Design of a Novel Fuzzy Sliding-Mode Control for Magnetic Ball Levitation System
01 Mar 2005-Journal of Intelligent and Robotic Systems (Kluwer Academic Publishers)-Vol. 42, Iss: 3, pp 295-316
TL;DR: The design of a novel fuzzy sliding-mode control (NFSMC) for the magnetic ball levitation system is presented and the Lyapunov stability analysis is given.
Abstract: This paper presents the design of a novel fuzzy sliding-mode control (NFSMC) for the magnetic ball levitation system. At first, we examine the nonlinear dynamic models of the magnetic ball system, where the singular perturbation method is used. Next, we address the design schemes of sliding mode control (SMC) and traditional fuzzy sliding-mode control (FSMC), where two kinds of FSMCs are introduced. Then we provide the design steps of the NFSMC, where the Lyapunov stability analysis is also given. Finally, a magnetic ball levitation system is used to illustrate the effectiveness of the proposed controller.
Citations
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TL;DR: The simulation results show that the FTSMC can provide much good tracking performance than that of the classical fuzzy sliding-mode controller (FSMC).
146 citations
Cites background from "Design of a Novel Fuzzy Sliding-Mod..."
...Recently, the concept of integrating fuzzy logic control and sliding-mode control has become a popular research subject [3,8,10,11,17,18,20,24,37,45,46]....
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TL;DR: In this paper, a robust fuzzy sliding mode control (FSMC) scheme for the synchronization of two chaotic nonlinear gyros subject to uncertainties and external disturbances is presented, where the reaching law required to drive the error state trajectory of the master-slave system to the sliding surface is inferred by a set of fuzzy logic rules based upon the output of a sliding mode controller.
118 citations
Cites background or methods from "Design of a Novel Fuzzy Sliding-Mod..."
...The corresponding fuzzy rule table is presented in Table 1 [27]....
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...Suppose the rules of fuzzy controller are based on SMC, and then it is called the FSMC [27]....
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...Fuzzy set theory was first presented by Zadeh [26], while fuzzy logic control (FLC) schemes have been widely developed for almost 40 years, and have been successfully deployed in many applications [27]....
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TL;DR: Simulation results show the FSMC not only can control the uncertain chaotic behaviors to a desired state without oscillator very fast, but also the switching function is smooth without chattering, implying that this strategy is feasible and effective for chaos control.
Abstract: This paper proposes a chattering-free fuzzy sliding-mode control (FSMC) strategy for uncertain chaotic systems. A fuzzy logic control is used to replace the discontinuous sign function of the reaching law in traditional sliding-mode control (SMC), and hence a control input without chattering is obtained in the chaotic systems with uncertainties. Base on the Lyapunov stability theory, we address the design schemes of integration fuzzy sliding-mode control, where the reaching law is proposed by a set of linguistic rules and the control input is chattering free. The Genesio chaotic system is used to test the proposed control strategy and the simulation results show the FSMC not only can control the uncertain chaotic behaviors to a desired state without oscillator very fast, but also the switching function is smooth without chattering. This result implies that this strategy is feasible and effective for chaos control.
117 citations
Cites background from "Design of a Novel Fuzzy Sliding-Mod..."
...The fuzzy logic control (FLC) schemes have been widely developed for almost 40 years, and have been successfully applied to many applications [21,28]....
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TL;DR: In this paper, a rule-based controller for a class of master-slave chaos synchronization is presented, where the fuzzy rules are constructed subject to a common Lyapunov function.
Abstract: The design of a rule-based controller for a class of master-slave chaos synchronization is presented in this paper. In traditional fuzzy logic control (FLC) design, it takes a long time to obtain the membership functions and rule base by trial-and-error tuning. To cope with this problem, we directly construct the fuzzy rules subject to a common Lyapunov function such that the master–slave chaos systems satisfy stability in the Lyapunov sense. Unlike conventional approaches, the resulting control law has less maximum magnitude of the instantaneous control command and it can reduce the actuator saturation phenomenon in real physic system. Two examples of Duffing–Holmes system and Lorenz system are presented to illustrate the effectiveness of the proposed controller.
110 citations
Cites background from "Design of a Novel Fuzzy Sliding-Mod..."
...The fuzzy logic control (FLC) schemes have been widely developed for almost 40 years, and have been successfully applied to many applications [8]....
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TL;DR: A new sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions, and the vector controller is one-dimensional less than the system.
Abstract: In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. More importantly, the vector controller is one-dimensional less than the system. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Chen chaotic system and an integer-order T chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen’s system and an integer-order hyperchaotic system, and the synchronization between a fractional-order hyperchaotic system based on Chen’s system and an integer-order Lorenz chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.
85 citations
Cites methods from "Design of a Novel Fuzzy Sliding-Mod..."
...Suppose the rules of fuzzy controller are based on SMC, and then it is called the FSMC [31]....
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References
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01 Jan 1973
TL;DR: By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.
Abstract: The approach described in this paper represents a substantive departure from the conventional quantitative techniques of system analysis. It has three main distinguishing features: 1) use of so-called ``linguistic'' variables in place of or in addition to numerical variables; 2) characterization of simple relations between variables by fuzzy conditional statements; and 3) characterization of complex relations by fuzzy algorithms. A linguistic variable is defined as a variable whose values are sentences in a natural or artificial language. Thus, if tall, not tall, very tall, very very tall, etc. are values of height, then height is a linguistic variable. Fuzzy conditional statements are expressions of the form IF A THEN B, where A and B have fuzzy meaning, e.g., IF x is small THEN y is large, where small and large are viewed as labels of fuzzy sets. A fuzzy algorithm is an ordered sequence of instructions which may contain fuzzy assignment and conditional statements, e.g., x = very small, IF x is small THEN Y is large. The execution of such instructions is governed by the compositional rule of inference and the rule of the preponderant alternative. By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.
8,547 citations
TL;DR: Design and analysis forVariable structure systems are surveyed in this paper and it is shown that advantageous properties result from changing structures according to this switching logic.
Abstract: Variable structure systems consist of a set of continuous subsystems together with suitable switching logic. Advantageous properties result from changing structures according to this switching logic. Design and analysis for this class of systems are surveyed in this paper.
5,076 citations
TL;DR: A tutorial account of variable structure control with sliding mode is presented, introducing in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach.
Abstract: A tutorial account of variable structure control with sliding mode is presented. The purpose is to introduce in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach. This approach is particularly attractive for the control of nonlinear systems. Prominent characteristics such as invariance, robustness, order reduction, and control chattering are discussed in detail. Methods for coping with chattering are presented. Both linear and nonlinear systems are considered. Future research areas are suggested and an extensive list of references is included. >
2,884 citations
Book•
01 Jan 1999
TL;DR: Sliding mode control (SMC) is gaining increasing importance as a universal design tool for the robust control of linear and nonlinear systems as mentioned in this paper, and is particularly useful for electro-mechanical systems because of its discontinuous structure.
Abstract: Sliding Mode Control (SMC) is gaining increasing importance as a universal design tool for the robust control of linear and nonlinear systems. The strengths of sliding mode controllers result from the ease and flexibility of the methodology for their design and implementation. They provide inherent order reduction, direct incorporation of robustness against system uncertainties and disturbances, and an implicit stability proof. They also allow for the design of high performance control systems at low costs. SMC is particularly useful for electro-mechanical systems because of its discontinuous structure. In fact, since the hardware of many electro-mechanical systems (such as electric motors) prescribes discontinuous inputs, SMC has become the natural choice for direct implementation. The book is intended primarily for engineers and establishes an interdisciplinary bridge between control science, electrical and mechanical engineering.
2,593 citations
Book•
01 Jan 1962TL;DR: This new edition of Automatic Control Systems features a new, accessible approach for students taking introductory courses on control systems while retaining the depth and rigor of Benjamin Kuos classic, best-selling text.
Abstract: From the Publisher:
Automatic Control Systems Seventh Edition Benjamin C. Kuo Updated to reflect the increasing use of computer-aided learning and design, the seventh edition of Automatic Control Systems features a new, accessible approach for students taking introductory courses on control systems while retaining the depth and rigor of Benjamin Kuos classic, best-selling text. This new edition integrates several real world applications throughout the text, covering both analysis and design. Other new features include:*demonstration of the solution of complex problems with the aid of computer software*thorough discussion of steady-state error analysis, including nonunity-feedback systems*discussion of circuit realization of controller transfer functions*simplified treatment of Nyquist criterion on systems with nonminimum-phase transfer functions*discussion of time-domain and frequency-domain designs side by side in one chapter*added chapter on design of discrete-data control systemsThe text also includes an abundance of illustrative examples, problems, and marginal notes to highlight important points and comments. Contents include full chapters on: mathematical foundation transfer functions, block diagrams, and signal-flow graphs mathematical modeling of physical systems state-variable analysis stability of linear control systems time-domain analysis of control systems root-locus techniques frequency-domain analysis design of control systems design of discrete-data control systems
2,519 citations