sensitive to uncertainties such as modelling error and sensor noise, and is both reliable and robust.

36 citations

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