Showing papers on "Describing function published in 2020"

Robust Quasi-Predictive Control of $LCL$ -Filtered Grid Converters

Abstract: This paper proposes a new control strategy for grid-connected $LCL$ -filtered voltage source converters (VSCs). It is realized by cascading a proportional-resonant (PR) controller, which regulates the grid-side current, and a finite-set model predictive controller (FS-MPC), which is responsible for controlling the filter's capacitor voltage and active damping of the resonance. The overall control circumvents the drawbacks of using only the FS-MPC to control the converter, such as steady state tracking error, weighting factor tuning complexity, and need to use long prediction horizons for optimal performance, but it keeps its advantageous properties. Namely, due to FS-MPC's direct manipulation of the VSC switches, the pulsewidth-modulation delay does not exist, while a high sampling rate leads to only insignificant computational delay. As a consequence, the system achieves far less magnitude and phase roll-off in the high-frequency region that allows considerable increase of dynamic performance compared to conventional control approaches. Moreover, the inner FS-MPC-based regulator exhibits a flat frequency response, which indicates that there is no need for designing a dedicated AD. The overall control design procedure is then largely simplified as only the proportional gain of the PR controller needs to be tuned. These properties are proved using a describing function method where a linear approximation of the FS-MPC regulated VSC and an inner $LC$ filter is derived in the frequency domain and integrated together with the model of the PR controller and grid side inductor. The controller has been analyzed analytically and validated through experimental results, where design correctness and robustness to grid-side inductance variations have been tested.

Characterization of Subsynchronous Oscillation with Wind Farms Using Describing Function and Generalized Nyquist Criterion

Abstract: Eigen-analysis is widely used in the studies of power system oscillation and small-signal stability. However, it may give inaccurate analyses on subsynchronous oscillation (SSO) when nonlinearity is not negligible. In this paper, a nonlinear analytical approach based on the describing function and generalized Nyquist criterion is proposed to analyze the characteristics of SSO with wind farms. The paper first presents describing function-based model reduction considering key nonlinear elements involved in SSO, and then uses a generalized Nyquist criterion for accurate estimation of SSO amplitude and frequency. The results are verified by time-domain simulations on a detailed model with different scenarios considering variations of the system condition and controller parameters.

Digital Multi-Loop Control of an LLC Resonant Converter for Electric Vehicle DC Fast Charging

Abstract: This paper proposes a digital control strategy for LLC resonant converters, specifically intended for EV battery charging applications. Two cascaded control loops, i.e. an external battery voltage loop and an internal battery current loop, are designed and tuned according to analytically derived expressions. Particular attention is reserved to the output current control analysis, due to its extremely non-linear behaviour. The well known seventh-order LLC small-signal model, derived with the extended describing function (EDF) method, is simplified to an equivalent first-order model at the resonance frequency. In these conditions, which are proven to be the most underdamped, the current control loop is tuned taking into account the delays introduced by the digital control implementation. Moreover, the adoption of a look-up table (LUT) in the feed-forward path is proposed to counteract the system non-linearities, ensuring high dynamical performance over the full frequency operating range. Finally, the proposed control strategy and controller design procedure are verified both in simulation and experimentally on a 15 kW LLC converter prototype.

A Bidirectional Wireless Power Transfer System Control Strategy Independent of Real-Time Wireless Communication

Abstract: For the bidirectional wireless power transfer (BWPT) technology, the phase synchronization between the transmitting and receiving converters is very essential and difficult to achieve by wireless communication between two sides because the delay and data transfer interval of wireless communication severely influence the control performance. This article proposes a novel control strategy for BWPT, which can achieve the phase synchronization and maximum efficiency point tracking independent of the real-time wireless communication. To solve the overshoot and oscillation problem incurred by the proposed control strategy and the nature of the system itself, the dynamics of a series–series compensated BWPT system is then analyzed and a small-signal model of this system is derived based on the generalized state space averaging and extended describing function methods. Using the small-signal model, a BWPT control system based on the proposed control strategy is designed and optimized. The validity of the proposed strategy and the performance of the control system are verified experimentally using a 3.3-kW prototype system.

Reduced-Order Modeling and Design of Single-Stage LCL Compensated IPT System for Low Voltage Vehicle Charging Applications

Abstract: In this paper, single-stage LCL inductive power transfer (IPT) system is proposed in low voltage vehicle charging applications to minimize the system complexity, and its reduced-order modeling and design approach is presented. To deal with the high-order resonant tank, the reduced-order methodology is applied throughout the paper, with which the behavior of resonant tank is investigated under multiple scales. Using the reduced-order time-domain model, the resonant waveform within switching period is accurately described with only one cycle's numerical computation. A novel parameter design principle for realizing ZVS condition and high averaged efficiency within full load range is then proposed and serves as parametric basis. Next, the low-order linear frequency-domain model is deduced using Extended Describing Function (EDF). It is found that six-order LCL-type system behaves as second-order underdamped system within frequency range of interest. Compared to existing models, the proposed reduced-order model features much more simplicity as it provides intuitive understanding into both steady and dynamic characteristic of the converter while facilitating the parameter and controller design. Through above work, the overall design consideration towards a single-stage LCL IPT system is elaborated. Finally, experimental results are given to verify accuracy of the models as well as the effectiveness of designed parameters and controller.

On Consensus of Second-Order Multiagent Systems With Actuator Saturations: A Generalized-Nyquist-Criterion-Based Approach.

Abstract: In this article, a frequency-domain approach is developed to deal with the global consensus problem for a class of general second-order multiagent systems (MASs) subject to actuator saturations. By employing the describing function and the generalized Nyquist criterion, the global consensus problem is thoroughly investigated for both undirected and directed topologies. First, the describing function is introduced to characterize the actuator saturations in the s-plane, and the inherent representation error is quantitatively analyzed from a frequency-domain perspective. Then, by means of the Kronecker product, the addressed consensus problem of the MAS is transformed into a corresponding stability analysis problem for a certain multi-input-multi-output (MIMO) system and, consequently, the generalized Nyquist criterion for MIMO systems is exploited to derive the condition for the global consensus of the MAS where the impact from the actuator saturation is explicitly reflected. Finally, numerical simulations are provided to illustrate the validity of the proposed theoretical result.

The Optimal Sequence for Reset Controllers

Abstract: The PID controller is one of the most used controllers in the industry. However, fundamental limitations due to linearity restrict its performances when higher bandwidth, stability, and precision are required simultaneously in today’s high-tech industry. Reset control is a promising nonlinear control strategy which can overcome these limitations. But it also brings new problems. High order harmonics are introduced into the system because of non-linearity which lead to unwanted dynamics and deterioration of performances. So it is necessary to reduce them as much as possible. It is found that the sequence of different parts of a reset controller has effects on the magnitude of high order harmonics. Through high order sinusoidal input describing functions (HOSIDOFs) tool, the optimal sequence of the open loop in which the magnitude of high order harmonics is minimum is achieved for a general reset controller. The superiority of the suggested sequence in the closed-loop system is validated through both simulation and experiments at a Lorentz-actuated precision positioning stage.

A Novel Accurate Adaptive Constant On-Time Buck Converter for a Wide-Range Operation

Abstract: The ripple-based constant on-time (COT) control with ripple compensation has been widely adopted in buck converters in the recent years because of its simplicity, fast transient response, and high light-load efficiency. However, this control has the potential issues of instability and excessive load transient response with wide input/output voltage range conditions in the power management integrated circuit (PMIC) applications. In this article, an accurate adaptive COT control scheme is proposed to solve these problems. The control scheme achieves accurate output voltage, and nearly constant quality factor and well transient response over a wide-range operation with simple circuit. The small-signal model is also derived based on the describing function (DF) technique for design optimization. Finally, the simulations and experimental verifications were conducted to verify the proposed concepts.

Compensation strategies based on Bode step concept for actuator rate limit effect on first-order plus time-delay systems

Abstract: Rate limit of system actuators is one of the major restrictions in the physical world. However, in classical and modern control design, the actuator rate limit has always been neglected. The rate limit generates amplitude attenuation and phase delay of the control signal, which will deteriorate closed-loop system performance, and may even lead to system instability. In this study, the Bode step control method was applied to the first-order plus time-delay system to achieve a better tolerance of smaller rate limit value. A rate limit compensation strategy is proposed based on the describing function and the onset frequency of the rate limiter. Both illustrative example and hardware-in-the-loop experiments are given to show the effectiveness of Bode step controller and the proposed rate limit compensation method.

Benefiting from Linear Behaviour of a Nonlinear Reset-Based Element at Certain Frequencies

Abstract: This paper addresses a phenomenon caused by resetting only one of the two states of a so-called second order “Constant in gain Lead in phase” (CgLp) element. CgLp is a recently introduced reset-based nonlinear element, bound to circumvent the well-known linear control limitation - the waterbed effect. The ideal behaviour of such a filter in the frequency domain is unity gain while providing a phase lead for a broad range of frequencies, which clearly violates the linear Bode's gain phase relationship. However, CgLp's ideal behaviour is based on a describing function, which is a first order approximation that neglects the effects of higher order harmonics in the output of the filter. Consequently, achieving the ideal behaviour is challenging when higher order harmonics are relatively large. It is shown in this paper that by resetting only one of the two states of a second order CgLp, the nonlinear filter will act as a linear one at a certain frequency, provided that some conditions are met. This phenomenon can be used to the benefit of reducing higher order harmonics of CgLp's output and achieving the ideal behaviour and thus better performance in terms of precision.

Nonlinear Stability Analysis for Three-Phase Grid-Connected PV Generators

Abstract: Numerous emerging oscillatory stability issues have recently arisen as renewable energy sources (RESs) are integrated into the power system. Some of the existing literature attempts to explain these issues through the corresponding simplification, which usually omits the influence of the nonlinear discontinuous elements in the system. Hence, the obtained results are incomplete. To fill this gap, this article proposes a stability analysis method based on the describing function (DF) method to explore the influence of nonlinear discontinuous elements in the system. Without loss of generality, taking the three-phase grid-connected photovoltaic (PV) generator as the research object, the perturbation and observation (P&O)-based power control, which is a typical nonlinear discontinuous element, was carefully studied. First, the complete mathematical model of the three-phase grid-connected PV generator was established, including the outermost P&O-based power control. Then, according to the DF method, the stability of the PV generator was analyzed, and the related influence factors were studied in detail. It was found that the nonlinear discontinuous P&O-based power control has a substantial influence on the stability of the PV generator and can result in the oscillation. At the same time, the DF method and the conventional method were compared, which shows that the proposed DF method can enhance the accuracy of the stability assessment. Especially regarding critical stability, the oscillation magnitude and frequency can be calculated accurately. All the theoretical analyses were verified by the real-time hardware-in-loop (HIL) tests.

NARMAX Identification Based Closed-Loop Control of Flow Separation over NACA 0015 Airfoil

Abstract: A closed-loop control algorithm for the reduction of turbulent flow separation over NACA 0015 airfoil equipped with leading-edge synthetic jet actuators (SJAs) is presented A system identification approach based on Nonlinear Auto-Regressive Moving Average with eXogenous inputs (NARMAX) technique was used to predict nonlinear dynamics of the fluid flow and for the design of the controller system Numerical simulations based on URANS equations are performed at Reynolds number of 106 for various airfoil incidences with and without closed-loop control The NARMAX model for flow over an airfoil is based on the static pressure data, and the synthetic jet actuator is developed using an incompressible flow model The corresponding NARMAX identification model developed for the pressure data is nonlinear; therefore, the describing function technique is used to linearize the system within its frequency range Low-pass filtering is used to obtain quasi-linear state values, which assist in the application of linear control techniques The reference signal signifies the condition of a fully re-attached flow, and it is determined based on the linearization of the original signal during open-loop control The controller design follows the standard proportional-integral (PI) technique for the single-input single-output system The resulting closed-loop response tracks the reference value and leads to significant improvements in the transient response over the open-loop system The NARMAX controller enhances the lift coefficient from 0787 for the uncontrolled case to 1315 for the controlled case with an increase of 671%

Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors

Abstract: We, herein, present a new model based on the framework of synchronization to describe a thermoacoustic system and capture the multiple bifurcations that such a system undergoes. Instead of applying flame describing function to depict the unsteady heat release rate as the flame’s response to acoustic perturbation, the new model considers the acoustic field and the unsteady heat release rate as a pair of nonlinearly coupled damped oscillators. By varying the coupling strength, multiple dynamical behaviors, including limit cycle oscillation, quasi-periodic oscillation, strange nonchaos, and chaos, can be captured. Furthermore, the model was able to qualitatively replicate the different behaviors of a laminar thermoacoustic system observed in experiments by Kabiraj et al. (Chaos (Woodbury, N Y) 22:023129, 2012). By analyzing the temporal variation of phase difference between heat release rate oscillations and pressure oscillations under different dynamical states, we show that the characteristics of the dynamical states depend on the nature of synchronization between the two signals, which is consistent with previous experimental findings.

Mitigating vortex-induced vibration by acceleration feedback control

Abstract: Vortex-induced vibration is a common phenomenon observed in many engineering applications and it is detrimental to the performances and health of the system. It is, therefore, imperative for engineers to make suitable design modifications or arrange for some type of control device to mitigate such oscillations. In this paper, the performance of the acceleration feedback control is compared with that of the simple passive vibration absorber. The effect of time-delay in the feedback loop is also investigated. The acceleration of the primary system is measured and passed through a second-order compensator. The active absorber is designed by setting the filter frequency same as the natural frequency of vibration and the optimum filter damping is numerically obtained. Nonlinear analysis is performed using the Describing Function method and the results are validated using direct numerical simulation performed in MATLAB Simulink. In the present paper, vortex shedding frequencies are selected from two different regions, one with vortex shedding frequency less than the natural frequency of the system and other having vortex shedding frequency higher than the natural frequency of the system. It is observed that the acceleration feedback control can effectively reduce the amplitude of vibration to a great extent. It is also observed that the amplitude of the system changes marginally (up to a certain value of time-delay) in the pre-locking and locking region. However, the effect of time-delay in post-locking zone is detrimental. Beyond a certain value of the time-delay, the amplitude becomes large and even the system may become unstable.

Closed-loop frequency analyses of reset systems.

Abstract: Today, linear controllers cannot satisfy requirements of high-tech industry due to fundamental limitations like the waterbed effect. This is one of the reasons why nonlinear controllers, such as reset elements, are receiving increased attention. To analyze reset elements in the frequency domain, researchers use the Describing Function (DF) method. However, it cannot accurately predict the closed-loop frequency responses of the system because it neglects high order harmonics. To overcome these barriers, this paper proposes a mathematical framework to model the closed-loop frequency responses of reset systems including the closed-loop high order harmonics. Furthermore, pseudo-sensitivities for reset systems are defined to make their analyses more straight-forward. In addition, a user-friendly toolbox is developed based on the proposed approach to facilitate frequency analyses of reset systems. To show the effectiveness of the method, multiple illustrative examples on a high-tech precision positioning stage are used to compare the results of the closed-loop frequency responses obtained using our proposed method with DF method. The results demonstrated that the proposed method is significantly more precise than the DF method. Indeed, this developed toolbox can enable reset controllers to be widely-used in industry and academia.

Tuning PID controllers with symmetric send-on-delta sampling strategy

Abstract: A procedure for tuning PID controllers with SSOD sampling for FOPTD systems is proposed. It is based on the definition of a new robustness measure to avoid limit cycle oscillations, called the Tsypkin margin (MT). This margin is based on the Tsypkin method and does not rely on the attenuation of high order harmonics, as the describing function approaches require. Therefore, the avoidance of limit cycle oscillations can be guaranteed for any system, as a difference with the describing function based procedures. The procedure allows to obtain the PID controller that minimizes the disturbance IAE while fulfilling constraints on robustness to oscillations and on control action bumps due to the SSOD sampling. A freely available Java tool has been developed in order to simplify the application of the tuning procedure. In case of a non FOPTD system, it first calculates an approximate FOPTD model. The paper shows that the derivative filter parameter, N is a critical tuning parameter in order to find a compromise between performance and control action bumps.

Analysis of Digital PCM-Controlled Boost Converter With Trailing-Edge Modulation Based on z -Domain and Describing-Function Model

Abstract: Digital trailing-edge modulated peak-current-mode (PCM) control scheme is commonly used in power converters, due to the similar excellent characteristics with its peer analog controller and being achieved easily in practice. However, the additional issues, such as time delays, quantization error, and resolution of the digital pulsewidth modulator (DPWM), in the digital controller, not only reduce the stability of the converter but also make the modeling and analysis more complicated. Taking the digital controlled boost converter as an example, this article presents a $z$ -domain model of the whole converter system on the basis of a describing-function method by considering the effects of the abovementioned problems. The influences of time delays from analog-to-digital conversion (ADC) and DPWM and resolution from the DPWM module can be analyzed clearly according to the proposed model. And more importantly, the critical resolution between stable and unstable operations of the converter can be determined by checking the eigenvalues. Furthermore, the stability analysis based on the presented $z$ -domain model is verified by the simulations and experiments.

A double input describing function approach for stability analysis in centerless grinding under interrupted cut

Abstract: This article presents a novel stability analysis of plunge centerless grinding. The analysis considers the nonlinearity associated to wheel-workpiece detachment under large waviness. The loss of contact is approximated by a harmonic linearization, in the frequency domain, by a double input describing function (DIDF). The stability analysis shows the effects of clipping and structural compliance: both clearly produce a waviness with a quasi-integer number of lobes. Our approach removes the need of additional hypotheses, sometime found in the literature. Under increasing lobes amplitude, clipping reduces waviness growth rate until a limit cycle is reached. Numerical and experimental verifications are provided.

Design-Oriented Equivalent Circuit Model for Resonant Converters

Abstract: Resonant converters are popular for their inherent soft-switching capability Small-signal models for those converters are critical for an optimal controller design The equivalent circuit models available so far are based on the fundamental harmonic approximation This requires the resonant tanks to behave as good band-pass filters Consequently, the models work well for series resonant converter (SRC) but not LLC converter Moreover, the resulting models are too complicated to be useful and the corresponding simplified versions further sacrifice the accuracy The recent modeling breakthrough is based on the describing function method The accurate analytical models for both SRC and LLC are presented for the first time Not surprisingly, the exact models are shown to be infinite-order systems In most of the applications, the frequency range of interest is below the switching frequency, meaning the models can be simplified into a proper reduced-order form This paper proposes a methodology to simplify the complicated results from the describing function method, and the corresponding equivalent circuit models is developed For example, the proposed third- order model for the LLC converter is accurate at half switching frequency In addition to the accuracy, the simplified models provide significant insights on the small-signal dynamics of resonant converters

Regular quantisation with hysteresis: a new sampling strategy for event-based PID control systems

Abstract: In this study, a new sampling strategy for networked control systems, called regular quantification with hysteresis (RQH), is proposed. This alternative presents some benefits with respect to symmetric-send-on-delta sampling, which is one of the most used strategies in the event-based proportional–integral–derivative (PID) control loops. The behaviour of the RQH is defined by two parameters, the signal quantification and hysteresis, whose effect on the overall system performance is studied and guidelines about its choice are given in terms of noise measurement and steady-state error. The limit cycle oscillations that could be induced by this sampling strategy are studied and new robustness measures to avoid them are proposed based on the describing function approach. The suitability of some tuning rules for continuous PI when applied to control systems with a RQH sampling is evaluated using the proposed measures. The results show that these tuning rules can be applied under certain conditions.

Linear Active Disturbance Rejection Control of LLC Resonant Converters for EV Chargers

Abstract: LLC resonant dc-dc converters have been increasingly adopted in electric vehicle (EV) charger applications because of high efficiency and power density. However, multiple disturbance factors and complex dynamic characteristics make the high performance control still a challenging problem. A new linear active disturbance rejection control (LADRC) strategy for the LLC converter is proposed to improve the dynamic performance and suppress the influence of internal and external disturbances on the output voltage in this paper. First, based on the extended describing function (EDF) method, the mathematical model of the LLC converter is established. Then, a second order LADRC controller is designed to eliminate various disturbances. In addition, a compensation function is proposed to reduce the computational burden of the linear extended state observer(LESO). Finally, simulations compared with traditional PI controller are used to show the feasibility and effectiveness of the proposed strategy.

Gust Response Computations with Control Surface Freeplay Using Random Input Describing Functions

Abstract: An analytical and computational investigation of the effect of control surface freeplay on aeroelastic behavior, including random gust response and limit cycle oscillations (LCO), is presented. An ...