Search results for: nonlinear dynamic systems

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

Abstract:

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. Zamani, M. H. Zarif

Abstract:

In this paper a method for designing of nonlinear controller for a fuzzy model of Double Inverted Pendulum is proposed. This system can be considered as a fuzzy large-scale system that includes offset terms and disturbance in each subsystem. Offset terms are deterministic and disturbances are satisfied a matching condition that is mentioned in the paper. Based on Lyapunov theorem, a nonlinear controller is designed for this fuzzy system (as a model reference base) which is simple in computation and guarantees stability. This idea can be used for other fuzzy large- scale systems that include more subsystems Finally, the results are shown.

Keywords: Controller, Fuzzy Double Inverted Pendulums, Fuzzy Large-Scale Systems, Lyapunov Stability.

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Authors: M. Pala Prasad Reddy, Jeevamma Jacob

Abstract:

Accurate dynamic modeling and analysis of flexible link manipulator (FLM) with non linear dynamics is very difficult due to distributed link flexibility and few studies have been conducted based on assumed modes method (AMM) and finite element models. In this paper a nonlinear dynamic model with first two elastic modes is derived using combined Euler/Lagrange and AMM approaches. Significant dynamics associated with the system such as hub inertia, payload, structural damping, friction at joints, combined link and joint flexibility are incorporated to obtain the complete and accurate dynamic model. The response of the FLM to the applied bang-bang torque input is compared against the models derived from LS-DYNA finite element discretization approach and linear finite element models. Dynamic analysis is conducted using LS-DYNA finite element model which uses the explicit time integration scheme to simulate the system. Parametric study is conducted to show the impact payload mass. A numerical result shows that the LS-DYNA model gives the smooth hub-angle profile.

 

Keywords: Flexible link manipulator, AMM, FEM, LS-DYNA, Bang-bang torque input.

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Authors: A. Brouri, F. Giri, A. Mkhida, F. Z. Chaoui, A. Elkarkri, M. L. Chhibat

Abstract:

Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. The problem of identifying Hammerstein-Wiener systems is addressed in the presence of linear subsystem of structure totally unknown and polynomial input and output nonlinearities. Presently, the system nonlinearities are allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method. First, the parameters of system nonlinearities are identified. In the second stage, a frequency approach is designed to estimate the linear subsystem frequency gain. All involved estimators are proved to be consistent.

Keywords: Nonlinear system identification, Hammerstein systems, Wiener systems, frequency identification.

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Authors: Youguo Wang, Lenan Wu

Abstract:

Stochastic resonance (SR) is a phenomenon whereby the signal transmission or signal processing through certain nonlinear systems can be improved by adding noise. This paper discusses SR in nonlinear signal detection by a simple test statistic, which can be computed from multiple noisy data in a binary decision problem based on a maximum a posteriori probability criterion. The performance of detection is assessed by the probability of detection error Per . When the input signal is subthreshold signal, we establish that benefit from noise can be gained for different noises and confirm further that the subthreshold SR exists in nonlinear signal detection. The efficacy of SR is significantly improved and the minimum of Per can dramatically approach to zero as the sample number increases. These results show the robustness of SR in signal detection and extend the applicability of SR in signal processing.

Keywords: Probability of detection error, signal detection, stochastic resonance.

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Authors: S. Anbu, N. Jaya

Abstract:

Nonlinearity is the inherent characteristics of all the industrial processes. The Classical control approach used for a generation often fails to show better results particularly for non-linear systems and in the systems, whose parameters changes over a period of time for a variety of reasons. Alternatively, adaptive control strategies provide very good performance. The Model Reference Adaptive Control based on Lyapunov stability analysis and classical PI control strategies are designed and evaluated for Continuous Stirred Tank Reactor, which shows appreciable dynamic nonlinear characteristics.

Keywords: Adaptive Control, CSTR, Lyapunov stability, MRAS, PID.

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Authors: Yoichi Ishikawa, Yuichi Masukake, Yoshihisa Ishida

Abstract:

This paper presents a novel control method based on radial basis function networks (RBFNs) for chaotic dynamical systems. The proposed method first identifies the nonlinear part of the chaotic system off-line and then constructs a model-following controller using only the estimated system parameters. Simulation results show the effectiveness of the proposed control scheme.

Keywords: Chaos, nonlinear plant, radial basis function network.

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Authors: Hongji Tang, Yanbo Gao, Yue Yu

Abstract:

This paper presents a new nonlinear integral-type sliding surface for synchronizing two different chaotic systems with parametric uncertainty. On the basis of Lyapunov theorem and average dwelling time method, we obtain the control gains of controllers which are derived to achieve chaos synchronization. In order to reduce the gains, the error system is modeled as a switching system. We obtain the sufficient condition drawn for the robust stability of the error dynamics by stability analysis. Then we apply it to guide the design of the controllers. Finally, numerical examples are used to show the robustness and effectiveness of the proposed control strategy.

Keywords: Chaos synchronization, Nonlinear sliding surface, Control gains, Sliding mode control.

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Authors: Toshinori Nawata

Abstract:

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

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Sachin Bhalekar, Varsha Daftardar-Gejji

Abstract:

In the present paper, we present a modification of the New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari [J. Math. Anal. Appl. 2006;316:753–763] and use it for solving systems of nonlinear functional equations. This modification yields a series with faster convergence. Illustrative examples are presented to demonstrate the method.

Keywords: Caputo fractional derivative, System of nonlinear functional equations, Revised new iterative method.

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Authors: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

Abstract:

In order to reduce numerical computations in the nonlinear dynamic analysis of seismically base-isolated structures, a Mixed Explicit-Implicit time integration Method (MEIM) has been proposed. Adopting the explicit conditionally stable central difference method to compute the nonlinear response of the base isolation system, and the implicit unconditionally stable Newmark’s constant average acceleration method to determine the superstructure linear response, the proposed MEIM, which is conditionally stable due to the use of the central difference method, allows to avoid the iterative procedure generally required by conventional monolithic solution approaches within each time step of the analysis. The main aim of this paper is to investigate the stability and computational efficiency of the MEIM when employed to perform the nonlinear time history analysis of base-isolated structures with sliding bearings. Indeed, in this case, the critical time step could become smaller than the one used to define accurately the earthquake excitation due to the very high initial stiffness values of such devices. The numerical results obtained from nonlinear dynamic analyses of a base-isolated structure with a friction pendulum bearing system, performed by using the proposed MEIM, are compared to those obtained adopting a conventional monolithic solution approach, i.e. the implicit unconditionally stable Newmark’s constant acceleration method employed in conjunction with the iterative pseudo-force procedure. According to the numerical results, in the presented numerical application, the MEIM does not have stability problems being the critical time step larger than the ground acceleration one despite of the high initial stiffness of the friction pendulum bearings. In addition, compared to the conventional monolithic solution approach, the proposed algorithm preserves its computational efficiency even when it is adopted to perform the nonlinear dynamic analysis using a smaller time step.

Keywords: Base isolation, computational efficiency, mixed explicit-implicit method, partitioned solution approach, stability.

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Authors: Seema Chopra, R. Mitra, Vijay Kumar

Abstract:

A neurofuzzy approach for a given set of input-output training data is proposed in two phases. Firstly, the data set is partitioned automatically into a set of clusters. Then a fuzzy if-then rule is extracted from each cluster to form a fuzzy rule base. Secondly, a fuzzy neural network is constructed accordingly and parameters are tuned to increase the precision of the fuzzy rule base. This network is able to learn and optimize the rule base of a Sugeno like Fuzzy inference system using Hybrid learning algorithm, which combines gradient descent, and least mean square algorithm. This proposed neurofuzzy system has the advantage of determining the number of rules automatically and also reduce the number of rules, decrease computational time, learns faster and consumes less memory. The authors also investigate that how neurofuzzy techniques can be applied in the area of control theory to design a fuzzy controller for linear and nonlinear dynamic systems modelling from a set of input/output data. The simulation analysis on a wide range of processes, to identify nonlinear components on-linely in a control system and a benchmark problem involving the prediction of a chaotic time series is carried out. Furthermore, the well-known examples of linear and nonlinear systems are also simulated under the Matlab/Simulink environment. The above combination is also illustrated in modeling the relationship between automobile trips and demographic factors.

Keywords: Fuzzy control, neuro-fuzzy techniques, fuzzy subtractive clustering, extraction of rules, and optimization of membership functions.

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Authors: Aras Adhami Mirhoseini, Mohammad J. Yazdanpanah

Abstract:

In this paper, we consider nested sliding mode control of SISO nonlinear systems, perturbed by bounded matched and unmatched uncertainties. The systems are assumed to be in strict-feedback form. A step wise procedure is introduced to obtain the controller. In each step, a continuous sliding mode controller is designed as virtual control law. Then the next step sliding surface is defined by using this virtual controller. These sliding surfaces are selected as nonlinear static functions of the system states. Finally in the last step, smooth static state feedback control law is determined such that the output reaches the desired set-point while the system is forced arbitrary close to the intersection of sliding surfaces and the states remain bounded.

Keywords: Sliding mode control, Strict-feedback form, Unmatched uncertainty, output regulation.

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Authors: Lianglin Xiong, Shouming Zhong, Mao Ye

Abstract:

This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.

Keywords: Switched neutral system, piecewise Lyapunov functional, nonlinear perturbation, Lyapunov-Metzler linear matrix inequality.

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Authors: Amin Almasi

Abstract:

Analysis of reciprocating equipment piston rod leads to nonlinear elastic-plastic deformation analysis of rod with initial imperfection under axial dynamic load. In this paper a new and effective model and analytical formulations are presented to evaluate dynamic deformation and elastic-plastic stresses of reciprocating machine piston rod. This new method has capability to account for geometric nonlinearity, elastic-plastic deformation and dynamic effects. Proposed method can be used for evaluation of piston rod performance for various reciprocating machines under different operation situations. Rod load curves and maximum allowable rod load are calculated with presented method for a refinery type reciprocating compressor. Useful recommendations and guidelines for rod load, rod load reversal and rod drop monitoring are also addressed.

Keywords: Deformation, Reciprocating Equipment, Rod.

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Authors: Toshinori Nawata

Abstract:

In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of nonlinear systems with constrained input is presented. When designed the control, a constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Toshinori Nawata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) using the gradient optimization automatic choosing functions for nonlinear systems. Constant terms which arise from sectionwise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics. Parameters included in the control are suboptimally selected by expanding a stable region in the sense of Lyapunov with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Elham Amini Boroujeni, Hamid Reza Momeni

Abstract:

Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach. Finally, the simulation results demonstrate validity and effectiveness of the proposed observer based controller.

Keywords: Fractional order calculus, Fractional order observer, Linear matrix inequality, Nonlinear Systems, Observer based Controller.

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Authors: A. Zanj, F. He

Abstract:

In the current paper, a domain independent conduction model compatible for multi-physical system dynamic investigations is suggested. By means of a port-based approach, a classical nonlinear conduction model containing physical states is first represented. A compatible discrete configuration of the thermal domain in line with the elastic domain is then generated through the enhancement of the configuration of the conventional thermal element. The presented simulation results of a sample structure indicate that the suggested conductive model can cover a wide range of dynamic behavior of the thermal domain.

Keywords: Multi-physical domain, conduction model, port-based modeling, dynamic interaction, physical modeling.

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Authors: Mohammad Moeini, Mehrdad Ghyabi, Kiarash Mohtasham Dolatshahi

Abstract:

This paper investigates seismic soil-pile interaction using the Beam on Nonlinear Winkler Foundation (BNWF) approach. Three soil types are considered to cover all the possible responses, as well as nonlinear site response analysis using finite element method in OpenSees platform. Excitations at each elevation that are output of the site response analysis are used as the input excitation to the soil pile system implementing multi-support excitation method. Spectral intensities of acceleration show that the extent of the response in sand is more severe than that of clay, in addition, increasing the PGA of ground strong motion will affect the sandy soil more, in comparison with clayey medium, which is an indicator of the sensitivity of soil-pile systems in sandy soil.

Keywords: Beam on nonlinear Winkler foundation method, multi-support excitation, nonlinear site response analysis, seismic soil-pile interaction.

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Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian

Abstract:

Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: Identification, Hammerstein-Wiener, optimization, quantization.

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

Abstract:

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: Mihai Lungu

Abstract:

The paper presents the design of a mini-UAV attitude controller using the backstepping method. Starting from the nonlinear dynamic equations of the mini-UAV, by using the backstepping method, the author of this paper obtained the expressions of the elevator, rudder and aileron deflections, which stabilize the UAV, at each moment, to the desired values of the attitude angles. The attitude controller controls the attitude angles, the angular rates, the angular accelerations and other variables that describe the UAV longitudinal and lateral motions. To design the nonlinear controller, by using the backstepping technique, the nonlinear equations and the Lyapunov analysis have been directly used. The designed controller has been implemented in Matlab/Simulink environment and its effectiveness has been tested with a campaign of numerical simulations using data from the UAV flight tests. The obtained results are very good and they are better than the ones found in previous works.

Keywords: Attitude angles, Backstepping, Controller, UAV.

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Authors: Masoud Sadeghian, Alireza Fatehi

Abstract:

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, the physical exertion and bilateral movement of air and materials, together with chemical reactions take place. Thus, this system has immensely complex and nonlinear dynamic equations. These equations have not worked out yet. Only in exceptional case; however, a large number of the involved parameter 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 presented nonlinear predictor and simulator models for a real cement rotary kiln by using nonlinear 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 fifteen minute prediction horizon for a cement rotary kiln is presented. These models are trained by LOLIMOT algorithm which is an incremental tree-structure algorithm. At the end, the characteristics of these models are expressed. Furthermore, we presented the pros and cons of these models. The data collected from White Saveh Cement Company is used for modeling.

Keywords: Cement rotary kiln, nonlinear identification, Locally Linear Neuro-Fuzzy model.

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Authors: Toshinori Nawata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input using weighted gradient optimization automatic choosing functions. Constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Tapas Kumar Sinha, Joseph Mathew

Abstract:

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: R. Masarova, M. Juhas, B. Juhasova, Z. Sutova

Abstract:

In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: Dynamic system, transfer matrix, inverse matrix, modeling.

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Authors: Kelong Zheng, Shouming Zhong

Abstract:

A new nonlinear sum-difference inequality in two variables which generalize some existing results and can be used as handy tools in the analysis of certain partial difference equation is discussed. An example to show boundedness of solutions of a difference value problem is also given.

Keywords: Sum-Difference inequality, Nonlinear, Boundedness.

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Authors: T. H. Lee, J. H. Park, S. M. Lee, S. C. Lee

Abstract:

In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as operating conditions, another constraint conditions, change of load current and so on. A change of load current is the significant one of these for good performance of the SOFC system. In order to keep the constant stack terminal voltage by changing load current, the nonlinear model predictive control (MPC) is proposed in this paper. After primary control method is designed to guarantee the fuel utilization as a proper constant, a nonlinear model predictive control based on the Wiener model is developed to control the stack terminal voltage of the SOFC system. Simulation results verify the possibility of the proposed Wiener model and MPC method to control of SOFC system.

Keywords: SOFC, model predictive control, Wiener model.

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Authors: J. Mbihi

Abstract:

This paper presents a dynamic architecture of digital duty-cycle modulation control drivers. Compared to most oversampling digital modulation schemes encountered in industrial electronics, its novelty is founded on a number of relevant merits including; embedded positive and negative feedback loops, internal modulation clock, structural simplicity, elementary building operators, no explicit need of samples of the nonlinear duty-cycle function when computing the switching modulated signal, and minimum number of design parameters. A prototyping digital control driver is synthesized and well tested within MATLAB/Simulink workspace. Then, the virtual simulation results and performance obtained under a sample of relevant instrumentation and control systems are presented, in order to show the feasibility, the reliability, and the versatility of target applications, of the proposed class of low cost and high quality digital control drivers in industrial electronics.

Keywords: Dynamic architecture, virtual simulation, duty-cycle modulation, digital control drivers, industrial electronics.

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