Nonlinear Identification Techniques Research Articles

An extended observer-based robust nonlinear speed sensorless controller for a PMSM

ABSTRACTThis work focuses on the problem of observer-based robust speed sensorless control of a 3-phase permanent magnet synchronous motor (PMSM). Nonlinear design techniques are employed for designing robust speed controller and observer that are able to withstand the effects of modelling uncertainties and load variations. A new cascaded observer scheme is proposed comprising a continuous sliding mode observer (SMO) and an extended high-gain observer (EHGO). The proposed cascaded observer reduces chattering, exhibits reasonable insensitivity to modelling inaccuracies and is capable of withstanding errors due to the finite boundary layer of continuous SMO. For the robust speed control, an integral sliding mode controller is designed that yields fast and accurate speed tracking performance even in the presence of bounded uncertainties and external disturbances. The complete scheme has been evaluated using simulations and experiments.

Modelling nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures

Mechanical properties of an electrodynamic loudspeaker are mainly determined by its suspensions (surround and spider) that behave nonlinearly and typically exhibit frequency dependent viscoelastic properties such as creep effect. The paper aims at characterizing the mechanical behaviour of electrodynamic loudspeaker suspensions at low frequencies using nonlinear identification techniques developed in recent years. A Generalized Hammerstein based model can take into account both frequency dependency and nonlinear properties. As shown in the paper, the model generalizes existing nonlinear or viscoelastic models commonly used for loudspeaker modelling. It is further experimentally shown that a possible input-dependent law may play a key role in suspension characterization.

Optimal Output-Feedback Power Control for the Hybrid Excitation Synchronous Aero-Generator in High Wind Speed Operation

This paper deals with the problem of controlling wind energy conversion systems operating at a high speed. We seek both the achievement of constant power operation and the minimization of Joule power losses in the aero-generator, which presently, is a hybrid excitation synchronous generator (HESG). Furthermore, the system safety over a wide range variation of the wind speed is taken into consideration in the control problem formulation. These energetic optimization and turbine safety requirements are achieved by using an output-feedback controller that is developed by nonlinear design techniques including a backstepping control, a high-gain observer and others. The controller consists of: (i) a sensorless online reference-speed optimizer designed to limit the extracted aerodynamic power in over speed mode; (ii) a power-limiter regulator based on the flux-weakening; (iii) an electromagnetic torque regulator ensuring power loss reduction in the HESG stator. The real-time implementation of the above objectives necessitates online measurements of the rotor flux, the rotor speed, the aerodynamic torque and the wind speed. The point is that the electromagnetic and the mechanical sensors are costly and entail reliability issues. Therefore, a state observer is designed to provide online estimates of all the required variables that are inaccessible to measurements. The output-feedback controller thus developed is formally analyzed using Lyapunov stability tools. The established theoretical performances are confirmed by a set of numerical simulations.

Enabling reduced-order data-driven nonlinear identification and modeling through naïve elastic net regularization

This work discusses an improved method of reduced-order modeling for existing data-driven nonlinear identification techniques through the incorporation of naïve elastic net regularization. The data-driven methods considered for this study operate using basis functions to represent the observed nonlinearity. Elastic net regularization is used to minimize the number of non-zero coefficients, thus modifying the basis functions and providing a compact representation. The ability of the naïve elastic net to provide reduced-order nonlinear models that can both accurately fit various data sets and computationally simulate new responses is illustrated through studies considering both synthetic data and experimental data. In both cases, the results obtained with the naïve elastic net are shown to match or outperform those from other traditional methods.

Oscillations-free PID control of anesthetic drug delivery in neuromuscular blockade

Background and ObjectivesThe PID-control of drug delivery or the neuromuscular blockade (NMB) in closed-loop anesthesia is considered. The NMB system dynamics portrayed by a Wiener model can exhibit sustained nonlinear oscillations under realistic PID gains and for physiologically feasible values of the model parameters. Such oscillations, also repeatedly observed in clinical trials, lead to under- and over-dosing of the administered drug and undermine patient safety. This paper proposes a tuning policy for the proportional PID gain that via bifurcation analysis ensures oscillations-free performance of the control loop. Online estimates of the Wiener model parameters are needed for the controller implementation and monitoring of the closed-loop proximity to oscillation. MethodsThe nonlinear dynamics of the PID-controlled NMB system are studied by bifurcation analysis. A database of patient models estimated under PID-controlled neuromuscular blockade during general anesthesia is utilized, along with the corresponding clinical measurements. The performance of three recursive algorithms is compared in the application at hand: an extended Kalman filter, a conventional particle filter (PF), and a PF making use of an orthonormal basis to estimate the probability density function from the particle set. ResultsIt is shown that with a time-varying proportional PID gain, the type of equilibria of the closed-loop system remains the same as in the case of constant controller gains. The recovery time and frequency of oscillations are also evaluated in simulation over the database of patient models. Nonlinear identification techniques based on model linearization yield biased parameter estimates and thus introduce superfluous uncertainty. The bias and variance of the estimated models are related to the computational complexity of the identification algorithms, highlighting the superiority of the PFs in this safety-critical application. ConclusionsThe study demonstrates feasibility of the proposed oscillation-free control strategy combining bifurcation theory based design and online parameter estimation by PF.

Finite-Time Regulation of Two-Spool Turbofan Engines With One Shaft Speed Control

Nonlinear control of aircraft engines has attracted much attention in consideration of the inherent nonlinearity of the engine dynamics. Most of the nonlinear design techniques, however, require the information from the rotational speeds of both high-pressure compressor and fan. This is not desirable from engine health management perspective, and this paper proposes a single sensor measurement and single actuator control approach. The proposed method can provide fast regulation of engine speed in a finite-time in comparison with conventional infinite time stability. Important results are obtained on both controller design and disturbance tolerance. Numerical examples are provided for validation of the proposed finite-time controller, demonstrating fast regulation property and remarkable disturbance tolerance capability.

Damping for large-amplitude vibrations of plates and curved panels, part 2: Identification and comparisons

A non-linear identification technique based on the harmonic balance method is presented to obtain the damping ratio and non-linear parameters of isotropic and laminated sandwich rectangular plates and curved panels, subjected to harmonic excitation orthogonal to the surface. The response of structures under consideration is approximated by a single-degree of freedom Duffing oscillator accounting for viscous damping, quadratic and cubic non-linear stiffness. The method uses experimental frequency-amplitude data and a least-squares technique to identify parameters and reconstruct frequency-response curves by spanning the excitation frequency in the neighborhood of the lowest natural frequencies. In particular, an iterative procedure is implemented to construct the mean displacement and identify the damping ratio. Close agreement is seen between the reconstructed non-linear frequency-amplitude curves, the experimental data and the results of the reduced-order model obtained in part 1 of the present study (Alijani et al., 2015 [1]). The proposed identification technique confirms the very large increase of damping during large-amplitude vibrations, as observed in part 1 of the present study, and demonstrates a non-linear correlation between damping, vibration amplitude and excitation level.

Design of Optimized Nonlinear Controller for CSTR Process

In this work, optimized Least Square Support Vector Machine (LSSVM) based Nonlinear Model Predictive Controller (NMPC) is proposed for the nonlinear Continuous Stirred Tank Reactor (CSTR) process. In NMPC, model of the dynamic system is needed to predict the controlled variable. The model of the nonlinear system is identified by either local linear models or through nonlinear model identification techniques viz., Neural Networks and LSSVM. The LSSVM overcomes the isssues involved in NN model such as overfitting and huge training set requirement issues. The regression performace of the LSSVM can be improved through the proper selection of its parameters viz., regularization parameter (C) and the kernel width parameter (σ). The Ant colony optimization (ACO) based Genetic Algorithm (GA) is proposed to tune the LSSVM parameters C and σ with different kernel function viz., linear, Radial Basis Function (RBF). To show the effectiveness of the proposed E-LSSVM scheme, it is presented to the CSTR process. Experimental evaluation under closed loop revealed Mean Square Error (MSE) value of 1.5210e-5 for 1500 prediction points with 100 training data under RBF kernel function which is better compares to previous approaches.

Support vector machine identification of a parallel cascade model of human ankle stiffness

Nonlinear systems identification techniques have been used to study the stretch reflex dynamics of the muscles of the human ankle. Kearney and Hunter (1988) suggested a parallel cascade structure consisting of two pathways to represent human ankle stiffness dynamics. The upper pathway contains a linear model that represents the intrinsic stiffness of the ankle while the reflex stiffness, the lower path, is modeled with a Hammerstein cascade. In this work, an algorithm for the identification of the parallel cascade model using SVM regression is developed. The model parameters have been identified by minimizing an epsilon insensitive cost functions based on either the sum of absolute residuals or the sum of square residuals. The proposed algorithm has been validated via simulation.

COMBINED DELAY AND GRAPH EMBEDDING OF EPILEPTIC DISCHARGES IN EEG REVEALS COMPLEX AND RECURRENT NONLINEAR DYNAMICS.

The dynamical structure of the brain's electrical signals contains valuable information about its physiology. Here we combine techniques for nonlinear dynamical analysis and manifold identification to reveal complex and recurrent dynamics in interictal epileptiform discharges (IEDs). Our results suggest that recurrent IEDs exhibit some consistent dynamics, which may only last briefly, and so individual IED dynamics may need to be considered in order to understand their genesis. This could potentially serve to constrain the dynamics of the inverse source localization problem.

Design Technique for Harmonic-Tuned RF Power Oscillators for High-Efficiency Operation

In this paper, we propose an advanced nonlinear design technique for harmonic-tuned RF power oscillators, where the feedback, source, and load networks are independently designed based on the derived design equations. They present the transistor with the optimum impedances at fundamental and harmonic frequencies which are determined from the source- and load-pull simulations. The proposed oscillator topology and design equations are verified by the simulations and measurements of RF oscillator using GaN high electron mobility transistors. The fabricated harmonic-tuned oscillator exhibits a maximum efficiency of 83% with an output power of 6.1 W at 2.45 GHz. To the authors' knowledge, this corresponds to the best efficiency performance among previously reported RF power oscillators. The phase noise is also as low as -138 dBc/Hz at an offset frequency of 1 MHz.

Comparison of several data‐driven non‐linear system identification methods on a simplified glucoregulatory system example

In this paper, several advanced data-driven nonlinear identification techniques are compared on a specific problem: a simplified glucoregulatory system modeling example. This problem represents a challenge in the development of an artificial pancreas for T1DM treatment, since for this application good nonlinear models are needed to design accurate closed-loop controllers to regulate the glucose level in the blood. Block-oriented as well as state-space models are used to describe both the dynamics and the nonlinear behavior of the insulin-glucose system, and the advantages and drawbacks of each method are pointed out. The obtained nonlinear models are accurate in simulating the patient's behavior, and some of them are also sufficiently simple to be considered in the implementation of a model-based controller to develop the artificial pancreas.

A Novel Neural Network Based Modeling for Control of NO<sub>x</sub> Emission in Power Plant

A novel neural network based modeling for non-linear model identification technique is proposed. It combines a nonlinear steady state model with a linear one, to describe the disturbance and dynamics in the coal-fired power plant. The modeling and training algorithm is used to develop a model of nitrogen oxides (NOx) emitted from the process where one-step ahead optimal prediction formula are developed. Two cases show that the resulting model provides a better prediction of NOx and fitting capabilities.

Reference voltage optimizer for maximum power point tracking in triphase grid-connected photovoltaic systems

The problem of maximum power point tracking (MPPT) in photovoltaic (PV) arrays is addressed considering a PV system including a PV panel, a PWM DC/AC inverter connected to triphase grid. Interestingly, the proposed PV system features higher reliability and reduced cost as it involves no chopper and no radiation/temperature sensors, unlike standard systems. We seek the achievement of three control objectives: (i) the voltage reference must be designed so as to achieve maximum power point tracking (MPPT), (ii) the DC link voltage must be tightly regulated over a wide range voltage-reference variation, (iii) and the power factor correction (PFC) requirement must be satisfactorily realized. To meet these objectives, a multiloop controller is designed, using nonlinear design techniques, based on the nonlinear system model. Then, it is formally demonstrated that the proposed controller actually meets the desired control objectives.

Material Demand Forecasting: An ERP System Perspective

This paper investigates various problems associated with the parameter specification for material requirements planning (MRP) in a typical ERP system. The choice of a suitable MRP procedure and its parameters can reduce excessive quantities of materials and, consequently, cost. The proposed approach is dedicated for MRP procedure based on the forecasting of material demand and inventory that can be obtained with the use of techniques for nonlinear function identification, such as fuzzy-neural system and neural networks. An example is presented which compares the different forecasting models for material demand and inventory.

Identification of Industrial Furnace Temperature for Sintering Process in Nuclear Fuel Fabrication Using NARX Neural Networks

Nonlinear system identification is becoming an important tool which can be used to improve control performance and achieve robust fault-tolerant behavior. Among the different nonlinear identification techniques, methods based on neural network model are gradually becoming established not only in the academia, but also in industrial application. An identification scheme of nonlinear systems for sintering furnace temperature in nuclear fuel fabrication using neural network autoregressive with exogenous inputs (NNARX) model investigated in this paper. The main contribution of this paper is to identify the appropriate model and structure to be applied in control temperature in the sintering process in nuclear fuel fabrication, that is, a nonlinear dynamical system. Satisfactory agreement between identified and experimental data is found with normalized sum square error 1.9e-03for heating step and6.3859e-08for soaking step. That result shows the model successfully predict the evolution of the temperature in the furnace.

Comparison of restoring force models for the identification of structures with hysteresis and degradation

Abstract When subjected to events such as earthquakes, engineering structures typically exhibit a nonlinear and hysteretic behaviour with stiffness and strength degradations. Though a reliable evaluation of safety conditions should take into account the nonlinear dynamic and evolutionary nature of the structural response, the experimental identification of a nonlinear behaviour under dynamic and seismic loading is, to date, an open problem. The present research aims at evaluating the potential of different restoring force models for simulating the seismic response of hysteretic structural systems, with special emphasis on the two main problems encountered when applying this approach to full-scale structures under intense excitation: (a) a markedly time-dependent behaviour; (b) need to compare among different restoring force models, either expressed in a parametric or polynomial form. In particular, polynomial models will be formulated both in terms of restoring force and its derivative, in order to present a comprehensive discussion of different strategies. The nonlinear identification technique employed in this paper is required to account for a time-dependent behaviour. In fact, in presence of degradation or any other time-varying characteristics, instantaneous identification certainly constitutes an enhancement of the classical restoring force based approach, and may as well provide checks on the consistency of the assumed models.

Frequency domain‐based nonlinearity detection and compensation in Lur'e systems

SUMMARYNonlinearities often lead to performance degradation in controlled dynamical systems. This paper provides a new, frequency domain‐based method, for detection and optimal compensation of performance degrading nonlinear effects in Lur'e‐type systems. It is shown that for such systems a sinusoidal response to a sinusoidal input is necessary and sufficient to show the existence of an equivalent linear and time invariant dynamical model that fully captures the systems’ dynamics for a well‐defined set of input signals and initial conditions. This allows to quantify nonlinear effects by using a frequency domain performance measure and yields a novel method to design optimized static compensator structures that minimize performance degrading nonlinear effects. Moverover, the methods discussed in this paper allow to quantify the performance of nonlinear systems on the basis of output measurements only while requiring little knowledge about the nonlinearity and other system dynamics, which yields a useful tool to optimize performance in practice without requiring advanced nonlinear modeling or identification techniques. Finally, the theoretical results are accompanied by examples that illustrate their application in practice.Copyright © 2013 John Wiley & Sons, Ltd.

Improved Matrix Fraction Approximation of Aerodynamic Transfer Matrices

Linearized aeroelastic stability and response analyses in the state domain may require the identification of an asymptotically stable finite-state aerodynamic subsystem from available aerodynamic transfer matrices, related to structural motions and gusts. To such an aim, the paper develops an improved rational matrix approximation, combining three nonlinear least squares identification techniques with a system reduction based on a double dynamic residualization. An alternative gust formulation is also presented that, by reconstructing generalized gust forces through the use of special structural motion-like modes called gust modes, makes it possible to determine a gust response even without the usual gust-penetration model in the frequency domain. Examples are presented to demonstrate the behavior of the proposed approaches applied to sample flutter and gust/turbulence response analyses.

Identification of non-linear predictor and simulator models of a cement rotary kiln by locally linear neuro-fuzzy technique

One of the most important parts of a cement factory is the cement rotary kiln which plays a key role in quality and quantity of produced cement. In this part of the process, the physical exertion and bilateral movement of air and materials, together with chemical reactions take place. Thus, this system has immensely complex and non-linear dynamic equations. These equations have not completely extracted yet. Even in special cases, however, a large number of the involved parameters were crossed out and an approximation model was presented instead. This issue caused many problems for designing a cement rotary kiln controller. In this paper, we present non-linear predictor and simulator models for a real cement rotary kiln by using non-linear identification technique on the locally linear neuro-fuzzy (LLNF) model. For the first time, a simulator model as well as a predictor one with a precise 15-minute horizon prediction for a cement rotary kiln are presented. These models are trained by LOLIMOT algorithm whi...