Search results for: Non Linear Control

Authors: Zhong-xi Gao, Hou-biao Li

Abstract:

Recently, some convergent results of the generalized AOR iterative (GAOR) method for solving linear systems with strictly diagonally dominant matrices are presented in [Darvishi, M.T., Hessari, P.: On convergence of the generalized AOR method for linear systems with diagonally dominant cofficient matrices. Appl. Math. Comput. 176, 128-133 (2006)] and [Tian, G.X., Huang, T.Z., Cui, S.Y.: Convergence of generalized AOR iterative method for linear systems with strictly diagonally dominant cofficient matrices. J. Comp. Appl. Math. 213, 240-247 (2008)]. In this paper, we give the convergence of the GAOR method for linear systems with strictly doubly diagonally dominant matrix, which improves these corresponding results.

Keywords: Diagonally dominant matrix, GAOR method, Linear system, Convergence

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Authors: Hong Son Hoang, Remy Baraille

Abstract:

The (sub)-optimal soolution of linear filtering problem with correlated noises is considered. The special recursive form of the class of filters and criteria for selecting the best estimator are the essential elements of the design method. The properties of the proposed filter are studied. In particular, for Markovian observation noise, the approximate filter becomes an optimal Gevers-Kailath filter subject to a special choice of the parameter in the class of given linear recursive filters.

Keywords: Linear dynamical system, filtering, minimum meansquare filter, correlated noise

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Authors: Sudeept Mohan, Surekha Bhanot

Abstract:

The problem of manipulator control is a highly complex problem of controlling a system which is multi-input, multioutput, non-linear and time variant. In this paper some adaptive fuzzy, and a new hybrid fuzzy control algorithm have been comparatively evaluated through simulations, for manipulator control. The adaptive fuzzy controllers consist of self-organizing, self-tuning, and coarse/fine adaptive fuzzy schemes. These controllers are tested for different trajectories and for varying manipulator parameters through simulations. Various performance indices like the RMS error, steady state error and maximum error are used for comparison. It is observed that the self-organizing fuzzy controller gives the best performance. The proposed hybrid fuzzy plus integral error controller also performs remarkably well, given its simple structure.

Keywords: Hybrid fuzzy, Self-organizing, Self-tuning, Trajectory tracking.

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Authors: J. Fernandez de Canete, S. Gonzalez-Perez, P. del Saz-Orozco

Abstract:

Neural networks offer an alternative approach both for identification and control of nonlinear processes in process engineering. The lack of software tools for the design of controllers based on neural network models is particularly pronounced in this field. SIMULINK is properly a widely used graphical code development environment which allows system-level developers to perform rapid prototyping and testing. Such graphical based programming environment involves block-based code development and offers a more intuitive approach to modeling and control task in a great variety of engineering disciplines. In this paper a SIMULINK based Neural Tool has been developed for analysis and design of multivariable neural based control systems. This tool has been applied to the control of a high purity distillation column including non linear hydrodynamic effects. The proposed control scheme offers an optimal response for both theoretical and practical challenges posed in process control task, in particular when both, the quality improvement of distillation products and the operation efficiency in economical terms are considered.

Keywords: Distillation, neural networks, software tools, identification, control.

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Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

Abstract:

In statistics parameter theory, usually the parameter estimations have two kinds, one is the least-square estimation (LSE), and the other is the best linear unbiased estimation (BLUE). Due to the determining theorem of minimum variance unbiased estimator (MVUE), the parameter estimation of BLUE in linear model is most ideal. But since the calculations are complicated or the covariance is not given, people are hardly to get the solution. Therefore, people prefer to use LSE rather than BLUE. And this substitution will take some losses. To quantize the losses, many scholars have presented many kinds of different relative efficiencies in different views. For the linear weighted regression model, this paper discusses the relative efficiencies of LSE of β to BLUE of β. It also defines two new relative efficiencies and gives their lower bounds.

Keywords: Linear weighted regression, Relative efficiency, Lower bound, Parameter estimation.

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Authors: Ahmed Bensenouci

Abstract:

This paper provides the design steps of a robust Linear Matrix Inequality (LMI) based iterative multivariable PID controller whose duty is to drive a sample power system that comprises a synchronous generator connected to a large network via a step-up transformer and a transmission line. The generator is equipped with two control-loops, namely, the speed/power (governor) and voltage (exciter). Both loops are lumped in one where the error in the terminal voltage and output active power represent the controller inputs and the generator-exciter voltage and governor-valve position represent its outputs. Multivariable PID is considered here because of its wide use in the industry, simple structure and easy implementation. It is also preferred in plants of higher order that cannot be reduced to lower ones. To improve its robustness to variation in the controlled variables, H∞-norm of the system transfer function is used. To show the effectiveness of the controller, divers tests, namely, step/tracking in the controlled variables, and variation in plant parameters, are applied. A comparative study between the proposed controller and a robust H∞ LMI-based output feedback is given by its robustness to disturbance rejection. From the simulation results, the iterative multivariable PID shows superiority.

Keywords: Linear matrix inequality, power system, robust iterative PID, robust output feedback control

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Authors: M. Ouassaid, M. Cherkaoui, A. Nejmi, M. Maaroufi

Abstract:

This study presents a novel means of designing a simple and effective torque controller for Permanent Magnet Synchronous Motor (PMSM). The overall stability of the system is shown using Lyapunov technique. The Lyapunov functions used contain a term penalizing the integral of the tracking error, enhancing the stability. The tracking error is shown to be globally uniformly bounded. Simulation results are presented to show the effectiveness of the approach.

Keywords: Integral action, Lyapunov Technique, Non Linear Control, Permanent Magnet Synchronous Motors, Torque Control, Stability.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, augmented linear system, nonlinear observer, formal linearization, electric power system.

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Authors: Ruming Yin, Jian Yuan, Qiuhua Yang, Xiuming Shan, Xiqin Wang

Abstract:

Linear cryptanalysis methods are rarely used to improve the security of chaotic stream ciphers. In this paper, we apply linear cryptanalysis to a chaotic stream cipher which was designed by strictly using the basic design criterion of cryptosystem – confusion and diffusion. We show that this well-designed chaos-based stream cipher is still insecure against distinguishing attack. This distinguishing attack promotes the further improvement of the cipher.

Keywords: Stream cipher, chaos, linear cryptanalysis, distinguishing attack.

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Authors: Geng Yuan, Yiwan Guo, Fahui Zhai, Shuhua Zhang

Abstract:

In this paper, we discuss some properties of left spectrum and give the representation of linear preserver map the left spectrum of diagonal quaternionic matrices.

Keywords: Quaternionic matrix, left spectrum, linear preserver map.

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Authors: M. Zamani, O. Kahar

Abstract:

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.

Keywords: Navier-Stokes, 'Non-linear grid system', Splitting method.

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Authors: Zunaira Asif, Zhi Chen

Abstract:

The sustainable measures on air quality management are recognized as one of the most serious environmental concerns in the mining region. The mining operations emit various types of pollutants which have significant impacts on the environment. This study presents a stochastic control strategy by developing the air pollution control model to achieve a cost-effective solution. The optimization method is formulated to predict the cost of treatment using linear programming with an objective function and multi-constraints. The constraints mainly focus on two factors which are: production of metal should not exceed the available resources, and air quality should meet the standard criteria of the pollutant. The applicability of this model is explored through a case study of an open pit metal mine, Utah, USA. This method simultaneously uses meteorological data as a dispersion transfer function to support the practical local conditions. The probabilistic analysis and the uncertainties in the meteorological conditions are accomplished by Monte Carlo simulation. Reasonable results have been obtained to select the optimized treatment technology for PM_2.5, PM₁₀, NO_x, and SO₂. Additional comparison analysis shows that baghouse is the least cost option as compared to electrostatic precipitator and wet scrubbers for particulate matter, whereas non-selective catalytical reduction and dry-flue gas desulfurization are suitable for NO_x and SO₂ reduction respectively. Thus, this model can aid planners to reduce these pollutants at a marginal cost by suggesting control pollution devices, while accounting for dynamic meteorological conditions and mining activities.

Keywords: Air pollution, linear programming, mining, optimization, treatment technologies.

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Authors: Lazim Abdullah, Nurhakimah Ab. Rahman

Abstract:

Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.

Keywords: Fuzzy linear systems, Jacobi, Jacobi Over- Relaxation, Refinement of Jacobi, Refinement of Jacobi Over- Relaxation.

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Authors: T. O. Olwal, K. Djouani, B. J. van Wyk, Y. Hamam, P. Siarry

Abstract:

Multi-Radio Multi-Channel Wireless Mesh Networks (MRMC-WMNs) operate at the backbone to access and route high volumes of traffic simultaneously. Such roles demand high network capacity, and long “online" time at the expense of accelerated transmission energy depletion and poor connectivity. This is the problem of transmission power control. Numerous power control methods for wireless networks are in literature. However, contributions towards MRMC configurations still face many challenges worth considering. In this paper, an energy-efficient power selection protocol called PMMUP is suggested at the Link-Layer. This protocol first divides the MRMC-WMN into a set of unified channel graphs (UCGs). A UCG consists of multiple radios interconnected to each other via a common wireless channel. In each UCG, a stochastic linear quadratic cost function is formulated. Each user minimizes this cost function consisting of trade-off between the size of unification states and the control action. Unification state variables come from independent UCGs and higher layers of the protocol stack. The PMMUP coordinates power optimizations at the network interface cards (NICs) of wireless mesh routers. The proposed PMMUP based algorithm converges fast analytically with a linear rate. Performance evaluations through simulations confirm the efficacy of the proposed dynamic power control.

Keywords: Effective band inference based power control algorithm (EBIA), Power Selection MRMC Unification Protocol (PMMUP), MRMC State unification Variable Prediction (MRSUP), Wireless Mesh Networks (WMNs).

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Authors: Shu-Xin Miao

Abstract:

In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm.

Keywords: Homotopy perturbation method, fuzzy linear systems, block linear system, fuzzy solution, embedding parameter.

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Authors: Jasmin Velagic, Nedim Osmic, Bakir Lacevic

Abstract:

In this paper the neural network-based controller is designed for motion control of a mobile robot. This paper treats the problems of trajectory following and posture stabilization of the mobile robot with nonholonomic constraints. For this purpose the recurrent neural network with one hidden layer is used. It learns relationship between linear velocities and error positions of the mobile robot. This neural network is trained on-line using the backpropagation optimization algorithm with an adaptive learning rate. The optimization algorithm is performed at each sample time to compute the optimal control inputs. The performance of the proposed system is investigated using a kinematic model of the mobile robot.

Keywords: Mobile robot, kinematic model, neural network, motion control, adaptive learning rate.

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Authors: Seema Chopra, R. Mitra, Vijay Kumar

Abstract:

A neurofuzzy approach for a given set of input-output training data is proposed in two phases. Firstly, the data set is partitioned automatically into a set of clusters. Then a fuzzy if-then rule is extracted from each cluster to form a fuzzy rule base. Secondly, a fuzzy neural network is constructed accordingly and parameters are tuned to increase the precision of the fuzzy rule base. This network is able to learn and optimize the rule base of a Sugeno like Fuzzy inference system using Hybrid learning algorithm, which combines gradient descent, and least mean square algorithm. This proposed neurofuzzy system has the advantage of determining the number of rules automatically and also reduce the number of rules, decrease computational time, learns faster and consumes less memory. The authors also investigate that how neurofuzzy techniques can be applied in the area of control theory to design a fuzzy controller for linear and nonlinear dynamic systems modelling from a set of input/output data. The simulation analysis on a wide range of processes, to identify nonlinear components on-linely in a control system and a benchmark problem involving the prediction of a chaotic time series is carried out. Furthermore, the well-known examples of linear and nonlinear systems are also simulated under the Matlab/Simulink environment. The above combination is also illustrated in modeling the relationship between automobile trips and demographic factors.

Keywords: Fuzzy control, neuro-fuzzy techniques, fuzzy subtractive clustering, extraction of rules, and optimization of membership functions.

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Authors: Santhakumar M., Asokan T.

Abstract:

This paper addresses the problem of trajectory tracking control of an underactuated autonomous underwater vehicle (AUV) in the horizontal plane. The underwater vehicle under consideration is not actuated in the sway direction, and the system matrices are not assumed to be diagonal and linear, as often found in the literature. In addition, the effect of constant bias of environmental disturbances is considered. Using backstepping techniques and the tracking error dynamics, the system states are stabilized by forcing the tracking errors to an arbitrarily small neighborhood of zero. The effectiveness of the proposed control method is demonstrated through numerical simulations. Simulations are carried out for an experimental vehicle for smooth, inertial, two dimensional (2D) reference trajectories such as constant velocity trajectory (a circle maneuver – constant yaw rate), and time varying velocity trajectory (a sinusoidal path – sinusoidal yaw rate).

Keywords: autonomous underwater vehicle, system matrices, tracking control, time – varying feed back, underactuated control.

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Authors: Bin Yu, Minghui Wang, Juntao Zhang

Abstract:

By the real representation of the quaternionic matrix, an iterative method for quaternionic linear equations Ax = b is proposed. Then the convergence conditions are obtained. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Quaternionic linear equations, Real representation, Iterative algorithm.

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Authors: Vivekanandan C., Prabhakar .R., Prema D.

Abstract:

This paper presents the application of discrete-time variable structure control with sliding mode based on the 'reaching law' method for robust control of a 'simple inverted pendulum on moving cart' - a standard nonlinear benchmark system. The controllers designed using the above techniques are completely insensitive to parametric uncertainty and external disturbance. The controller design is carried out using pole placement technique to find state feedback gain matrix , which decides the dynamic behavior of the system during sliding mode. This is followed by feedback gain realization using the control law which is synthesized from 'Gao-s reaching law'. The model of a single inverted pendulum and the discrete variable structure control controller are developed, simulated in MATLAB-SIMULINK and results are presented. The response of this simulation is compared with that of the discrete linear quadratic regulator (DLQR) and the advantages of sliding mode controller over DLQR are also presented

Keywords: Inverted pendulum, Variable Structure, Sliding mode control, Discrete-time systems, Nonlinear systems.

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Authors: Keny Ordaz-Hernandez, Xavier Fischer, Fouad Bennis

Abstract:

In a particular case of behavioural model reduction by ANNs, a validity domain shortening has been found. In mechanics, as in other domains, the notion of validity domain allows the engineer to choose a valid model for a particular analysis or simulation. In the study of mechanical behaviour for a cantilever beam (using linear and non-linear models), Multi-Layer Perceptron (MLP) Backpropagation (BP) networks have been applied as model reduction technique. This reduced model is constructed to be more efficient than the non-reduced model. Within a less extended domain, the ANN reduced model estimates correctly the non-linear response, with a lower computational cost. It has been found that the neural network model is not able to approximate the linear behaviour while it does approximate the non-linear behaviour very well. The details of the case are provided with an example of the cantilever beam behaviour modelling.

Keywords: artificial neural network, validity domain, cantileverbeam, non-linear behaviour, model reduction.

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Authors: Tadatsugu Kitamoto

Abstract:

Recently, a quality of motors is inspected by human ears. In this paper, I propose two systems using a method of speech recognition for automation of the inspection. The first system is based on a method of linear processing which uses K-means and Nearest Neighbor method, and the second is based on a method of non-linear processing which uses neural networks. I used motor sounds in these systems, and I successfully recognize 86.67% of motor sounds in the linear processing system and 97.78% in the non-linear processing system.

Keywords: Acoustical diagnosis, Neural networks, K-means, Short-time Fourier transformation

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Authors: Mohd Sazli Saad, Hishamuddin Jamaluddin, Intan Zaurah Mat Darus

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This paper presents the development of an active vibration control using direct adaptive controller to suppress the vibration of a flexible beam system. The controller is realized based on linear parametric form. Differential evolution optimisation algorithm is used to optimize the controller using single objective function by minimizing the mean square error of the observed vibration signal. Furthermore, an alternative approach is developed to systematically search for the best controller model structure together with it parameter values. The performance of the control scheme is presented and analysed in both time and frequency domain. Simulation results demonstrate that the proposed scheme is able to suppress the unwanted vibration effectively.

Keywords: flexible beam, finite difference method, active vibration control, differential evolution, direct adaptive controller

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Authors: S. J. Hosseini Ghoncheh, M. Paripour

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In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.

Keywords: Fuzzy number, fuzzy linear systems, Huang's method.

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Authors: Rabiˆı DARITI, El Mamoun SOUIDI

Abstract:

Linear error-block codes are a natural generalization of linear error correcting codes. The purpose of this paper is to generalize some results on the packing and the covering radii to the error-block case. We study their properties when a code undergoes some specific modifications and combinations with another code. We give a few bounds on the packing and the covering radii of these codes.

Keywords: Linear error-block codes, π-distance, Correction capacity, Packing radius, Covering radius.

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Authors: B. Selma, S. Chouraqui

Abstract:

Nonlinear system identification is becoming an important tool which can be used to improve control performance. This paper describes the application of adaptive neuro-fuzzy inference system (ANFIS) model for controlling a car. The vehicle must follow a predefined path by supervised learning. Backpropagation gradient descent method was performed to train the ANFIS system. The performance of the ANFIS model was evaluated in terms of training performance and classification accuracies and the results confirmed that the proposed ANFIS model has potential in controlling the non linear system.

Keywords: Adaptive neuro-fuzzy inference system (ANFIS), Fuzzy logic, neural network, nonlinear system, control

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Authors: Attitude Stabilization of Satellites Using Random Dither Quantization

Abstract:

Recently, the effectiveness of random dither quantization method for linear feedback control systems has been shown in several papers. However, the random dither quantization method has not yet been applied to nonlinear feedback control systems. The objective of this paper is to verify the effectiveness of random dither quantization method for nonlinear feedback control systems. For this purpose, we consider the attitude stabilization problem of satellites using discrete-level actuators. Namely, this paper provides a control method based on the random dither quantization method for stabilizing the attitude of satellites using discrete-level actuators.

Keywords: Quantized control, nonlinear systems, random dither quantization.

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Authors: Javad Khazaei, Rick S. Blum

Abstract:

Distributed control is an efficient and flexible approach for coordination of multi-agent systems. One of the main challenges in designing a distributed controller is identifying the governing dynamics of the dynamical systems. Data-driven system identification is currently undergoing a revolution. With the availability of high-fidelity measurements and historical data, model-free identification of dynamical systems can facilitate the control design without tedious modeling of high-dimensional and/or nonlinear systems. This paper develops a distributed control design using consensus theory for linear and nonlinear dynamical systems using sparse identification of system dynamics. Compared with existing consensus designs that heavily rely on knowing the detailed system dynamics, the proposed model-free design can accurately capture the dynamics of the system with available measurements and input data and provide guaranteed performance in consensus and tracking problems. Heterogeneous damped oscillators are chosen as examples of dynamical system for validation purposes.

Keywords: Consensus tracking, distributed control, model-free control, sparse identification of dynamical systems.

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Authors: I. M. Abd Rahim, H. Abdul Rahim, R. Ghazali

Abstract:

There is numerous non-invasive blood glucose measurement technique developed by researchers, and near infrared (NIR) is the potential technique nowadays. However, there are some disagreements on the optimal wavelength range that is suitable to be used as the reference of the glucose substance in the blood. This paper focuses on the experimental data collection technique and also the analysis method used to analyze the data gained from the experiment. The selection of suitable linear and non-linear model structure is essential in prediction system, as the system developed need to be conceivably accurate.

Keywords: Invasive, linear, near-infrared (Nir), non-invasive, non-linear, prediction system.

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Authors: Arian Bahrami, Mojtaba Tafaoli-Masoule, Mansour Nikkhah Bahrami

Abstract:

This paper demonstrates the potential of applying PD-like fuzzy logic controller for active vibration control of piezoelectric Stewart platforms. Through simulation, the control authority of the piezo stack actuators for effectively damping the Stewart platform vibration can be evaluated for further implementation of the system. Each leg of the piezoelectric Stewart platform consists of a linear piezo stack actuator, a collocated velocity sensor, a collocated displacement sensor and flexible tips for the connections with the two end plates. The piezoelectric stack is modeled as a bar element and the electro-mechanical coupling property is simulated using Matlab/Simulink software. Then, the open loop and closed loop dynamic responses are performed for the system to characterize the effect of the control on the vibration of the piezoelectric Stewart platform. A significant improvement in the damping of the structure can be observed by using the PD-like fuzzy controller.

Keywords: Active vibration control, Fuzzy controller, Piezoelectric stewart platform.

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