statistical linearization
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Author(s):  
Y. O. Denisov ◽  
O. I. Denisov ◽  
O. O. Bursala

Goal The purpose of the article is to further develop analytical methods for calculating and synthesizing power electronics systems with deep pulse width modulation (PWM). A three-circuit linear electric drive system for positioning the working body of the mechanism of onboard aircraft equipment, in which the linear electric motor is controlled from a pulse width converter (PWC), is considered. The power converter is included in the current loop. It has a noticeable effect on the level of current ripple, travel speed and positioning accuracy of the operating mechanism of a linear electric drive. Methodology. To analyze the processes in the current loop, a discrete transfer function of a pulse-width converter for PWM in the final zone and «in the large» is obtained on the basis of the statistical linearization of the modulation characteristics of the multi-loop PWM model. The modulation characteristic of each circuit of the model is obtained as a result of the Fourier series expansion in Walsh functions of the output voltage of the PWM during the PWM process. Statistical linearization of modulation characteristics is performed based on Hermite polynomials. Results. During the analysis, discrete transfer functions of closed current loops, velocity and open loop position were obtained, for which a digital controller was synthesized in the form of a recursive filter. Originality. The parameters of the regulator links are found, which make it possible to complete the transient process in four PWC switching periods with an overshoot of no more than 6 %. The analysis of the speed-optimized positioning process of a linear electric drive based on the LED AT 605TU motor is carried out. Practical significance. The purpose of the analysis was to establish the relationship between the switching period of the PWM and the value of the uncompensated constant, at which the pulsations of the positioning process are minimal while ensuring the minimum overshoot and maximum speed. It was found that the specified requirements are satisfied by the ratio between the switching period, PWC and uncompensated constant in the range of one or two.


2021 ◽  
Author(s):  
Leandro Souza Pinheiro da Silva ◽  
Nataliia Sergiienko ◽  
Boyin Ding ◽  
Benjamin Cazzolato ◽  
Celso Pesce ◽  
...  

2021 ◽  
Vol 88 (5) ◽  
Author(s):  
Fan Kong ◽  
Pol D. Spanos

Abstract A statistical linearization approach is proposed for determining the response of the single-degree-of-freedom of the classical Bouc–Wen hysteretic system subjected to excitation both with harmonic and stochastic components. The method is based on representing the system response as a combination of a harmonic and of a zero-mean stochastic component. Specifically, first, the equation of motion is decomposed into a set of two coupled non-linear differential equations in terms of the unknown deterministic and stochastic response components. Next, the harmonic balance method and the statistical linearization method are used for the determination of the Fourier coefficients of the deterministic component, and the variance of the stochastic component, respectively. This yields a set of coupled algebraic equations which can be solved by any of the standard apropos algorithms. Pertinent numerical examples demonstrate the applicability, and reliability of the proposed method.


2021 ◽  
Author(s):  
Fan Kong ◽  
Renjie Han ◽  
Yuanjin Zhang

Abstract A method based on statistical linearization is proposed, for determining response of the single-degree-of-freedom (SDOF) hysteretic system endowed with fractional derivatives and subjected to combined periodic and white/colored excitation. The method is developed by decomposing the system response into a combination of a periodic and of a zero-mean stochastic components. In this regard, first, the equation of motion is cast into two sets of coupled fractional-order non-linear differential equations with unknown deterministic and stochastic response components. Next, the harmonic balance method and the statistical linearization for the fractional-order deterministic and stochastic subsystems are used, to obtain the Fourier coefficients of the deterministic component and the variance of the stochastic component, respectively. This yields two sets of coupled non-linear algebraic equations which can be solved by appropriate standared numerical method. Pertinent numerical examples, including both softening and hardening Bouc-Wen hysteretic system endowed with different fractional-orders, are used to demonstrate the applicability and accuracy of the proposed method.


Author(s):  
Cheng Ning Loong ◽  
Chih-Chen Chang

The energy scavenged from a vibrating building installed with distributed electromagnetic energy harvesters under random excitation is analyzed. Each harvester is connected to an energy harvesting circuit made of a full-wave bridge rectifier connecting a resistor in parallel with a capacitor. Statistical linearization is adopted to estimate the stationary response of the harvester-structure system. As an illustrative example, a 20-story building equipped with 16 harvesters on each story is examined. Results show that the scavenged energy mainly concentrates at the higher stories. The vibration mitigation and energy scavenging performance of the harvesters can be enhanced simultaneously with the proper design of harvesters and circuits. Gradient ascent approach with the first-order perturbation approximation is proposed to determine the optimal design of distributed harvesters with nonlinear circuits that maximizes the total mean output power. Results show that output power decreases due to circuit nonlinearity. The maximum total mean output power obtained from the 20-story building under wind excitations with mean speed of 5 m/s is around 1.32–2.17 kW for harvesters having short-circuit damping coefficient ranging 100–300 kNs/m. These results show that scavenging energy from structural vibration is a feasible technology even considering the negative effect of circuit nonlinearity.


Author(s):  
P.P. Krutskikh ◽  
O.V. Tsarik

The actual research problem of operations is development of methods of increase of a management efficiency by processes of the conflict nature. Article is devoted to development of methods of increase of a management efficiency by such processes. The purpose of article is the substantiation of the approach to parametrical synthesis of optimum control by multi-step stochastic minimax processes and procedures of the numerical analysis of likelihood dynamic characteristics of process. Formalization of process consists in definition of its type, a vector of phase coordinates and corresponding restrictions, the task of set of the actions sold by each the parties, efficiency of each action, control parameters (varied parameters of process) which task of values each of the parties influences a course of process, control restrictions, criteria of efficiency of the parties expressed through elements of a vector of phase coordinates. Discrete final stochastic process is considered. Change of phase coordinates occurs during the discrete moments of time, named steps of process. Phase coordinates depend on values of two groups of control parameters (controls of the counteracting parties). Within the limits of the modern theory of optimization of stochastic systems procedure of synthesis of optimum control is realized two-phase. At the first stage with use of analytical methods the structure of optimum control is determined. For these purposes the simplified determined model of process can to be used. At the second stage parametrical control optimization with use of algorithmic methods and computing procedures statistical linearization is carried out. Dynamics of process is described vectorial finite-difference equation. It is necessary to distinguish cases when there is saddle a point and when saddle the point is absent. Parametrical synthesis of optimum control is possible only in the first case. It is considered three basic variants of the equation: the linear equation; the nonlinear equation with optimum controls on border of a range of definition; the nonlinear equation with optimum controls inside of a range of definition. For the first variant there is an effective algorithm of parametrical synthesis of optimum control. For the second variant of synthesis of optimum control it is possible, but the algorithm is not effective. For the third variant to determine optimum managements it is not possible. Procedure statistical linearization is offered. Procedure consists in generation of set of realizations of the casual process set by the vector equation, calculation of optimum control for each concrete realization and the further statistical processing of the received results. The process described by the piecewise linear vector equation, is a special case of nonlinear process. At that it keeps property of independence of optimum control from coordinates of process. It provides expansion of a scope of effective computing procedure of synthesis of optimum control on a new class of piecewise linear processes. Property of a constancy process Hamiltonian can be used as criterion of correctness of calculation of optimum control in concrete cases. Application of the offered procedure provides use of methods of statistical modelling for the decision of tasks of the analysis of dynamics of the conflict and synthesis of optimum control in view of nonlinearity of functions of losses of the parties, dependence of efficiency of means used by them on the random factors formalized in the form of stochastic functions with various likelihood distributions, and also uncertainty concerning actions of the opponent.


2020 ◽  
Vol 25 (4) ◽  
pp. 597-608
Author(s):  
Sudhir Kaul

This paper investigates the influence of the nonlinearities of a vibration isolation system on the planar dynamics of a motorcycle. The use of a nonlinear isolation system is often necessitated by design and packaging constraints. Although the use of a vibration isolation system is uncommon in motorcycles, it is used in some cases to enhance ride comfort by mitigating vibrations transmitted to the rider due to shaking forces. In such cases, the handling of the motorcycle can be influenced due to the coupled dynamics of the rear unsprung mass and the swing arm. In this paper, a stochastic analysis has been performed by using the statistical linearization method to specifically examine nonlinearities associated with the vibration isolation system. An eight degree-of-freedom planar model has been developed, and each isolator is represented by a modified multi-axial Kelvin-Voigt model. It has been observed that the model developed in this study can capture the coupled dynamics between the rear suspension and the vibration isolation system. Results indicate that the nonlinear design of the vibration isolation system can be useful in enhancing ride comfort in the lower frequency range without an adverse impact on handling. Furthermore, it has been observed that the parameters associated with the nonlinear vibration isolation system can be tuned to enhance ride comfort while meeting the design requirements of spatial dynamics.


Author(s):  
Leandro S. P. da Silva ◽  
Nataliia Y. Sergiienko ◽  
Benjamin S. Cazzolato ◽  
Boyin Ding ◽  
Celso P. Pesce ◽  
...  

Abstract Wave energy devices operate in resonant conditions to optimize power absorption, which leads to large displacements. As a result, nonlinearities play an important role in the system dynamics and must be accounted for in the numerical models for realistic prediction of the power generated. In general, time domain (TD) simulations are employed to capture the effects of the nonlinearities. However, the computational cost associated with these simulations is considerably higher compared to linear frequency domain (FD) methods. In this regard, the following work deals with the nonlinear analysis of an oscillating wave surge converter (OWSC) in the FD via the statistical linearization (SL) technique. Four nonlinearities for the proposed device are addressed: Coulomb-like torque regulated by the direction of motion, viscous drag torque, nonlinear buoyant net torque, and parametric excitation torque modulated by the flap angle. The reliability of the SL technique is compared with nonlinear TD simulations in terms of response probability distribution and power spectrum density (PSD) of the response and torque; and mean power produced. The results have demonstrated a good agreement between TD simulations and SL, while the computation time of the SL model is approximately 3 orders of magnitude faster. As a result, SL is a valuable tool to assess the OWSC performance under various wave scenarios over a range of design parameters, and can assist the development of such wave energy converters (WECs).


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