Showing papers on "Describing function published in 2018"
TL;DR: In this article, the authors proposed a feedback linearized control strategy for LLC resonant converter, which can achieve better performance with elimination of the nonlinear characteristics with load feedback linearization.
Abstract: LLC resonant converter is a nonlinear system, limiting the use of typical linear control methods. This paper proposed a new nonlinear control strategy, using load feedback linearization for an LLC resonant converter. Compared with the conventional PI controllers, the proposed feedback linearized control strategy can achieve better performance with elimination of the nonlinear characteristics. The LLC resonant converter's dynamic model is built based on fundamental harmonic approximation using extended describing function. By assuming the dynamics of resonant network is much faster than the output voltage and controller, the LLC resonant converter's model is simplified from seven-order state equations to two-order ones. Then, the feedback linearized control strategy is presented. A double loop PI controller is designed to regulate the modulation voltage. The switching frequency can be calculated as a function of the load, input voltage, and modulation voltage. Finally, a 200 W laboratory prototype is built to verify the proposed control scheme. The settling time of the LLC resonant converter is reduced from 38.8 to 20.4 ms under the positive load step using the proposed controller. Experimental results prove the superiority of the proposed feedback linearized controller over the conventional PI controller.
59 citations
TL;DR: In this article, a hybrid mode shape based modal superposition method was proposed for the determination of steady state vibration response of nonlinear structures, where the response of the nonlinear system is written in terms of hybrid modes instead of the modes of the underlying linear system.
32 citations
TL;DR: In this paper, the rotor bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain, which captures the relationship between the amplitude of the fundamental input to nonlinearity and the fundamental output.
29 citations
26 Oct 2018
TL;DR: The hybrid control design provides more design freedom compared to the equivalent linear control design, which leads to a factor two improvement in low-frequency disturbance suppression of a state-of-the-art scanning stage of an industrial wafer scanner.
Abstract: In this paper a hybrid low-pass filter is developed and subsequently embedded in a PID-based control design. The hybrid element switches between gain and integrator mode, depending on the evaluation of specifically designed switching conditions. Given the properties of the hybrid low-pass filter, which are mainly expressed by reduced phase lag as compared to a linear-equivalent low-pass filter, the bandwidth of the PID-based control design can potentially be increased. Based on describing function analysis, this bandwidth increase is obtained while identical robustness properties of the closed-loop system in terms of bounds imposed on the closed-loop sensitivity function are guaranteed. In this sense, the hybrid control design provides more design freedom compared to the equivalent linear control design, which leads to a factor two improvement in low-frequency disturbance suppression of a state-of-the-art scanning stage of an industrial wafer scanner.
28 citations
TL;DR: Simulation results demonstrate that the estimations can be as accurate as those obtained with relay identification methods for time-driven control systems based on other approaches (state-space, curve fitting, Laplace transform, etc.).
Abstract: This paper presents a method to estimate the parameters of first and second order systems with time delays with different accuracy levels for autotuning of event-based PI control loops. In particular, the event-based sampling condition applied in this work is based on the sampling strategy known as symmetric-send-on-delta (SSOD). The method is based on forcing the system to enter into a limit cycle and on using the information achieved from the oscillation to estimate the transfer function parameters. By manipulating the PI controller, the system can reach different limit cycles as a consequence of the intersections of the Nyquist map of the process with the describing function reciprocal of the event-based sampler. The frequency and amplitude of the limit cycle selected to apply the method define the quality of the estimations, avoiding the inaccuracy that relay identification methods based on describing function produce. Simulation results demonstrate that the estimations can be as accurate as those obtained with relay identification methods for time-driven control systems based on other approaches (state-space, curve fitting, Laplace transform, etc.)
25 citations
TL;DR: The transition interval of the PWM DC–DC converter from a stable region to an unstable region can be determined exactly by the proposed stability analysis method, which is helpful to determine the stability margin in real engineering applications.
Abstract: The nonlinearity of the switching process in DC–DC converters can result in the inaccuracy and invalidation of traditional stability criterion based on linear modeling, which is very harmful in practice, especially for the DC-DC converters with high stability requirements. In this paper, the describing function method is adopted for the modeling of switching process, namely, pulse width modulation (PWM), in DC–DC converters, and the describing function of the PWM is derived in detail. Considering the nonlinear items in the obtained describing function of PWM, the selection of the parameters in these nonlinear items are first provided and proved in this paper. With the obtained describing function, the stability of the PWM DC–DC converter can be analyzed exactly. Taken a PWM boost converter as an example, the nonlinear model based on describing function and the linear model are established, respectively; furthermore, the stability analysis based on these two kinds of models are carried out. Comparing with the traditional linear stability criterion, the simulation and experimental results validate the effectiveness and accuracy of the stability analysis based on describing function method. Furthermore, the transition interval of the PWM DC–DC converter from a stable region to an unstable region can be determined exactly by the proposed stability analysis method, which is helpful to determine the stability margin in real engineering applications. Therefore, this paper provides a practical stability analysis method for PWM DC–DC converters.
20 citations
TL;DR: In this paper, a first-order plus time-delay (FOPTD) system class with actuator rate limit is considered and the describing function of the rate limiter is derived to obtain the describing functions of the closed-loop and open-loop systems, and the onset frequency in the Nichols chart is used to analyze the rate limit effects in frequency domain.
20 citations
TL;DR: An enhanced event-based identification procedure for process control has been developed based on the information obtained from the oscillations that an event- based sampler introduces in the feedback loop, and can be extended to estimate models of any structure with five or more parameters.
Abstract: An enhanced event-based identification procedure for process control has been developed based on the information obtained from the oscillations that an event-based sampler introduces in the feedback loop. The describing function analysis is used to explain the basis of the method because the event-based sampler behaves as a static nonlinearity. Features of the method are (a) the event-based procedure does not require a priori process information, (b) noniterative algorithms are sufficient to derive the process parameters, (c) only one test is needed, and (d) it allows identifying the process at a user-specified phase angle in the third quadrant. The method is presented for estimation of most common transfer functions found in chemical and process industry: first and second order, as well as integrating processes with non-minimum-phase dynamics. Furthermore, the procedure can be extended to estimate models of any structure with five or more parameters.
16 citations
TL;DR: This paper presents the design of a linear state feedback controller for the stabilization of two inverted pendulums, namely, Furuta pendulum and pendubot, which allows eliminating the limit cycle that appears in the systems due to the effect of a nonlinearity, that is, dead-zone, which is induced by static friction at the motor shaft.
Abstract: This paper presents the design of a linear state feedback controller for the stabilization of two inverted pendulums, namely, Furuta pendulum and pendubot. Such a controller design allows eliminating the limit cycle that appears in the systems due to the effect of a nonlinearity, that is, dead-zone, which is induced by static friction at the motor shaft. To do this, the differential flatness approach is applied to the linear approximate model of the inverted pendulums under study. Then, the resulting flat systems are translated to the frequency domain for which a control scheme is proposed. Subsequently, the dead-zone nonlinearity is treated off-line as an approximation obtained through the describing function method. Since this is an approach intrinsically based on frequency response, the frequency response-based approach is suitable for tuning the gains of the proposed control scheme. An advantage of using the frequency response-based approach along with the describing function method is that they allow obtaining precise formulas that simplify the tuning of the proposed control scheme, so that the limit cycle caused by the dead-zone is eliminated. This must be contrasted with a time response-based approach, proposed recently by the authors, where precise formulas were not obtained and intuitive ideas have to be used to eliminate limit cycle. Finally, the procedure of the controller design herein proposed is verified via experimental tests.
16 citations
TL;DR: In this article, a new method to represent a given Flame Describing Function by analytical expressions is proposed, motivated by the observation that different types of expressions can be represented by different functions.
Abstract: In the present work, we formulate a new method to represent a given Flame Describing Function by analytical expressions. The underlying idea is motivated by the observation that different types of ...
13 citations
01 Jan 2018
TL;DR: It is concluded that the combined magnitude and combined phase are not mature enough to rely on during loop shaping and further work in this direction is required.
Abstract: PID is the most popular controller in the industry. PID controllers are linear, and thus have fundamental limitations, such that certain performance criteria cannot be achieved. To overcome these limitations, nonlinear reset control can be used. Reset control can achieve less overshoot and a faster response time than linear controllers. However, the resetting mechanism has a jump function which causes jumps in the control input, which can result in limit cycles. Linear filters and controllers are designed in the industry using loop shaping, which is done in the frequency domain. In this study it is investigated how to analyse reset systems in the frequency domain. A reset system is nonlinear, so transfer functions needs to be approximated by describing functions. The sinusoidal input describing function considers only the first harmonic of the output and therefore does not capture all the dynamics of the element. The effects of the higher order harmonics are important in precision systems, since unwanted dynamics should not be excited nor should performance be affected. In this thesis, the higher order sinusoidal input describing functions (HOSIDF) are derived analytically. The HOSIDF shows the magnitude and phase response per harmonic, such that stability and performance analysis can be improved. Because the HOSIDF shows multiple responses, it is not trivial how to do loop shaping. The information from the HOSIDF is combined, creating a combined magnitude and combined phase response. It is seen that the combined magnitude looks promising, but the combined phase has jumps. It is concluded that the combined magnitude and combined phase are not mature enough to rely on during loop shaping and further work in this direction is required.
TL;DR: The dynamical model of the DC-DC buck converter is identified by the relay feedback method using the gain and phase angle criteria and the converter dynamics obtained are compared with that estimated using the state-space averaging method.
Abstract: Accurate dynamics of power converters are necessary to achieve good control performance. In this study, the dynamical model of the DC-DC buck converter is identified by the relay feedback method. The relay is connected in the closed loop to produce a limit cycle output. The important information of the oscillatory output is used for the identification. The relay is approximated using dual-input describing function (DIDF) in the mathematical modelling. DIDF can handle symmetric and asymmetric limit cycle outputs. The converter is modelled as a second-order plus dead-time system. Using the gain and phase angle criteria, analytical expressions are derived to estimate the dynamics. The converter dynamics obtained from the proposed method are compared with that estimated using the state-space averaging method. The model is also identified from the real-time experiment. To check the efficacy of the identified model, a model validation test is performed.
25 May 2018
TL;DR: To achieve precise identification of backlash in gear systems, a new identification method is proposed on the basis of hysteresis backlash model and the describing function method, which results reveal can achieve precise backlash identification.
Abstract: To achieve precise identification of backlash in gear systems, a new identification method is proposed on the basis of hysteresis backlash model and the describing function method. A Discrete Fourier Transform is used to extract the fundamental components from the system output digital. Then the relationship between the phase angle of describing function and that of the fundamental components is utilized to identify backlash. A sinusoidal excitation with small amplitude and low frequency is applied as the system input, in order to reduce the impact and collision between meshing teeth, highlight the hysteresis effect and improve identification accuracy. A gear transmission system with backlash is considered as a numerical model, simulation results reveal this method can achieve precise backlash identification. Numerical tests with multi-group excitations are conducted, the results reveal that the effects of the selection of amplitude and frequency of excitation on the accuracy of the identification method can't be ignored.
01 Sep 2018
TL;DR: In this article, the authors proposed a more accurate small-signal equivalent circuit model based on perturbation on the state plane and describing function method for series resonant converter (SRC).
Abstract: Resonant converters operate the switching frequency close to the resonant frequency to achieve soft switching. However, this also posts a great challenge on the small-signal modeling. Based on the fundamental approximation, E. Yang develops the first small-signal equivalent circuit model. Recently, the authors propose a simpler model based on the average concept on a rotating state plane. The assumptions of the two models are shown to be equivalent. This implies the two approaches are applicable only when there is an effective bandpass filter. However, the resonant tank in more popular resonant converters such as LLC converter does not behave like a good band-pass filter. Therefore, this paper aims at providing a more accurate small-signal modeling. It is based on perturbation on the state plane and describing function method. Using the series resonant converter (SRC) as an example, the model shows a perfect match to a simulation result. Based on the fact that the system poles can be captured by the natural response, a simplified, yet accurate, second-order model for an SRC is provided. All the small-signal dynamic are well-explained using the proposed model. The proposed modeling and simplification methods show a promising extension to model the LLC converter.
01 Jan 2018
TL;DR: The paper presents a basic description and examples of the use of so called descriptive functions, allowing analysing the influence of inherent and indispensable components of all mechatronic systems mechanical subsystems so called hard nonlinearities.
Abstract: The paper presents a basic description and examples of the use of so called descriptive functions, allowing analysing the influence of inherent and indispensable components of all mechatronic systems mechanical subsystems so called hard nonlinearities. These parts "causing" in addition to the centrifugal and Coriolis generalized forcesthe nonlinearity of the system, can be analysed by the abovementioned method from the point of view of their origin and the estimation of the basic parameters of their frequent consequences so-called limit cycles. After a short introduction, which introduces and explains describing functions using the example of a nonlinear system taken from the literature, some of the socalled hard nonlinear subsystems (such as the mechanical chain of robots) are shown to be used. The paper is the first part of a more extensive description analysis of nonlinear systems concept using these functions in order to enable analysis and prediction of limit cycles.
TL;DR: Numerical results for a system involving a proportional–integral feedback controller are presented to demonstrate the advantage of the IHB-based approach over the DFM in approximating the harmonic response of the hysteretic system.
27 Jun 2018
TL;DR: In this paper, a novel reset control synthesis method is proposed: CRONE reset control, combining a robust fractional CRONE controller with non-linear reset control to overcome waterbed effect.
Abstract: In this paper a novel reset control synthesis method is proposed: CRONE reset control, combining a robust fractional CRONE controller with non-linear reset control to overcome waterbed effect. In CRONE control, robustness is achieved by creation of constant phase behaviour around bandwidth with the use of fractional operators, also allowing more freedom in shaping the open-loop frequency response. However, being a linear controller it suffers from the inevitable trade-off between robustness and performance as a result of the waterbed effect. Here reset control is introduced in the CRONE design to overcome the fundamental limitations. In the new controller design, reset phase advantage is approximated using describing function analysis and used to achieve better open-loop shape. Sufficient quadratic stability conditions are shown for the designed CRONE reset controllers and the control design is validated on a Lorentz-actuated nanometre precision stage. It is shown that for similar phase margin, better performance in terms of reference-tracking and noise attenuation can be achieved.
TL;DR: In this article, a modified relay feedback experiment for the generation of sustained oscillations in a class of dead-time plants and their mathematical modeling is presented in a real-time fashion.
Abstract: In this article, a modified relay feedback experiment for the generation of sustained oscillations in a class of dead-time plants and their mathematical modeling is presented in a real-time fashion. For the ease of calculation, an equivalent gain of the relay is considered using well-known describing function method and further utilized in the derivation of a set of simple analytical expressions for the estimation of plant model parameters. Simulation studies are considered to show the validation of the proposed models with the model obtained from Matlab System Identification Toolbox (SIT) and literature through integral absolute error index. Yokogawa distributed control system is considered as an experimental platform to conduct the relay autotuning test for the identification of a real-time liquid level control system in-terms of dead-time transfer function models. Finally, the accuracy of proposed models is demonstrated through frequency response plots as well as relay response plots in comparison with models obtained from Ziegler–Nichols tests and Matlab SIT.
TL;DR: In this paper, a novel reset control synthesis method is proposed: CRONE reset control, combining a robust fractional CRONE controller with non-linear reset control to overcome waterbed effect.
Abstract: In this paper a novel reset control synthesis method is proposed: CRONE reset control, combining a robust fractional CRONE controller with non-linear reset control to overcome waterbed effect. In CRONE control, robustness is achieved by creation of constant phase behaviour around bandwidth with the use of fractional operators, also allowing more freedom in shaping the open-loop frequency response. However, being a linear controller it suffers from the inevitable trade-off between robustness and performance as a result of the waterbed effect. Here reset control is introduced in the CRONE design to overcome the fundamental limitations. In the new controller design, reset phase advantage is approximated using describing function analysis and used to achieve better open-loop shape. Sufficient quadratic stability conditions are shown for the designed CRONE reset controllers and the control design is validated on a Lorentz-actuated nanometre precision stage. It is shown that for similar phase margin, better performance in terms of reference-tracking and noise attenuation can be achieved.
TL;DR: In this paper, the authors investigated the efficacy of a displacement feedback technique in generating self-excited oscillation at the desired mode(s) in a multiple degrees-of-freedom mechanical system.
Abstract: Many devices and processes utilize self-excited oscillation to enhance performance. Recently, much research work has been devoted to the induction of self-excited oscillation in mechanical systems by nonlinear feedback. The present paper investigates the efficacy of a displacement feedback technique in generating self-excited oscillation at the desired mode(s) in a multiple degrees-of-freedom mechanical system. The controller couples the system with a bank of second-order filters and generates the required control force as a nonlinear function of the filter output. The describing function method theoretically explores the dynamics of the system with the control law. The control cost of the controller is studied for the proper choice of the filter parameters. The analytical results are substantiated by the numerical simulation results. The present study reveals that the proposed control laws, if used in an appropriate way, can generate self-excited oscillation in the system at the desired mode(s).
01 Jan 2018
TL;DR: First-order SM, hysteresis relay control, twisting algorithm and sub-optimal algorithm are compared in terms of the gain margins of the averaged dynamics that can describe the propagation of external signals through a SM control system.
Abstract: In this book chapter, analysis of first-order and second-order sliding-mode (SM) control systems from the perspective of the gain margins of the averaged dynamics is done. These averaged dynamics result from the fact of the existence of chattering, so that averaging on the period of chattering can be considered. Analysis is done via the describing function method and the locus of a perturbed relay system method. First-order SM, hysteresis relay control, twisting algorithm and sub-optimal algorithm are compared in terms of the gain margins of the averaged dynamics that can describe the propagation of external signals through a SM control system.
02 May 2018
TL;DR: In this article, an analog of the direct Lyapunov method for differential inclusions was used to solve the stabilization problem in the Keldysh model of flutter suppression and rigorous approaches to its analysis.
Abstract: This work is devoted to the Keldysh model of flutter suppression and rigorous approaches to its analysis. To solve the stabilization problem in the Keldysh model we use an analog of direct Lyapunov method for differential inclusions. The results obtained here are compared with the results of Keldysh obtained by the method of harmonic balance (describing function method), which is an approximate method for analyzing the existence of periodic solutions. The limitations of the use of describing function method for the study of systems with dry friction and stationary segment are demonstrated.This work is devoted to the Keldysh model of flutter suppression and rigorous approaches to its analysis. To solve the stabilization problem in the Keldysh model we use an analog of direct Lyapunov method for differential inclusions. The results obtained here are compared with the results of Keldysh obtained by the method of harmonic balance (describing function method), which is an approximate method for analyzing the existence of periodic solutions. The limitations of the use of describing function method for the study of systems with dry friction and stationary segment are demonstrated.
TL;DR: System approximations are provided that can add more insight into the local behaviour of biomolecular signalling systems than standard linearisation, compute responses to other periodic inputs and to analyse limit cycles.
Abstract: Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of analytical and computational approaches, the authors adapt and develop the method of describing functions to represent the input-output responses of biomolecular signalling systems. They approximate representative systems exhibiting various saturating and hysteretic dynamics in a way that is better than the standard linearisation. Furthermore, they develop analytical upper bounds for the computational error estimates. Finally, they use these error estimates to augment the limit cycle analysis with a simple and quick way to bound the predicted oscillation amplitude. These results provide system approximations that can add more insight into the local behaviour of these systems than standard linearisation, compute responses to other periodic inputs and to analyse limit cycles.
TL;DR: Within this manuscript a nonlinear model of a CLLC DCDC converter is derived by means of the extended describing function method and a dq decomposition to allow for a small signal analysis of the system.
01 Oct 2018
TL;DR: Large-signal sequence impedance modeling for three-phase voltage source converters (VSC) with dq-current control and PLL is presented, leveraging the dominating influence of hard nonlinearities such as pulse-width modulation saturation and limiters over soft non linearities in shaping the converter large-signals behavior.
Abstract: Resonance problems have become a major hurdle in the large-scale grid integration of renewable energy. It is important to be able to predict the amplitude of resonance-induced distortions for the protection and control design of power electronic converters. We recently presented an impedance-based approach for the prediction of resonance amplitude. It was shown that the impedance response of a converter starts changing with the amplitude of resonance; this blocks the amplitude growth beyond a certain point where the converter forms a limit cycle mode of sustained oscillations. The large-signal impedance of a converter captures the change in its impedance response with the resonance amplitude, and it can be used to predict the resonance amplitude under different operation conditions. This paper presents large-signal sequence impedance modeling for three-phase voltage source converters (VSC) with dq-current control and PLL. Modeling challenges encountered in the absence of the small-signal approximation are addressed by a) leveraging the dominating influence of hard nonlinearities such as pulse-width modulation saturation and limiters over soft nonlinearities in shaping the converter large-signal behavior and b) modeling the large-signal gain of hard nonlinearities using appropriate describing functions. Developed large-signal impedance models are validated using numerical simulations. Measurements of the large-signal impedance responses of a commercial 1-MW VSC-based inverter are also presented to experimentally demonstrate the effects of the injected perturbation amplitude on impedance response as predicted by the developed model.
13 Jun 2018
TL;DR: It has been proved that the mentioned stability analysis method for flyback converter is precise by comparing the simulation and experimental results.
Abstract: Flyback converter is widely used in switching power supply and the stability analysis for it is critical. However, the result of the stability analysis method based on the traditional linear small-signal model is not accurate enough because the nonlinear characteristics of the switching process are ignored in the analysis process. In this paper, the accurate modeling and stability analysis for flyback converter are carried out by using describing function method. Firstly, the linear and nonlinear small-signal model are respectively established for flyback converter. Following that, the stability criterions are derived from the two above models accordingly. Finally, according to the two criterions, the stability analysis results are respectively presented. It has been proved that the mentioned stability analysis method is precise by comparing the simulation and experimental results.
01 Sep 2018
TL;DR: A high frequency accurate small signal model for IQCOT control has been derived using describing function method and an auto-tuning method for Q-value control is proposed in this paper.
Abstract: These days, constant on-time current mode (COTCM) control schemes are very popular in the multiphase voltage regulator (VR) controllers because of its higher light load efficiency and better small signal characteristics. The issue of these ripple based COTCM control in multiphase operation is that when the inductor current ripple becomes very small at certain duty cycles due to ‘ripple cancellation effect’, control becomes very noise sensitive. Recently, a novel non-ripple based ‘Inverse Charge Constant On-Time (IQCOT)’ control has been proposed which can operate seamlessly at ripple cancellation point in multiphase operation. This new control improves the transient response in single and multiphase operations too. However, a high frequency small signal model for this new IQCOT control is required for its high bandwidth control loop design. In this paper, a high frequency accurate small signal model for IQCOT control has been derived using describing function method. Form the derived model it is found that the quality factor (Q) of one double pole set varies with duty cycle change which makes the high bandwidth design very challenging for a wide duty cycle range. To overcome this challenge, an auto-tuning method for Q-value control is also proposed in this paper. The derived high frequency model and auto-tuning method are also verified by small signal bode plot simulation and test results.
01 Jan 2018
TL;DR: While there is an improvement in tracking and steady state precision performance by using CgLp compared to normal PID, there is deterioration of the performance although describing function predicted an improvement, this thesis focuses on a performance analysis and tuning of a novel reset element called ’Constant in Gain, Lead in Phase’.
Abstract: The high-tech industry is pushing the motion system technology towards faster, more precise and more robust system. One of the keys to this growing demand is the advancement of motion control. To this day, Proportional-Integral-Derivative (PID) has been the workhorse for the industry system control. This is because PID is simple to design and implement and adapt to industrial loopshaping method. Nevertheless, PID suffers fundamental limitations of linear control. To deal with this, a nonlinear control should be utilized. Reset control is a nonlinear control that is still easy but can overcome the limitation of linear control and more importantly, loop shaping method can be used to reset control by using describing function analysis which is pseudo-approximation of nonlinear system that based on the first harmonic. However, reset control also introduces higher order harmonics into the system that can negatively affect system performance. This is because these harmonics may cause some unwanted dynamics present in system response. Describing function which is the common tool to analyze and design reset control is not accurate enough since higher order harmonics are not considered. Recently, a tool to visualize higher order harmonics in frequency domain is developed. This open the possibilities to study the behavior of higher order harmonics and its effect to system performance. This thesis focuses on a performance analysis and tuning of a novel reset element called ’Constant in Gain, Lead in Phase’(CgLp). It is shown by the literature that reset control is often utilized to provide phase lag reduction but CgLp has shown the use of reset control to provide phase compensation and this improves system performance. Since its introduction, no guidelines available in the literature to design and tune CgLp. Looking at its potential to be industry standard for motion control, finding guidelines to tune CgLp is an important step to achieve this goal. To do the optimal tuning of reset element, higher order harmonics should be considered so that the effect of unwanted response can be minimized while maintaining the advantage of reset control. Therefore, the work in this thesis is performed by doing performance analysis of CgLp through describing function and HOSIDF. It is shown that while there is an improvement in tracking and steady state precision performance by using CgLp compared to normal PID, there is deterioration of the performance although describing function predicted an improvement. This is because there is a trade-off between improvement by CgLp and the rise of higher order harmonics gain. In this work, the higher order harmonics was considered at the bandwidth frequency and normalized over its first harmonic. It was observed that the optimal performance is achieved when the highest gain value of normalized 3rd harmonic is around half of maximum possible value of normalized 3rd harmonic.
20 May 2018
TL;DR: This paper focuses on tuned WPT systems and proposes the reduced-order dynamical models, which are derived from the energy point of view and have much lower orders and simpler formulae as compared to the existing models.
Abstract: Dynamical models are of primary interest when studying the dynamical control of wireless power transfer (WPT) systems. Most existing dynamical models of WPT systems are derived using the generalized state space averaging method, extended describing functions, or the concept of coupled modes. These models are applicable to both tuned and detuned WPT systems but suffer from high orders and complex formulae. This paper focuses on tuned WPT systems and proposes the reduced-order dynamical models, which are derived from the energy point of view. The proposed models have much lower orders and simpler formulae as compared to the existing models. Experimental results are presented for verification.
01 Sep 2018
TL;DR: The proposed stability criterion for two-stage cascaded DC-DC converters system is proposed by combining the describing function method and linearization of source converter or load converter and verified by simulation and experimental results.
Abstract: Though the sub-module works stably alone, the cascaded DC-DC converters system may work unstably on account of the interaction among the sub-modules. Therefore, the stability analysis of cascaded DC-DC converters system is a hot issue. In this paper, at the beginning, the stability criterion for single DC-DC converter based on describing function method is reviewed. Following that, taking two-stage cascaded boost converters system as an example, the linearization of source converter or load converter is applied to analyze the stability of cascaded DC-DC converters system. What's more, the stability criterion for two-stage cascaded DC-DC converters system is proposed by combining the describing function method and linearization of source converter or load converter. Finally, the proposed stability criterion in this paper is verified by simulation and experimental results, which provides a novel stability analysis approach for cascaded DC-DC converters system based on describing function method.