Nonlinear Output Research Articles

Nonlinear observer-based adaptive output feedback tracking control of underactuated ships with input saturation

Nonlinear observer-based adaptive output feedback tracking control of underactuated ships with input saturation

A multi-scale dual-stage model for PV array fault detection, classification, and monitoring technique

The output generated by photovoltaic arrays is influenced mainly by the irradiance, which has non-uniform distribution in a day. This has resulted in the current-limiting nature and nonlinear output characteristics, and conventional protection devices cannot detect and clean faults appropriately. This paper proposes a low-cost model for a multi-scale dual-stage photovoltaic fault detection, classification, and monitoring technique developed through MATLAB/Simulink. The main contribution of this paper is that it can detect multiple common faults, be applied on multi-scale photovoltaic arrays regardless of environmental conditions, and be beneficial for photovoltaic system maintenance work. The experimental results show that the developed algorithm using supervised learning algorithms mutual with k-fold cross-validation has produced good performances in identifying six common faults of photovoltaic arrays, achieved 100% accuracy in fault detection, and achieved good accuracy in fault classification. Challenges and suggestions for future research direction are also suggested in this paper. Overall, this study shall provide researchers and policymakers with a valuable reference for developing photovoltaic system fault detection and monitoring techniques for better feasibility, safety, and energy sustainability.

Analysis of nonlinear vibrations and health assessment of a bearing-rotor with rub-impact based on a data-driven approach

Affected by manufacture, assembly, and operating conditions, the rotor is prone to rub-impact fault, resulting in instability of a system. The nonlinearity of a system response includes instability and fault characteristics. Based on this, this paper proposes a novel health assessment approach for bearing-rotor system that combines data-driven and NOFRFs (nonlinear output frequency response functions), revealing the intrinsic relationship between NOFRFs-based feature and rub-impact fault. Before utilizing the approach, the vibration and stability of the bearing-rotor with rub-impact are simulated and analyzed. Based on Hertz contact theory, the nonlinear bearing forces are obtained. Then the dynamic model of the rolling bearing-rotor system considering unbalance and rub-impact is established. The influence of rub-impact on the nonlinear vibration and stability of the bearing-rotor system is analyzed by combining the orbit, the Poincaré map, and the bifurcation diagram. A rolling bearing-rotor test rig is built, and the rub-impact experiment was completed. The data-driven model of the system is identified by the filtered vibration displacement. The NOFRF-based feature of the data-driven model is extracted. With the increase of rub-impact severity, the dispersion of feature gradually increases, and the stability of the system decreases. The standard deviation of the feature is solved as a new health indicator. The result shows it is more effective for the evaluation of rub-impact than the conventional indicators.

Identification of a Class of Precision Motion Systems with Uncertain Hysteretic Nonlinearities

In this paper, we propose a nonrecursive identification algorithm for a class of precision motion systems with uncertain hysteresis nonlinearities. This class of precision motion systems can be modeled by a Hammerstein system with a hysteresis nonlinearity. The hysteresis nonlinearity can be symmetric, asymmetric, rate-independent, or rate-dependent. The proposed identification algorithm is a two-stage algorithm that identifies the hysteresis nonlinearity and the linear system using measurements of the input and output of the Hammerstein system. The first stage of the algorithm uses a delayed impulse signal with simple least squares to identify the linear part of the Hammerstein system. The delayed impulse signal is shown to be persistently exciting of a sufficient order for the considered model structure. The second stage of the algorithm uses a sinusoidal input and the identified linear model obtained from the first stage to construct an estimate of the unknown intermediate signal, which represents the output of the hysteresis nonlinearity. Finally, a model of the hysteresis nonlinearity is obtained using the sinusoidal input and the constructed estimate of the intermediate signal. The identification algorithm is demonstrated on an experimental setup that includes a piezoelectric actuator, which exhibits a hysteresis nonlinearity and badly damped dynamics.

On nonlinear robust state estimation for generalized Persidskii systems

A state observer is designed for a class of generalized Persidskii systems with nonlinear measurements, state disturbances, and output noise. We assume that all nonlinearities are diagonal and belong to a sector. The robust stability and convergence conditions for the estimation error are obtained by applying the theory of input-to-output stability. These conditions are established in the form of linear matrix inequalities. We provide numerical examples to demonstrate the efficacy and performances of the proposed observer.

A computational model of stereoscopic prey capture in praying mantises.

We present a simple model which can account for the stereoscopic sensitivity of praying mantis predatory strikes. The model consists of a single “disparity sensor”: a binocular neuron sensitive to stereoscopic disparity and thus to distance from the animal. The model is based closely on the known behavioural and neurophysiological properties of mantis stereopsis. The monocular inputs to the neuron reflect temporal change and are insensitive to contrast sign, making the sensor insensitive to interocular correlation. The monocular receptive fields have a excitatory centre and inhibitory surround, making them tuned to size. The disparity sensor combines inputs from the two eyes linearly, applies a threshold and then an exponent output nonlinearity. The activity of the sensor represents the model mantis’s instantaneous probability of striking. We integrate this over the stimulus duration to obtain the expected number of strikes in response to moving targets with different stereoscopic disparity, size and vertical disparity. We optimised the parameters of the model so as to bring its predictions into agreement with our empirical data on mean strike rate as a function of stimulus size and disparity. The model proves capable of reproducing the relatively broad tuning to size and narrow tuning to stereoscopic disparity seen in mantis striking behaviour. Although the model has only a single centre-surround receptive field in each eye, it displays qualitatively the same interaction between size and disparity as we observed in real mantids: the preferred size increases as simulated prey distance increases beyond the preferred distance. We show that this occurs because of a stereoscopic “false match” between the leading edge of the stimulus in one eye and its trailing edge in the other; further work will be required to find whether such false matches occur in real mantises. Importantly, the model also displays realistic responses to stimuli with vertical disparity and to pairs of identical stimuli offering a “ghost match”, despite not being fitted to these data. This is the first image-computable model of insect stereopsis, and reproduces key features of both neurophysiology and striking behaviour.

Characterization, Measurement and Specification of Device Imperfections in Optical Coherent Transceivers

Transceiver imperfections become the primary source of impairment as baud rate and modulation order grow in advanced optical coherent communications. Thus, transceiver imperfections, both linear and nonlinear, need to be appropriately characterized, measured, and specified. Treatments for linear imperfections are relatively mature. This study reviews the transceiver's linear imperfection modeling, characterization, and measurement technologies. In practical applications, in-field measurement using the transceiver and a few low speed additional devices is preferred. In the case of nonlinear imperfections, the situation is complex. One important task is to estimate the nonlinear system performance from the nonlinear characteristics of the devices. In this study, we attempt to establish a connection between them by examining different technologies. Although the orthogonal component has a good correlation with nonlinear system performance, its measurement is prohibitively complex. In the nonlinear noise to power ratio measurement, a certain frequency component of the input signal is notched, and the re-growth component at the notch frequency is measured at the nonlinear device output. The ratio between the re-growth component power and the output signal power is the noise to power ratio. While this method is easy to carry out, it does not correctly estimate nonlinear impairment in general. The reason for this is that the signal incurs different nonlinear responses in two conditions, i.e., with or without a notch. This method accurately estimates the nonlinear impairment in some special but useful cases, such as Gaussian input signals and nonlinear systems whose dominant nonlinear term is the even order term.

Nonlinear correction method of pressure sensor based on data fusion

Piezoresistive sensors are widely used in the design of underwater pressure transmitters, whose nonlinear output is easily affected by the temperature of oil and gas medium. Most of the published literature focuses on hardware, software, or hybrid correction methods, but they are inflexible, have low accuracy and large temperature drift, especially can not retain the nonlinear characteristics of the sensor itself. This paper presents a nonlinear correction method for pressure sensors based on data fusion. Firstly, the pressure and temperature coupling model is established by using ANSYS software, and the extra thermal stress caused by temperature is analyzed, which makes the pressure sensor have strong nonlinear. Secondly, a nonlinear correction method combining polynomial fitting, BP neural network activated by wavelet function, and BP optimization algorithm based on particle swarm optimization (PF-W_BP-PSO_BP) is proposed. This method combines the advantages of numerical calculation and machine learning, retains the nonlinear characteristics of sensor output and restrains the influence of temperature, and proves that this method is superior to the existing correction methods. Finally, pressure and temperature data acquisition experiments are designed, which verifies the scientific nature and effectiveness of the nonlinear correction method in this paper. The method has been applied to the development project of a pressure and temperature integrated transmitter 1500 m underwater, and its practicability has been verified.

Using a Network Physiology Approach to Prescribe Exercise for Exercise Oncology.

Current American College of Sports Medicine (ACSM) exercise guidelines for exercise oncology survivors are generic one-size fits all recommendations, which assume ideal or prototypic health and fitness state in order to prescribe. Individualization is based on the objective evaluation of the patient's baseline physiological status based on a linear dose response relationship of endpoints. This is only a partial snapshot of both the acute and chronic responses exercise can provide. Each acute exercise session represents a unique challenge to whole-body homeostasis and complex acute and adaptive responses occur at the cellular and systemic levels. Additionally, external factors must be considered when prescribing exercise. Network physiology views the human organism in terms of physiological and organ systems, each with structural organization and functional complexity. This organizational approach leads to complex, transient, fluctuating and nonlinear output dynamics which should be utilized in exercise prescription across health states. Targeting health outcomes requires a multi-system approach as change doesn't happen in only one system at a time or in one direction Utilizing a multi-system or person-centered approach, allows for targeting and personalization and understands and targets non-linear dynamics of change. Therefore, the aims of this review are to propose a paradigm shift towards a Network Physiology approach for exercise prescription for cancer survivors. Cancer treatment affects multiple systems that interact to create symptoms and disruptions across these and therefore, prescribing exercise utilizing both external daily factors and internal physiological networks is of the highest order.

Fuzzy-weighted differential evolution computing paradigm for fractional order nonlinear wiener systems

The parameter estimation of fractional order nonlinear Wiener system is complex and challenging task due to the presence of significant nonlinearity at the output block, unknown fractional order, unknown parameters of the linear/nonlinear blocks, and the unmeasurable intermediate variables as well as the states. In this study, a novel design of fuzzy-weighted differential evolution is presented for parameter estimation of fractional order nonlinear Wiener (FO-NW) systems which are designed as an extension of conventional Wiener type models subjected to be fractional order system by exploiting Grunwald-Letnikov fractional derivative. The parameter estimation problem of FO-NW systems is constructed by defining a merit/error function between the true and estimated response via knacks of approximation theory in mean square error sense. Fuzzy Weighted Differential evolution algorithm is employed as an optimization mechanism to estimate the parameters of FO-NW systems with various output nonlinearities of polynomial, sinusoidal and sigmoidal kernels for low/high noisy environments in the system dynamics. Comparative studies based on rigorous statistics endorse the accurate, effective, stable and robust performance of fuzzy-weighted differential evolution algorithm.

Dynamic Event-triggered State Estimation for Nonlinear Coupled Output Complex Networks Subject to Innovation Constraints

This letter investigates the recursive state estimation (RSE) problem for a class of coupled output complex networks via the dynamic event-triggered communication mechanism (DETCM) and innovation constraints (ICs). Firstly, a DETCM is employed to regulate the transmission sequences. Then, in order to improve the reliability of network communication, a saturation function is introduced to constrain the measurement outliers. A new RSE method is provided such that, for all output coupling, DETCM and ICs, an upper bound of state estimation error covariance (SEEC) is presented in a recursive form, whose trace can be minimized via parameterizing the state estimator gain matrix (SEGM). Moreover, the theoretical analysis is given to guarantee that the error dynamic is uniformly bounded. Finally, a simulation example is illustrated to show the effectiveness of the proposed RSE method.

A Fault Diagnosis Method for PV Arrays Based on New Feature Extraction and Improved the Fuzzy C-Mean Clustering

Photovoltaic (PV) array fault diagnosis is vital for the safe and stable operation of PV systems. Up to now, there are many methods to diagnose and classify PV array faults successfully. However, the difficulty of fault diagnosis is increased because the PV arrays have nonlinear output characteristics and complex working environments. In practice, the difference in characteristic parameters of different faults is not apparent, and it is not easy to effectively obtain labels of many samples. In order to address the above problems, this article proposes a new fault detection method for PV arrays based on the output current–voltage ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> ) characteristic, an improved fuzzy C-mean clustering (FCM) algorithm to identify four common PV array faults. The measured <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> characteristic curves are used to extract the initial feature parameters and then calculate the initial parameters to obtain characteristic parameters. In addition, it used characteristic parameters as feature variables of the FCM fault diagnosis model. Finally, classification results are verified by inner cluster maximum mean discrepancy and reclassification pseudoparameter based on the relationship between characteristic parameters. This method defines new characteristic parameters and achieves the purpose of fault detection by reclassification; in addition, we verify the high accuracy and simplicity of the method through simulation and experiment.

An LMI-based discrete time nonlinear observer for Light-Emitting Diode optical communication

Light-Emitting Diode (LED) optical wireless communication is a potentially low-cost, sustainable approach for enabling high-speed free-space and underwater transmissions within a limited communication range. Establishing a tightly controlled line of sight (LOS) between transmitter and receiver is a significant challenge because the angle of the alignment is not directly measured and has to be estimated. To address this problem, we propose a novel switched-gain discrete-time nonlinear observer for an LED-based optical communication model in which the nonlinear output functions are composed of nonlinear vector functions of multi-scalar combinations of the states. Lyapunov function-based analysis that ensures global stability is used to design the proposed observer in each piecewise monotonic region of the LED output functions. Furthermore, we prove via a quadratic Lyapunov-based approach that a constant stabilizing observer gain design approach has no feasible solution when the entire LED optical communication range is considered. Therefore, a suitable switched-gain nonlinear observer is derived for non-monotonic output measurement equations. Simulation results are shown together with extensive comparisons with the Extended Kalman Filter (EKF) to illustrate the performance of the proposed switched-gain observer design.

On high-gain observer design for nonlinear systems with delayed output measurements

In this paper, we propose a high-gain observer design for nonlinear systems with time-varying delayed output measurements. Based on a recent high-gain like observer design method, called HG/LMI observer, a larger bound of the time-delay is allowed compared to that obtained by using the standard high-gain methodology. Such a HG/LMI observer adopts a lower value of the tuning parameter, which results in the reduction of the value of the observer gain, and an increase in the maximum bound of the delay required to ensure exponential convergence. Indeed, an explicit relation between the maximum bound of the delay and the observer tuning parameter is derived by using a Lyapunov–Krasovskii functional jointly with the Halanay inequality. Such a relation shows clearly the superiority of HG/LMI observer design methodology. An application to nonlinear systems with sampled measurements is provided. Furthermore, the proposed methodology is extended to systems with nonlinear outputs. This extension provides more general synthesis conditions and encompasses the linear case as a particular situation. Finally, two numerical examples are proposed to illustrate the performance of the proposed observer design procedure, and comparison to standard approaches is also provided.

A piezoelectric–electromagnetic hybrid flutter-based wind energy harvester: Modeling and nonlinear analysis

This paper presents a piezoelectric–electromagnetic hybrid flutter-based energy harvester (HFEH), where the piezoelectric part and electromagnetic part are coupled with each other by magnetic forces. The working principle is explained in detail and the corresponding theoretical model of the HFEH is established based on Lagrange’s equations, Newton’s second law, Kirchhoff’s law, a semi-empirical nonlinear aerodynamic model, and a magnetic dipole model. The advantages of the HFEH, output performance, and nonlinear output characteristics under different magnet distances and load resistances are analyzed. Results show that the cut-in wind speed and the output power of the HFEH are, respectively, lower and higher than those of the typical flutter-based piezoelectric energy harvester (FPEH). When the distance between magnets A and B and that between magnets C and D is small, the amplitude jump phenomenon occurs, and the electromagnetic part has a satisfactory output power near the jump points. The output power of the piezoelectric part and the electromagnetic part of the HFEH, respectively, reaches 1.35 mW and 36.63 mW at a wind speed of 6.70 m/s. Overall, this study provides a theoretical framework for the design of high-efficiency wind energy harvesters.

Exploring the Essence of Servo Pump Control

The electrohydraulic servo variable speed volume pump control system (hereinafter referred to as ESPCS) is integrated with a permanent magnet synchronous motor (hereinafter referred to as servo motor), a fixed-displacement pump, and a hydraulic cylinder. By controlling the servo motor speed, the output flow of the system can be controlled, as can the displacement, force, and speed of the hydraulic cylinder. Compared with the traditional electro-hydraulic servo valve control system, the ESPCS has the advantages of high power-to-weight ratio, energy saving, and environmental friendliness. However, due to the extremely nonlinear flow output of the ESPCS, further improvement of system control performance is greatly hindered. This paper focuses on the nonlinear characteristics of servo motor, fixed-displacement pump, hydraulic cylinder, and other key components in the system. A compensation method based on nonlinear characteristic mapping is proposed. Compared with the traditional PID control method (pressure control accuracy ± 0.12 MPa), the pressure control accuracy of the system is greatly improved (pressure control accuracy ± 0.037 MPa), which opens up a new way to improve the pressure control accuracy of the ESPCS.

Analysis of the DC-Link Voltage Ripple for the Three-Phase Voltage Source Converter under Nonlinear Output Current

The dc-link voltage ripple plays an important role in dc capacitor design for three-phase voltage source converters (VSCs). However, the analytical models of the dc-link voltage ripple have rarely been reported for VSCs with nonlinear output current. This paper first derived the LOH voltages expressions in the dc-link. It reveals that each LOH component in ac current would induce two dc-link LOH voltages. Then the switching frequency harmonic voltages (SHVs) and their envelope expressions are formulated. Moreover, the proposed analytical models could be very much simplified when applied to special cases in the previous literature. Finally, an easy to design dc capacitor equation under nonlinear output current is also derived. Both simulation and experimental results validate the proposed method.

Event-triggered adaptive control of multi-agent systems with saturated input and partial state constraints

In this paper, we study the consensus tracking control problem of a class of strict-feedback multi-agent systems (MASs) with uncertain nonlinear dynamics, input saturation, output and partial state constraints (PSCs) which are assumed to be time-varying. An adaptive distributed control scheme is proposed for consensus achievement via output feedback and event-triggered strategy in directed networks containing a spanning tree. To handle saturated control inputs, a linear form of the control input is adopted by transforming the saturation function. The radial basis function neural network (RBFNN) is applied to approximate the uncertain nonlinear dynamics. Since the system outputs are the only available data, a high-gain adaptive observer based on RBFNN is constructed to estimate the unmeasurable states. To ensure that the constraints of system outputs and partial states are never violated, a barrier Lyapunov function (BLF) with time-varying boundary function is constructed. Event-triggered control (ETC) strategy is applied to save communication resources. By using backstepping design method, the proposed distributed controller can guarantee the boundedness of all system signals, consensus tracking with a bounded error and avoidance of Zeno behavior. Finally, the correctness of the theoretical results is verified by computer simulation.

A Novel Mode-Localized Accelerometer Employing a Tunable Annular Coupler

The tunable coupling structure is proved to be an effective way to improve the adjustability of sensitivity of mode-localized sensors. However, the non-linearity introduced by the electrical coupling structure brings difficulties to its practical application. In this paper, a mechanical sensitivity adjustment method is proposed with lower output non-linearity of amplitude ratio and larger measurement range of acceleration. The proposed accelerometer is tested under closed-loop circuit to obtain 37% sensitivity adjustment range with 0.42% output non-linearity. The experimental results demonstrate 1.45/g initial sensitivity over 40g linear measurement range. The accelerometer also demonstrates <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$13.65 \mu \text{g}/\surd $ </tex-math></inline-formula> Hz noise floor and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$22 \mu \text{g}$ </tex-math></inline-formula> bias-instability. The linear dynamic range is calculated to be 140.2 dB, which provides a very promising solution for acceleration measurement in high-end industrial applications.

A neural network based heading and position control system of a ship

Heading and position control system of ships has remained a challenging control problem. It is a nonlinear multiple input multiple output system. Moreover, the dynamics of the system vary with operating as well as environmental conditions. Conventionally, simple Proportional Integral Derivative controller is used which has well known limitations. Other conventional control techniques have also been investigated but they require an accurate mathematical model of a ship. Unfortunately, accuracy of mathematical models is very difficult to achieve. During the past few decades computational intelligence techniques such as artificial neural networks have been very successful when an accurate mathematical model is not available. Therefore, in this paper, an artificial neural network controller is proposed for heading and position control system. For simulation purposes, a mathematical model with four effective thrusters have been chosen to test the performance of the proposed controller. The final closed loop system has been analysed and tested through simulation studies. The results are very encouraging.