Typical Nonlinear System Research Articles

Improving the weak aperiodic signal by three kinds of vibrational resonance

The aperiodic vibrational resonance (VR) is investigated in a typical nonlinear system with fractional-order deflection. The character signal used to express the useful information is an aperiodic binary signal. The informationless auxiliary signal used to induce VR is of a square waveform. We study the classic aperiodic VR at first. If the strength of the auxiliary signal is a control parameter, we find that the value and the location of the resonance peak on the cross-correlation coefficient curve are independent of the fractional-order exponent. However, for a smaller value of the fractional-order exponent, the aperiodic signal can be improved to a greater extent. Moreover, if the minimal random pulse width of the aperiodic signal is small, the classic aperiodic VR cannot occur. We propose two methods to solve this problem. The first one is the re-scaled aperiodic VR method in which the scale parameter is the key factor. The second one is the twice sampling aperiodic VR method in which the sampling transform ratio is the key factor. Through some examples, we verify the validity of the two proposed methods. By the two methods, we can improve the aperiodic signal with an arbitrary minimal random pulse width. Further, the methods proposed in this paper not only can improve the aperiodic bipolar binary signal, but also can deal with other kinds of signals.

A New Non-Singular Terminal Sliding Mode Control and Its Application to Chaos Suppression in Interconnected Power System

Abstract Interconnected power system is a typical nonlinear dynamical system, it will cause great harm to the interconnected power system when the chaos occurred. This paper analyses the nonlinear dynamical behavior of the interconnected power system with a uncertain electromagnetic disturbance amplitude, and the influence of the electromagnetic disturbance amplitude on the stability of the system is obtained. Thus, this paper proposes a novel non-singular terminal sliding mode control to restrain the chaos, then the system will reach a stable state in a fixed time. According to the theoretical analysis, by introducing the saturation function, the control method can solve the singularity problem in the sliding mode control, and the interconnected power system will be stable in a short time when it’s in chaos. The simulation prove the correctness of the method.

A Modified Artificial Bee Colony Algorithm for Parameter Estimation of Fractional-Order Nonlinear Systems

In this paper, a modified artificial bee colony (MABC) algorithm is proposed to estimate the unknown fractional-order nonlinear systems. First, the parameter estimation problem can be mathematically transformed into a multi-dimensional continuous function optimization problem, which is solved via the MABC algorithm. The proposed MABC algorithm well combines the original artificial bee colony algorithm (ABC) and the Nelder-Mead simplex method (NMS) in a very simple way, which takes full advantage of the exploration ability of the ABC algorithm and the exploitation ability of the NMS. And in the meanwhile, the proposed algorithm improves the speed of convergence. To evaluate the effectiveness of the proposed MABC algorithm, numerical simulations contain two typical uncertain fractional-order nonlinear systems. The results show that compared with the other population-based algorithm and ABC-variants, the proposed MABC for solving the problem of parameter estimation get the faster convergence speed and higher calculation accuracy.

Study on simulation and experiment of control for multiple launch rocket system by computed torque method

Poor dispersion characteristics of rockets, due to the orientation of the launcher for multiple launch rocket system (MLRS) departing from that intended, have always restricted the MLRS development for several decades. Orienting control is a key technique to improve the dispersion characteristics of rockets. The purpose of this paper is to propose an orienting control method for launcher of the MLRS in a salvo firing. Because the MLRS is a typical nonlinear system, the major difficulty in designing the orienting controller lies in the nonlinearity. To deal with the nonlinearity, the concept of computed torque control is introduced. The MLRS equation of motion is established using Lagrange method. The inner loop feedforward and the outer loop feedback are adopted to design the controllers for the azimuth and elevation axes of MLRS. By combining the inner and outer control loops together, the PID-computed torque controller is designed. The numerical simulation is implemented to show the control performance, and then, the effectiveness and applicability of the proposed controller are demonstrated by the firing experiment of a salvo of three rockets.

Robust Control for the Relay ICPT System Under External Disturbance and Parametric Uncertainty

The relay inductively coupled power transfer (ICPT) system is a typical nonlinear and high-order system that is composed of the inverter, the resonant tanks, the relay structure, the rectifier, and the filter. Additionally, the disturbance signals (such as external disturbance) and dynamic perturbations (such as parametric uncertainties) are unavoidable in this system. Therefore, a closed-loop system with an $H_{\infty }$ controller is designed under the external disturbance and parametric uncertainties in this paper. In order to achieve the robust stability and the robust performance (RSRP) of the closed-loop system with an $H_{\infty }$ controller, the generalized state-space averaging method is used to establish the linear model of the relay ICPT system first, and a linear fractional transformation of the nominal model and the parametric uncertainties is discussed then. The RSRP of the designed $H_{\infty }$ controller is tested by the structured singular value. The results of the practical experiment further verify the RSRP of the closed-loop system.

Neural Network Learning and Robust Stabilization of Nonlinear Systems With Dynamic Uncertainties.

Due to the existence of dynamical uncertainties, it is important to pay attention to the robustness of nonlinear control systems, especially when designing adaptive critic control strategies. In this paper, based on the neural network learning component, the robust stabilization scheme of nonlinear systems with general uncertainties is developed. Through system transformation and employing adaptive critic technique, the approximate optimal controller of the nominal plant can be applied to accomplish robust stabilization for the original uncertain dynamics. The neural network weight vector is very convenient to initialize by virtue of the improved critic learning formulation. Under the action of the approximate optimal control law, the stability issues for the closed-loop form of nominal and uncertain plants are analyzed, respectively. Simulation illustrations via a typical nonlinear system and a practical power system are included to verify the control performance.

Dynamic output-feedback control for positive Roesser system under the switched and T-S fuzzy rules

This paper is concerned with the dynamic output-feedback controller design for the positive Roesser type nonlinear system, which is intrinsically characterized by the switched mechanism and subtly decomposed into the linear form under the Takagi–Sugeno fuzzy rules. Firstly, based on the co-positive Lyapunov function and the average dwell time method, sufficient conditions are presented, under which the resulting closed-loop system is exponentially stable and has l1-gain bound γ. Then, explicit expressions are also given to derive the expected controller gain matrices with desired l1-gain bound. Finally, effectiveness of the proposed results is illustrated by two numerical examples.

Robust Just-in-time Learning Approach and Its Application on Fault Detection

In data-driven state estimation and process monitoring, the correctness of results mainly rely on the accuracy of measurement. Actually, noises, outliers and measured errors always exist in real industrial systems. Just-in-time learning (JITL) is an useful on-line learning method and can be applied for data-based state estimation. Due to the reality of inaccurate measurement, an improved JITL method with strengthen robustness is necessary to be studied. In this paper, a robust version of just-in-time learning strategy is proposed. It is inspired from the leverage weight. By calculating the leverage impact, the outliers in high leverage cases are treated to reduce their weight and affect less on output prediction. A typical nonlinear system experiment is employed to prove the robust and veracity of the proposed strategy. Finally, the robust JITL is implemented for fault detection on a three-tank system to verify its applicability.

Adaptive fuzzy sliding mode control for electric power steering system

The Electric power steering (EPS) system, a typical non-linear system, is easy to be influenced by parameters perturbation and disturbance of the road. Traditional linear control method based on a simplified linear model such as PID control cannot reach good dynamic performance. To reduce the influence of parameters perturbation and disturbance of the road and enhance the robustness of the system, an Adaptive fuzzy sliding mode control (AFSMC) method is proposed in this paper. First, fuzzy sliding mode control is employed to enhance the dynamic performance of the system. Then, to improve the precision of the controller, genetic algorithm is used to optimize the control rules which are essential to fuzzy control. The experimental results on non-linear EPS model demonstrate that AFSMC is more stable than Sliding mode control (SMC) method and more efficient to the non-linear system than SFPID control method. They can also prove that AFSMC can provide a stable driving in the presence of parameters perturbation and disturbance of the road.

General description and understanding of the nonlinear dynamics of mode-locked fiber lasers

As a type of nonlinear system with complexity, mode-locked fiber lasers are known for their complex behaviour. It is a challenging task to understand the fundamental physics behind such complex behaviour, and a unified description for the nonlinear behaviour and the systematic and quantitative analysis of the underlying mechanisms of these lasers have not been developed. Here, we present a complexity science-based theoretical framework for understanding the behaviour of mode-locked fiber lasers by going beyond reductionism. This hierarchically structured framework provides a model with variable dimensionality, resulting in a simple view that can be used to systematically describe complex states. Moreover, research into the attractors’ basins reveals the origin of stochasticity, hysteresis and multistability in these systems and presents a new method for quantitative analysis of these nonlinear phenomena. These findings pave the way for dynamics analysis and system designs of mode-locked fiber lasers. We expect that this paradigm will also enable potential applications in diverse research fields related to complex nonlinear phenomena.

Research on Coupling Method of Watershed Initial Water Rights Allocation in Daling River

As a typical abnormal, nonlinear and multidimensional system decision-making problem, watershed initial water rights allocation involves various resource distribution, economic, social and environment objectives. Because of the large subjectivity of weight determination, different from the traditional methods, we adopt a new coupling method which is a dimension reduction method in this study to solve the watershed initial water rights allocation problem. The data allocated in Daling watershed can be calculated in optimum projection direction to gain the watershed initial water rights allocation scheme in low-dimensional space.

Control of Blow-Down Wind Tunnel Using Combined Extended Kalman and Nonlinear Predictive Filters

A blow-down wind tunnel is a typical nonlinear time-varying system facing the coupling effects between the pressure and temperature during the short-time test procedure. The control of blow-down wind tunnels has been discussed for a long time and a satisfactory general solution to this problem is still of interests. This paper aims to model the internal relationship of the state variables of the wind tunnel by using thermodynamic theories. With the developed model, a new control method combining extended Kalman filter (EKF) together with auxiliary nonlinear predictive filter (NPF) is proposed to improve the control performance of the blow-down wind tunnel controller, in terms of accuracy and robustness. The transient coupling effects between the pressure and temperature are fully considered in the proposed approach. The results from the simulation and experiments are consistent and demonstrate that the controller based on EKF combined together with NPF can work better than previously proposed EKF-based controller.

Neuro-Fuzzy Network Based Adaptive Tracking Controller for a Nonlinear System

In this paper, a neuro-fuzzy network-based adaptivetracking controller is suggested for controlling a type ofnonlinear system. Where two neuro-fuzzy networks have beenused to learn the system dynamics uncertainty bounds by usingLyapunov method. Then the output of these two networks isused to build a sliding mode controller. The stability of thecontrol system is proved and stable neuro-fuzzy controllerparameters adjustment laws are selected using Lyapunovtheory. The simulation case study shows that the controlled systemtracking the reference model effectively with smooth controleffort and robust performance has been achieved.

PARAMETER IDENTIFICATION OF NONLINEAR VIBRATION SYSTEMS BASED ON THE HILBERT-HUANG TRANSFORM

Parameters of time-varying damping systems and nonlinear vibration systems, such as the Duffing and Van der Pol vibration systems, were identified by the Hilbert-Huang transform (HHT) in this study. The nonlinear vibration signal was first decomposed into free vibration and forced vibration components by the empirical mode decomposition. Subsequently, the amplitude envelope and the instantaneous frequency of the decomposed components were computed by the empirical envelop method. Damping ratios and other parameters of the nonlinear vibration systems were finally identified by using the least square method. Compared with the results from the wavelet analysis, the proposed method is proven to be more effective through numerical simulations of three typical nonlinear vibration systems and is featured by a higher level of accuracy.

Kinematics and Dynamic Modeling and Simulation Analysis of Three-wheeled Mobile Robot

Mobile robot is a typical nonlinear control system with nonholonomic constraints, so the system presents some complex features, and the system control becomes quite difficult. But nonholonomic makes robot structure has higher flexibility and reliability. Kinematics model and dynamic model are the foundations for system design and analysis of dynamic and kinematics performance, and are also the guarantee of controller practicability. After finishing nonholonomic characteristic analysis, coordinate transformation method and Lagrange equation method are used to establish kinematics and dynamic model of three-wheeled mobile robot with two driving wheels in this paper. The rationality and validity of the models are verified by simulation result of trajectory tracking.

Research on Electro-Hydraulic Force Servo Control System Based on Specialist PID Control Strategy

There is flexibility load in the electro-hydraulic force servo control system researched in this paper, and it results in that there is a lower oscillation frequency secondary differential element in radical of the transmit function of the system. The flexibility load and the secondary differential element seriously impact the bandwidth of the system and let the bandwidth rise difficultly, and that the flexibility load and the secondary differential element make the system oscillation even instability easily. Aiming at this special characteristic and the smaller system gain characteristic of the electrohydraulic force servo control system, the specialist PID control theory applied to the electro-hydraulic force servo control system which is the typical nonlinear system. The mathematic model of the system is built and the simulation and the experiment research is finished in the work of this paper, at the same time, the author of this paper compares the control result of the new controller designed according to the specialist PID control theory with the control result of traditional PID controller. The simulation and the experiment results indicate that the new controller designed according to the specialist PID control theory not only enlarge the bandwidth of system, improve the accuracy, reduce control error, but also accelerate the response speed obviously, increase the dynamic property of the system.

Multi-scale symbolic time reverse analysis of gas–liquid two-phase flow structures

Gas–liquid two-phase flows are widely encountered in production processes of petroleum and chemical industry. Understanding the dynamic characteristics of multi-scale gas–liquid two-phase flow structures is of great significance for the optimization of production process and the measurement of flow parameters. In this paper, we propose a method of multi-scale symbolic time reverse (MSTR) analysis for gas–liquid two-phase flows. First, through extracting four time reverse asymmetry measures (TRAMs), i.e. Euclidean distance, difference entropy, percentage of constant words and percentage of reversible words, the time reverse asymmetry (TRA) behaviors of typical nonlinear systems are investigated from the perspective of multi-scale analysis, and the results show that the TRAMs are sensitive to the changing of dynamic characteristics underlying the complex nonlinear systems. Then, the MSTR analysis is used to study the conductance signals from gas–liquid two-phase flows. It is found that the multi-scale TRA analysis can effectively reveal the multi-scale structure characteristics and nonlinear evolution properties of the flow structures.

비선형 진동계 정규모드의 수치적 계산 연구

Nonlinear normal modes(NNMs) is a branch of periodic solution of nonlinear dynamic systems. Determination of stable periodic solution is very important in many engineering applications since the stable periodic solution can be an attractor of such nonlinear systems. Periodic solutions of nonlinear system are usually calculated by perturbation methods and numerical methods. In this study, numerical method is used in order to calculate the NNMs. Iteration of the solution is presented by multiple shooting method and continuation of solution is presented by pseudo-arclength continuation method. The stability of the NNMs is analyzed using Floquet multipliers, and bifurcation points are calculated using indirect method. Proposed analyses are applied to two nonlinear numerical models. In the first numerical model nonlinear spring-mass system is analyzed. In the second numerical model Jeffcott rotor system which has unstable equilibria is analyzed. Numerical simulation results show that the multiple shooting method can be applied to self excited system as well as the typical nonlinear system with stable equilibria.

Design of Mexican Hat Wavelet neural networks for solving Bratu type nonlinear systems

In this paper a Mexican Hat Wavelet based neural network is designed and applied for solving the nonlinear Bratu type equation. This equation is widely used in fuel ignition models, electrically conducting solids and heat transfer studies. The Mexican Hat Wavelet Differential equation artificial neural networks (MHW-DEANN) are used for the first time to construct an energy function of the system in an unsupervised manner. The tunable parameters of MHW-DEANN are trained with a hybrid evolutionary computing approach: we exploit the strength of Genetic Algorithms (GA) and Sequential Quadratic Programming (SQP) to find the best weights. Monte-Carlo simulations are performed for the proposed scheme with statistical analysis to validate the effectiveness and convergence of the proposed method for Bratu-type equations. It is observed that the proposed method converges in all cases and can solve the equation with high accuracy and reliability.

An enhanced chiller FDD strategy based on the combination of the LSSVR-DE model and EWMA control charts

Development of the fault detection and diagnosis (FDD) for chiller systems is very important for improving the equipment reliability and saving energy consumption. The results of FDD performance are strongly dependent on the accuracy of chiller models. Since the accuracy of the chiller models depends on the indefinite model parameters which are normally chosen by experiments or experiences, an accurate chiller model is difficult to build. Therefore, optimization of model parameters is very useful to increase the accuracy of chiller models. This paper presents a new FDD strategy for centrifugal chillers of building air-conditioning systems, which is the combination between the nonlinear least squares support vector regression (LSSVR) based on the differential evolution (DE) algorithm and the exponentially weighted moving average (EWMA) control charts. In this strategy, the nonlinear LSSVR, which is a reformulation of SVR model with better generalization performances, is adopted to develop the reference feature parameter models in a typical non-linear chiller system. The DE algorithm which is a real-coding optimal algorithm with powerful global searching capacity is employed to enhance the accuracy of LSSVR models. The exponentially weighted moving average (EWMA) control charts are introduced to improve the fault detection capability as well as to reduce the Type II errors in a t-statistics-based way. Six typical faults of the chiller from the real-time experimental data of ASHRAE RP-1043 project are chosen to validate proposed FDD methods. Comprehensive comparisons between the proposed method and two similarly previous studies are performed. The comparison results show that the proposed method has achieved significant improvement in accuracy and reliability, especially at low severity levels. The proposed DE-LSSVR-EWMA strategy is robust for fault detection and diagnosis in centrifugal chiller systems.