Search results for: nonlinear practical constraints

Authors: Farhad Namdari, Reza Sedaghati

Abstract:

Economic dispatch (ED) has been considered to be one of the key functions in electric power system operation which can help to build up effective generating management plans. The practical ED problem has non-smooth cost function with nonlinear constraints which make it difficult to be effectively solved. This paper presents a novel heuristic and efficient optimization approach based on the new Bat algorithm (BA) to solve the practical non-smooth economic dispatch problem. The proposed algorithm easily takes care of different constraints. In addition, two newly introduced modifications method is developed to improve the variety of the bat population when increasing the convergence speed simultaneously. The simulation results obtained by the proposed algorithms are compared with the results obtained using other recently develop methods available in the literature.

Keywords: Non-smooth, economic dispatch, bat-inspired, nonlinear practical constraints, modified bat algorithm.

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Authors: S. Kahvecioglu, A. Karamancioglu, A. Yazici

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In this paper, a nonlinear model predictive swing-up and stabilizing sliding controller is proposed for an inverted pendulum-cart system. In the swing up phase, the nonlinear model predictive control is formulated as a nonlinear programming problem with energy based objective function. By solving this problem at each sampling instant, a sequence of control inputs that optimize the nonlinear objective function subject to various constraints over a finite horizon are obtained. Then, this control drives the pendulum to a predefined neighborhood of the upper equilibrium point, at where sliding mode based model predictive control is used to stabilize the systems with the specified constraints. It is shown by the simulations that, due to the way of formulating the problem, short horizon lengths are sufficient for attaining the swing up goal.

Keywords: Inverted pendulum, model predictive control, swingup, stabilization.

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Authors: I. A. Farhat

Abstract:

The The dynamic economic dispatch (DED) problem is one of the complex constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand. Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

Keywords: Artificial Immune System (AIS), Dynamic Economic Dispatch (DED).

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Authors: I. A. Farhat

Abstract:

The dynamic economic dispatch (DED) problem is one of the complex constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand.  Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

Keywords: Artificial Immune System (AIS), Dynamic Economic Dispatch (DED).

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Authors: Raghvendra Kumar, Lillie Dewan

Abstract:

Exchange algorithm with constraints on magnitude and phase error separately in new way is presented in this paper. An important feature of the algorithms presented in this paper is that they allow for design constraints which often arise in practical filter design problems. Meeting required minimum stopband attenuation or a maximum deviation from the desired magnitude and phase responses in the passbands are common design constraints that can be handled by the methods proposed here. This new algorithm may have important advantages over existing technique, with respect to the speed and stability of convergence, memory requirement and low ripples.

Keywords: Least square estimation, Constraints, Exchange algorithm.

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Authors: H. Bouadi, M. Tadjine

Abstract:

In this paper; we are interested in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation and new control scheme. We present after the development and the synthesis of a stabilizing control laws design based on sliding mode in order to perform best tracking results. It ensures locally asymptotic stability and desired tracking trajectories. Nonlinear observer is then synthesized in order to estimate the unmeasured states and the effects of the external disturbances such as wind and noise. Finally simulation results are also provided in order to illustrate the performances of the proposed controllers.

Keywords: Dynamic modelling, nonholonomic constraints, sliding mode, nonlinear observer.

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Authors: Fouad Salha , X. Guillaud

Abstract:

Directional over current relays (DOCR) are commonly used in power system protection as a primary protection in distribution and sub-transmission electrical systems and as a secondary protection in transmission systems. Coordination of protective relays is necessary to obtain selective tripping. In this paper, an approach for efficiency reduction of DOCRs nonlinear optimum coordination (OC) is proposed. This was achieved by modifying the objective function and relaxing several constraints depending on the four constraints classification, non-valid, redundant, pre-obtained and valid constraints. According to this classification, the far end fault effect on the objective function and constraints, and in consequently on relay operating time, was studied. The study was carried out, firstly by taking into account the near-end and far-end faults in DOCRs coordination problem formulation; and then faults very close to the primary relays (nearend faults). The optimal coordination (OC) was achieved by simultaneously optimizing all variables (TDS and Ip) in nonlinear environment by using of Genetic algorithm nonlinear programming techniques. The results application of the above two approaches on 6-bus and 26-bus system verify that the far-end faults consideration on OC problem formulation don-t lose the optimality.

Keywords: Backup/Primary relay, Coordination time interval (CTI), directional over current relays, Genetic algorithm, time dial setting (TDS), pickup current setting (Ip), nonlinear programming.

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Authors: M. A. Tayfun, M. A. Alkhalidi

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The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is reexamined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: Ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness.

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Authors: Tomoaki Hashimoto

Abstract:

Recently, optimal control problems subject to probabilistic constraints have attracted much attention in many research field. Although probabilistic constraints are generally intractable in optimization problems, several methods haven been proposed to deal with probabilistic constraints. In most methods, probabilistic constraints are transformed to deterministic constraints that are tractable in optimization problems. This paper examines a method for transforming probabilistic constraints into deterministic constraints for a class of probabilistic constrained optimal control problems.

Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints.

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Authors: Xiangbin Zhu

Abstract:

Advances in computing applications in recent years have prompted the demand for more flexible scheduling models for QoS demand. Moreover, in practical applications, partly violated temporal constraints can be tolerated if the violation meets certain distribution. So we need extend the traditional Liu and Lanland model to adapt to these circumstances. There are two extensions, which are the (m, k)-firm model and Window-Constrained model. This paper researches on weakly hard real-time constraints and their combination to support QoS. The fact that a practical application can tolerate some violations of temporal constraint under certain distribution is employed to support adaptive QoS on the open real-time system. The experiment results show these approaches are effective compared to traditional scheduling algorithms.

Keywords: Weakly Hard Real-Time, Real-Time, Scheduling, Quality of Service.

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Authors: Md. Sayeed Salam

Abstract:

This paper presents an efficient emission constrained economic dispatch algorithm that deals with nonlinear cost function and constraints. It is then incorporated into the dynamic programming based hydrothermal coordination program. The program has been tested on a practical utility system having 32 thermal and 12 hydro generating units. Test results show that a slight increase in production cost causes a substantial reduction in emission.

Keywords: Emission constraint, Hydrothermal coordination, and Economic dispatch algorithm.

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Authors: H. Nikzad, S. Yoshitomi

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This study investigates and develops the structural optimization method. The effect of size constraints on practical solution of reinforced concrete (RC) building structure with shear wall is proposed. Cross-sections of beam and column, and thickness of shear wall are considered as design variables. The objective function to be minimized is total cost of the structure by using a simple and efficient automated MATLAB platform structural optimization methodology. With modification of mathematical formulations, the result is compared with optimal solution without size constraints. The most suitable combination of section sizes is selected as for the final design application based on linear static analysis. The findings of this study show that defining higher value of upper bound of sectional sizes significantly affects optimal solution, and defining of size constraints play a vital role in finding of global and practical solution during optimization procedures. The result and effectiveness of proposed method confirm the ability and efficiency of optimal solutions for 3D RC shear wall-frame structure.

Keywords: Structural optimization, linear static analysis, ETABS, MATLAB, RC shear wall-frame structures.

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Authors: M. Zareiee, A. Dideban, P. Nazemzadeh

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This paper deals with the problem of constructing constraints in non safe Petri Nets and then reducing the number of the constructed constraints. In a system, assigning some linear constraints to forbidden states is possible. Enforcing these constraints on the system prevents it from entering these states. But there is no a systematic method for assigning constraints to forbidden states in non safe Petri Nets. In this paper a useful method is proposed for constructing constraints in non safe Petri Nets. But when the number of these constraints is large enforcing them on the system may complicate the Petri Net model. So, another method is proposed for reducing the number of constructed constraints.

Keywords: discrete event system, Supervisory control, Petri Net, Constraint

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Authors: Yongping Ren, Zongli Li, Fan Zhang

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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: Kazuo Komatsu, Hitoshi Takata

Abstract:

This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, nonlinear observer, formal linearization, Chebyshev interpolation.

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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: 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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Authors: Tomoaki Hashimoto

Abstract:

In recent decades, probabilistic constrained optimal control problems have attracted much attention in many research fields. Although probabilistic constraints are generally intractable in an optimization problem, several tractable methods haven been proposed to handle probabilistic constraints. In most methods, probabilistic constraints are reduced to deterministic constraints that are tractable in an optimization problem. However, there is a gap between the transformed deterministic constraints in case of known and unknown probability distribution. This paper examines the conservativeness of probabilistic constrained optimization method for unknown probability distribution. The objective of this paper is to provide a quantitative assessment of the conservatism for tractable constraints in probabilistic constrained optimization with unknown probability distribution.

Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints.

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Authors: M. Pourgholi, V.J.Majd

Abstract:

This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.

Keywords: Adaptive observer, linear matrix inequality, nonlinear systems, nonlinear observer, resilient observer, robust estimation.

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Authors: Hossein Riazoshams, Midi Habshah, Jr., Mohamad Bakri Adam

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The detection of outliers is very essential because of their responsibility for producing huge interpretative problem in linear as well as in nonlinear regression analysis. Much work has been accomplished on the identification of outlier in linear regression, but not in nonlinear regression. In this article we propose several outlier detection techniques for nonlinear regression. The main idea is to use the linear approximation of a nonlinear model and consider the gradient as the design matrix. Subsequently, the detection techniques are formulated. Six detection measures are developed that combined with three estimation techniques such as the Least-Squares, M and MM-estimators. The study shows that among the six measures, only the studentized residual and Cook Distance which combined with the MM estimator, consistently capable of identifying the correct outliers.

Keywords: Nonlinear Regression, outliers, Gradient, LeastSquare, M-estimate, MM-estimate.

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Authors: Tapas Kumar Sinha, Joseph Mathew

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Based on the Lagrangian for the Gross –Pitaevskii equation as derived by H. Sakaguchi and B.A Malomed [5] we have derived a double well model for the nonlinear optical lattice. This model explains the various features of nonlinear optical lattices. Further, from this model we obtain and simulate the probability for tunneling from one well to another which agrees with experimental results [4].

Keywords: Double well model, nonlinear optical lattice, Solitons, tunneling.

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Authors: G. Chandana Sushma, T. R. Jyothsna

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This paper presents optimal Phasor Measurement Unit (PMU) Placement in network using a genetic algorithm approach as it is infeasible and require high installation cost to place PMUs at every bus in network. This paper proposes optimal PMU allocation considering observability and redundancy utilizing Genetic Algorithm (GA) approach. The nonlinear constraints of buses are modeled to give accurate results. Constraints associated with Zero Injection (ZI) buses and radial buses are modeled to optimize number of locations for PMU placement. GA is modeled with ZI bus constraints to minimize number of locations without losing complete observability. Redundancy of every bus in network is computed to show optimum redundancy of complete system network. The performance of method is measured by Bus Observability Index (BOI) and Complete System Observability Performance Index (CSOPI). MATLAB simulations are carried out on IEEE -14, -30 and -57 bus-systems and compared with other methods in literature survey to show the effectiveness of the proposed approach.

Keywords: Constraints, genetic algorithm, observability, phasor measurement units, redundancy, synchrophasors, zero injection bus.

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Authors: Abolhassan Razminia, Mohammad-Ali Sadrnia

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Chua’s circuit is one of the most important electronic devices that are used for Chaos and Bifurcation studies. A central role of secure communication is devoted to it. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. In this paper, we try to derive a new adaptive control scheme for Chua’s circuit controlling because control of chaos is often very important in practical operations. The novelty of this approach is for sake of its robustness against the external perturbations which is simulated as an additive noise in all measured states and can be generalized to other chaotic systems. Our approach is based on Lyapunov analysis and the adaptation law is considered for the feedback gain. Because of this, we have named it NAFT (Nonlinear Adaptive Feedback Technique). At last, simulations show the capability of the presented technique for Chua’s circuit.

Keywords: Chaos, adaptive control, nonlinear control, Chua's circuit.

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Authors: Gilberto Gonzalez-A, Gerardo Jaimes-A

Abstract:

A methodology to design a nonlinear observer in a bond graph approach is proposed. The class of nonlinear observer with multivariable nonlinearities is considered. A junction structure of the bond graph observer is proposed. The proposed methodology to an electrical transformer and a DC motor including the nonlinear saturation is applied. Nonlinear observers for the transformer and DC motor based on multivariable circle criterion in the physical domain are proposed. In order to show the saturation effects on the transformer and DC motor, 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: T. Yamaguchi, M. Watanabe, M. Sasajima, C. Yuan, S. Maruyama, T. B. Ibrahim, H. Tomita

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This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses.

Keywords: Dynamic response, Nonlinear impact response, Finite Element analysis, Numerical analysis.

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Authors: Jae Won Kang

Abstract:

The purpose of this study was to examine a broader range of sport constraints perceived by young Koreans in Australia who may need to adjust to changing behavioral expectations due to the socio-cultural transitions. Regardless of gender, in terms of quantitative findings, the most important participation constraints within the seven categories were resources, access, interpersonal, affective, religious, socio-cultural, and physical in that order. The most important constraining items were a lack of time, access, information, adaptive skills, and parental and family support in that order. Qualitative research found young Korean’s participation constraints among three categories (time, parental control and interpersonal constraints). It is possible that different ethnic groups would be constrained by different factors; however, this is outside the scope of this study.

Keywords: Constraints, cultural adjustment, Sport, Young Koreans in Australia.

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Authors: Yuichi Masukake, Yoshihisa Ishida

Abstract:

In this paper, we proposed a method to design a model-following adaptive controller for linear/nonlinear plants. Radial basis function neural networks (RBF-NNs), which are known for their stable learning capability and fast training, are used to identify linear/nonlinear plants. Simulation results show that the proposed method is effective in controlling both linear and nonlinear plants with disturbance in the plant input.

Keywords: Linear/nonlinear plants, neural networks, radial basisfunction networks.

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Authors: M. Sasajima, T. Yamaguchi, Y. Koike, A. Hara

Abstract:

This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings.

Keywords: Nonlinear Vibration, Finite Element Method, Chaos , Small Earphone.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

In this paper we consider a nonlinear control design for nonlinear systems by using two-stage formal linearization and twotype LQ controls. The ordinary LQ control is designed on almost linear region around the steady state point. On the other region, another control is derived as follows. This derivation is based on coordinate transformation twice with respect to linearization functions which are defined by polynomials. The linearized systems can be made up by using Taylor expansion considered up to the higher order. To the resulting formal linear system, the LQ control theory is applied to obtain another LQ control. Finally these two-type LQ controls are smoothly united to form a single nonlinear control. Numerical experiments indicate that this control show remarkable performances for a nonlinear system.

Keywords: Formal Linearization, LQ Control, Nonlinear Control, Taylor Expansion, Zero Function.

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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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