Search results for: nonlinear dynamic systems

Authors: Yongping Ren, Zongli Li, Fan Zhang

Abstract:

A new nonlinear PID controller and its stability analysis are presented in this paper. A nonlinear function is deduced from the similarities between the control effort and the electric-field effect of a capacitor. The conventional linear PID controller can be modified into a nonlinear one by this function. To analyze the stability of the nonlinear PID controlled system, an idea of energy equivalence is adapted to avoid the conservativeness which is usually arisen from some traditional theorems and Criterions. The energy equivalence is naturally related with the conceptions of Passivity and T-Passivity. As a result, an engineering guideline for the parameter design of the nonlinear PID controller is obtained. An inverted pendulum system is tested to verify the nonlinear PID control scheme.

Keywords: Nonlinear PID controller, stability, gain equivalence, dissipative, T-Passivity.

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Authors: T. Yamaguchi, Y. Kurosawa, S. Maruyama, K. Tobita, Y. Hirano, K. Yokouchi, K. Kihara, T. Sunaga

Abstract:

This paper describes dynamic analysis using proposed fast finite element method for a shock absorbing structure including a sponge. The structure is supported by nonlinear concentrated springs. The restoring force of the spring has cubic nonlinearity and linear hysteresis damping. To calculate damping properties for the structures including elastic body and porous body, displacement vectors as common unknown variable are solved under coupled condition. Under small amplitude, we apply asymptotic method to complex eigenvalue problem of this system to obtain modal parameters. And then expressions of modal loss factor are derived approximately. This approach was proposed by one of the authors previously. We call this method as Modal Strain and Kinetic Energy Method (MSKE method). Further, using the modal loss factors, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. As a numerical example of a shock absorbing structures, we adopt double skins with a sponge. The double skins are supported by nonlinear concentrated springs. We clarify influences of amplitude of the input force on nonlinear and chaotic responses.

Keywords: Dynamic response, Nonlinear and chaotic motions, Finite Element analysis, Numerical analysis.

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Authors: M. Schukat, M.P. Cullen, D. O'Beirne

Abstract:

This paper describes a UDP over IP based, server-oriented redundant host configuration protocol (RHCP) that can be used by collaborating embedded systems in an ad-hoc network to acquire a dynamic IP address. The service is provided by a single network device at a time and will be dynamically reassigned to one of the other network clients if the primary provider fails. The protocol also allows all participating clients to monitor the dynamic makeup of the network over time. So far the algorithm has been implemented and tested on an 8-bit embedded system architecture with a 10Mbit Ethernet interface.

Keywords: Ad-Hoc Networks, Collaborating Embedded Systems, Dynamic Host Configuration, Redundancy.

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Authors: Shumin Hou, Yourong Li, Sanxing Zhao

Abstract:

Much time series data is generally from continuous dynamic system. Firstly, this paper studies the detection of the nonlinearity of time series from continuous dynamics systems by applying the Phase-randomized surrogate algorithm. Then, the Delay Vector Variance (DVV) method is introduced into nonlinearity test. The results show that under the different sampling conditions, the opposite detection of nonlinearity is obtained via using traditional test statistics methods, which include the third-order autocovariance and the asymmetry due to time reversal. Whereas the DVV method can perform well on determining nonlinear of Lorenz signal. It indicates that the proposed method can describe the continuous dynamics signal effectively.

Keywords: Nonlinearity, Time series, continuous dynamics system, DVV method

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Authors: Toshinori Nawata, Hitoshi Takata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input. Constant terms which arise from section wise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics.Parameters included in the control are suboptimally selectedby extremizing a combination of Hamiltonian and Lyapunov functions with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented Automatic Choosing Control, NonlinearControl, Genetic Algorithm, Hamiltonian, Lyapunovfunction

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Authors: Nicolò Vaiana, Giorgio Serino

Abstract:

The nonlinear time history analysis of seismically base-isolated structures can require a significant computational effort when the behavior of each seismic isolator is predicted by adopting the widely used differential equation Bouc-Wen model. In this paper, a nonlinear exponential model, able to simulate the response of seismic isolation bearings within a relatively large displacements range, is described and adopted in order to reduce the numerical computations and speed up the nonlinear dynamic analysis. Compared to the Bouc-Wen model, the proposed one does not require the numerical solution of a nonlinear differential equation for each time step of the analysis. The seismic response of a 3d base-isolated structure with a lead rubber bearing system subjected to harmonic earthquake excitation is simulated by modeling each isolator using the proposed analytical model. The comparison of the numerical results and computational time with those obtained by modeling the lead rubber bearings using the Bouc-Wen model demonstrates the good accuracy of the proposed model and its capability to reduce significantly the computational effort of the analysis.

Keywords: Base isolation, computational efficiency, nonlinear exponential model, nonlinear time history analysis.

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Authors: Andre A. Keller

Abstract:

The optimal control is one of the possible controllers for a dynamic system, having a linear quadratic regulator and using the Pontryagin-s principle or the dynamic programming method . Stochastic disturbances may affect the coefficients (multiplicative disturbances) or the equations (additive disturbances), provided that the shocks are not too great . Nevertheless, this approach encounters difficulties when uncertainties are very important or when the probability calculus is of no help with very imprecise data. The fuzzy logic contributes to a pragmatic solution of such a problem since it operates on fuzzy numbers. A fuzzy controller acts as an artificial decision maker that operates in a closed-loop system in real time. This contribution seeks to explore the tracking problem and control of dynamic macroeconomic models using a fuzzy learning algorithm. A two inputs - single output (TISO) fuzzy model is applied to the linear fluctuation model of Phillips and to the nonlinear growth model of Goodwin.

Keywords: fuzzy control, macroeconomic model, multiplier - accelerator, nonlinear accelerator, stabilization policy.

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Authors: Caigen Zhou, Haibo Jiang

Abstract:

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive singular perturbed systems with time-varying delay is investigated by employing Lyapunov functions. The nonlinear delay system is built based on the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for global exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs), which can be easily solved by LMI technique. Some simulations illustrate the effectiveness of the proposed method.

Keywords: T–S fuzzy model, singular perturbed systems, time-varying delay, robust control.

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Authors: V. Ten

Abstract:

An approach of design of stable of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers. Theoretical part presents an analysis of designed nonlinear second-order control systems. As more important the integrators in series, canonical controllable form and Jordan forms are considered. The analysis resumes that due to added controllers systems become stable and insensitive to any disturbance of parameters. Experimental part presents MATLAB simulation of design of control systems of epidemic spread, aircrafts angular motion and submarine depth. The results of simulation confirm the efficiency of offered method of design. KeywordsCatastrophes, robust control, simulation, uncertain parameters.

Keywords: Catastrophes, robust control, simulation, uncertain parameters.

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Authors: A. R. Tavakolpour-Saleh, H. Jokar

Abstract:

Liquid level control of conical tank system is known to be a great challenge in many industries such as food processing, hydrometallurgical industries and wastewater treatment plant due to its highly nonlinear characteristics. In this research, an adaptive fuzzy PID control scheme is applied to the problem of liquid level control in a nonlinear tank process. A conical tank process is first modeled and primarily simulated. A PID controller is then applied to the plant model as a suitable benchmark for comparison and the dynamic responses of the control system to different step inputs were investigated. It is found that the conventional PID controller is not able to fulfill the controller design criteria such as desired time constant due to highly nonlinear characteristics of the plant model. Consequently, a nonlinear control strategy based on gain-scheduling adaptive control incorporating a fuzzy logic observer is proposed to accurately control the nonlinear tank system. The simulation results clearly demonstrated the superiority of the proposed adaptive fuzzy control method over the conventional PID controller.

Keywords: Adaptive control, fuzzy logic, conical tank, PID controller.

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Authors: Banaja Mohanty, Prakash Kumar Hota

Abstract:

This paper presents a differential evolution algorithm to design a robust PI and PID controllers for Load Frequency Control (LFC) of nonlinear interconnected power systems considering the boiler dynamics, Governor Dead Band (GDB), Generation Rate Constraint (GRC). Differential evolution algorithm is employed to search for the optimal controller parameters. The proposed method easily copes of with nonlinear constraints. Further the proposed controller is simple, effective and can ensure the desirable overall system performance. The superiority of the proposed approach has been shown by comparing the results with published fuzzy logic controller for the same power systems. The comparison is done using various performance measures like overshoot, settling time and standard error criteria of frequency and tie-line power deviation following a 1% step load perturbation in hydro area. It is noticed that, the dynamic performance of proposed controller is better than fuzzy logic controller. Furthermore, it is also seen that the proposed system is robust and is not affected by change in the system parameters.

Keywords: Automatic Generation control (AGC), Generation Rate Constraint (GRC), Governor Dead Band (GDB), Differential Evolution (DE)

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Authors: Azizan Bin Saaban, Adyda Binti Ibrahim, Mohammad Shehzad, Israr Ahmad

Abstract:

In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on Lyapunov stability theory and using non-linear active control algorithm, it has been shown that the proposed schemes have excellent transient performance using only two nonlinear controllers and have shown analytically as well as graphically that synchronization is asymptotically globally stable.

Keywords: Nonlinear Active Control, Chen and Tigan Chaotic systems, Lyapunov Stability theory, Synchronization.

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Authors: Andrei A. Kolyshkin

Abstract:

In the present paper some recommendations for the use of software package “Mathematica" in a basic numerical analysis course are presented. The methods which are covered in the course include solution of systems of linear equations, nonlinear equations and systems of nonlinear equations, numerical integration, interpolation and solution of ordinary differential equations. A set of individual assignments developed for the course covering all the topics is discussed in detail.

Keywords: Numerical methods, "Mathematica", e-learning.

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Authors: Fotis N. Koumboulis, Michael G. Skarpetis, Maria P. Tzamtzi

Abstract:

The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.

Keywords: System theory, uncertain systems, robust control, singular systems.

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Authors: Tomohiro Hachino, Hitoshi Takata, Shigeru Nakayama, Ichiro Iimura, Seiji Fukushima, Yasutaka Igarashi

Abstract:

This paper presents a nonparametric identification of continuous-time nonlinear systems by using a Gaussian process (GP) model. The GP prior model is trained by artificial bee colony algorithm. The nonlinear function of the objective system is estimated as the predictive mean function of the GP, and the confidence measure of the estimated nonlinear function is given by the predictive covariance of the GP. The proposed identification method is applied to modeling of a simplified electric power system. Simulation results are shown to demonstrate the effectiveness of the proposed method.

Keywords: Artificial bee colony algorithm, Gaussian process model, identification, nonlinear system, electric power system.

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Authors: S.M. Lee, J.H. Koo, J.H. Park, S.C. Won

Abstract:

In this paper, we propose synchronization of an array of nonlinear systems with time delays. The array of systems is decomposed into isolated systems to establish appropriate Lyapunov¬Krasovskii functional. Using the Lyapunov-Krasovskii functional, a sufficient condition for the synchronization is derived in terms of LMIs(Linear Matrix Inequalities). Delayed feedback control gains are obtained by solving the sufficient condition. Numerical examples are given to show the validity the proposed method.

Keywords: Synchronization, Delay, Lyapunov method, LMI.

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Authors: David A. Roke, M. R. Hasan

Abstract:

Conventional concentrically-braced frame (CBF) systems have limited drift capacity before brace buckling and related damage leads to deterioration in strength and stiffness. Self-centering concentrically-braced frame (SC-CBF) systems have been developed to increase drift capacity prior to initiation of damage and minimize residual drift. SC-CBFs differ from conventional CBFs in that the SC-CBF columns are designed to uplift from the foundation at a specified level of lateral loading, initiating a rigid-body rotation (rocking) of the frame. Vertically-aligned post-tensioning bars resist uplift and provide a restoring force to return the SC-CBF columns to the foundation (self-centering the system). This paper presents a parametric study of different prototype buildings using SC-CBFs. The bay widths of the SC-CBFs have been varied in these buildings to study different geometries. Nonlinear numerical analyses of the different SC-CBFs are presented to illustrate the effect of frame geometry on the behavior and dynamic response of the SC-CBF system.

Keywords: Earthquake resistant structures, nonlinear analysis, seismic analysis, self-centering structural systems.

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Authors: T. Yamaguchi, Y. Fujii, A. Takita, T. Kanai

Abstract:

To compute dynamic characteristics of nonlinear viscoelastic springs with elastic structures having huge degree-of-freedom, Yamaguchi proposed a new fast numerical method using finite element method [1]-[2]. In this method, restoring forces of the springs are expressed using power series of their elongation. In the expression, nonlinear hysteresis damping is introduced. In this expression, nonlinear complex spring constants are introduced. Finite element for the nonlinear spring having complex coefficients is expressed and is connected to the elastic structures modeled by linear solid finite element. Further, to save computational time, the discrete equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. In this report, the proposed method is applied to simulation for impact responses of a viscoelastic shock absorber with an elastic structure (an S-shaped structure) by colliding with a concentrated mass. The concentrated mass has initial velocities and collides with the shock absorber. Accelerations of the elastic structure and the concentrated mass are measured using Levitation Mass Method proposed by Fujii [3]. The calculated accelerations from the proposed FEM, corresponds to the experimental ones. Moreover, using this method, we also investigate dynamic errors of the S-shaped force transducer due to elastic mode in the S-shaped structure.

Keywords: Transient response, Finite Element analysis, Numerical analysis, Viscoelastic shock absorber, Force transducer.

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Authors: A. Puras Trueba, J. R. Llata García

Abstract:

A nonlinear optimal controller with a fuzzy gain scheduler has been designed and applied to a Line-Of-Sight (LOS) stabilization system. Use of Linear Quadratic Regulator (LQR) theory is an optimal and simple manner of solving many control engineering problems. However, this method cannot be utilized directly for multigimbal LOS systems since they are nonlinear in nature. To adapt LQ controllers to nonlinear systems at least a linearization of the model plant is required. When the linearized model is only valid within the vicinity of an operating point a gain scheduler is required. Therefore, a Takagi-Sugeno Fuzzy Inference System gain scheduler has been implemented, which keeps the asymptotic stability performance provided by the optimal feedback gain approach. The simulation results illustrate that the proposed controller is capable of overcoming disturbances and maintaining a satisfactory tracking performance.

Keywords: Fuzzy Gain-Scheduling, Gimbal, Line-Of-SightStabilization, LQR, Optimal Control

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point theory, we study the existence and multiplicity of the positive solutions for systems of nonlinear third-order differential equations with p-laplacian, which improve and generalize the result of related paper.

Keywords: p-Laplacian, cone, fixed point theorem, positive solution.

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Authors: Nina Øystad-Larsen, Miran Cemalovic, Amir M. Kaynia

Abstract:

The nonlinear static and dynamic analysis procedures presented in EN 1998-1 for the structural response of a RC wall-frame building are assessed. The structure is designed according to the guidelines for high ductility (DCH) in 1998-1. The finite element packages SeismoStruct and OpenSees are utilized and evaluated. The structural response remains nearly in the elastic range even though the building was designed for high ductility. The overstrength is a result of oversized and heavily reinforced members, with emphasis on the lower storey walls. Nonlinear response history analysis in the software packages give virtually identical results for displacements.

Keywords: Behaviour factor, Dual system, OpenSEES, Overstrength, SeismoStruct.

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Authors: D.Elleuch, T.Damak

Abstract:

In this paper, the performance of two adaptive observers applied to interconnected systems is studied. The nonlinearity of systems can be written in a fractional form. The first adaptive observer is an adaptive sliding mode observer for a Lipchitz nonlinear system and the second one is an adaptive sliding mode observer having a filtered error as a sliding surface. After comparing their performances throughout the inverted pendulum mounted on a car system, it was shown that the second one is more robust to estimate the state.

Keywords: Adaptive observer, Lipchitz system, Interconnected fractional nonlinear system, sliding mode.

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Authors: Qiaozhen Song

Abstract:

Based on the feature of model disturbances and uncertainty being compensated dynamically in auto – disturbances-rejection-controller (ADRC), a new method using ADRC is proposed for the decoupling control of dispenser longitudinal movement in big flight envelope. Developed from nonlinear model directly, ADRC is especially suitable for dynamic model that has big disturbances. Furthermore, without changing the structure and parameters of the controller in big flight envelope, this scheme can simplify the design of flight control system. The simulation results in big flight envelope show that the system achieves high dynamic performance, steady state performance and the controller has strong robustness.

Keywords: ADRC, ESO, nonlinear system

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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: P.-W. Tsai, W.-L. Hong, C.-W. Chen, C.-Y. Chen

Abstract:

In this paper, we present a neural-network (NN) based approach to represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov Stability, Parallel Particle Swarm Optimization, Linear Differential Inclusion, Artificial Intelligence.

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Authors: Gorazd Karer, Igor Skrjanc, Borut Zupancic

Abstract:

The complex hybrid and nonlinear nature of many processes that are met in practice causes problems with both structure modelling and parameter identification; therefore, obtaining a model that is suitable for MPC is often a difficult task. The basic idea of this paper is to present an identification method for a piecewise affine (PWA) model based on a fuzzy clustering algorithm. First we introduce the PWA model. Next, we tackle the identification method. We treat the fuzzy clustering algorithm, deal with the projections of the fuzzy clusters into the input space of the PWA model and explain the estimation of the parameters of the PWA model by means of a modified least-squares method. Furthermore, we verify the usability of the proposed identification approach on a hybrid nonlinear batch reactor example. The result suggest that the batch reactor can be efficiently identified and thus formulated as a PWA model, which can eventually be used for model predictive control purposes.

Keywords: Batch reactor, fuzzy clustering, hybrid systems, identification, nonlinear systems, PWA systems.

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Authors: E. Farshidi

Abstract:

This paper presents the design of a low power second-order continuous-time sigma-delta modulator for low power applications. The loop filter of this modulator has been implemented based on the nonlinear transconductance-capacitor (Gm-C) by employing current-mode technique. The nonlinear transconductance uses floating gate MOS (FG-MOS) transistors that operate in weak inversion region. The proposed modulator features low power consumption (<80uW), low supply voltage (1V) and 62dB dynamic range. Simulation results by HSPICE confirm that it is very suitable for low power biomedical instrumentation designs.

Keywords: Sigma-delta, modulator, Current-mode, Nonlinear Transconductance, FG-MOS.

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Authors: Gilberto Gonzalez-A , Israel Nuñez

Abstract:

A bond graph model of an electrical transformer including the nonlinear saturation is presented. A nonlinear observer for the transformer based on multivariable circle criterion in the physical domain is proposed. In order to show the saturation and hysteresis effects on the electrical transformer, simulation results are obtained. Finally, the paper describes that convergence of the estimates to the true states is achieved.

Keywords: Bond graph, nonlinear observer, electrical transformer, nonlinear saturation.

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Authors: B. Baigzadeh, V.Nazarzehi, H.Khaloozadeh

Abstract:

The two cart inverted pendulum system is a good bench mark for testing the performance of system dynamics and control engineering principles. Devasia introduced this system to study the asymptotic tracking problem for nonlinear systems. In this paper the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a sinusoidal reference inputs via introducing a novel method for solving finite-horizon nonlinear optimal control problems is presented. In this method, an iterative method applied to state dependent Riccati equation (SDRE) to obtain a reliable algorithm. The superiority of this technique has been shown by simulation and comparison with the nonlinear approach.

Keywords: Nonlinear optimal control, State dependent Riccatiequation, Asymptotic tracking, inverted pendulum

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Authors: S. H. Teh, S. Malawaraarachci, W. P. Chan, A. Nassirharand

Abstract:

The purpose of this paper is to present the design and instrumentation of a new benchmark multivariable nonlinear control laboratory. The mathematical model of this system may be used to test the applicability and performance of various nonlinear control procedures. The system is a two degree-of-freedom robotic arm with soft and hard (discontinuous) nonlinear terms. Two novel mechanisms are designed to allow the implementation of adjustable Coulomb friction and backlash.

Keywords: Nonlinear control, describing functions, AdjustableCoulomb friction, Adjustable backlash.

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