Closed-loop Transfer Function Research Articles

The Frequency- and the Time-Domain Design of a Dual Active Bridge Converter Output Voltage Regulator Based on the D-Decomposition Technique

Commonly used variants of the proportional-integral, PI, and the integral-proportional, IP, compensator gains selections, merged with the $\mathfrak {D}$ -decomposition technique are presented in this paper. The motivation to this work is the willingness to check whether such a combination can lead to unified and perhaps simplified approach in this matter. Therefore, the $\mathfrak {D}$ -decomposition technique has been effectively combined with the frequency- and the time-domain driven requirements regarding the control dynamics. Criteria such as the gain- and phase-margins, $(GM, PM)$ , the sensitivity, $M_{\text {S}}$ , the pole placements by means of the $(\sigma, \omega _{\text {d}})$ and the $(\xi, \omega _{\text {n}})$ , and the overshoot with the rise time $(\delta, t_{\text {r}})$ are considered. It has been shown that the control design effort can be reduced by the means of the $\mathfrak {D}$ -decomposition to intuitive judgments in the proportional and integral gains coordinates $(K_{\text {P}}, K_{\text {I}})$ with parametric curves. As such it can be thought of as a promising scenario in a case considered. The analyses are presented and discussed in details. They are conducted basing on example of output voltage closed loop control of the Dual Active Bridge, DAB, converter. The circuit operates under the phase shift control scheme. The control-to-output transfer function identification and the control circuit delays are included in the analyses. The case analysis have shown that the time domain requirements are less effectively met with the PI regulator when compared to its IP configuration. This is due to the commonly used simplifications during conversion between the $(\xi, \omega _{\text {n}})$ and the $(\delta, t_{\text {r}})$ in presence of uncompensated zero of the closed loop transfer function. The paper contains complete and intelligible approach to dedicated mathematical investigations verified experimentally.

Analysis of the influence of control parameters on the interaction between direct-driven wind turbines

In order to study the influence of control parameters on the interaction between direct-driven wind turbines, this paper presents the interaction model and analysis method of direct-driven wind turbines. Firstly, the harmonic linearization method is used to establish the interaction model of two direct-driven wind turbines, and the interaction mechanism between the two units is studied; secondly, the influence of phase-locked loop and DC voltage loop on the interaction between the two units is analyzed from the perspective of bandwidth and damping ratio of second-order closed-loop transfer function, and the interaction law of phase-locked loop and DC voltage loop on the interaction between the two units is studied and summarized; finally, the time-domain simulation of the two units grid-connected system is carried out, and the results are compared with the frequency domain analysis results to verify the rationality of the theoretical analysis.

Active and Passive Suspension System Performance under Random Road Profile Excitations

Passive suspensions are designed to satisfy the conflicting criteria of riding comfort and vehicle handling. An active suspension system attempts to overcome these compromises to provide the best performance for vehicle control. Different types of mathematical models have been used to study the suspension system of a vehicle. The quarter vehicle model is used for initial investigation. Later, the half vehicle and full vehicle models are used for the study, which is closer to the actual model of a vehicle suspension. In this paper, the behavior of a suspension system is analyzed using the full vehicle model. In the current work, the dynamic equation and their state-space formulation are presented for the full vehicle model to understand the system prior to the controller design. The open-loop response of the full vehicle suspension system, when subjected to various road excitations, is also studied. The procedure of modeling a SIMULINK model for passive suspensions system is discussed in detail. Design of the simple Proportional Integral Derivative (PID) feedback and feed-forward controller is presented for the active suspension system using transfer functions. Closed-loop transfer functions are also derived and their responses are plotted. To analyze the rollover behavior simulation for cornering is also performed in the current study.

In-Run Scale Factor Compensation for MEMS Gyroscope Without Calibration and Fitting

This paper presents an in-run scale factor error compensation for the micro-electro-mechanical system (MEMS) gyroscope without system calibration and data fitting. The causes of three scale factor errors (instability, nonlinearity, and asymmetry) are analyzed. Next, the instability and nonlinearity by open-loop detection (Mode I), and closed-loop detection (Mode II) are discussed according to the specific comb capacitance and the front-end detection circuit. The closed-loop detection transfer function is studied, and a series of equivalent conversions are performed to obtain a method (Mode III) for improving the temperature stability of scale factor. The results of the experiment indicated that the nonlinearity and asymmetry of the Mode II and Mode III are increased by 1.8 times and 3.5 times than that of Mode I. Furthermore, the instability of Mode II and Mode III is reduced by 10 times and 19 times over -20°C to 40°C. Besides, the mode III does not affect the static and dynamic performance of gyroscope according to the test results of bias and bandwidth.

Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback Systems

It is shown that the classic Nyquist criterion can be extended in a straightforward way to feedback systems of fractional order. The proof of this extension merely requires basic notions of vector analysis and of closed-loop system transfer functions. The criterion can be used not only to ascertain the stability of a fractional-order system but also to detect the presence of closed-loop poles inside any given sector of the complex plane. The test is finally applied to three examples of didactic value.

Robust current control scheme for single‐phase PWM rectifiers based on improved μ ‐synthesis in electric locomotive

The parameter perturbation of grid-side equivalent inductance is a significant feature of the uncertainty in the single-phase pulse-width modulation rectifiers system for the electric locomotive. This characteristic tends to reduce the robustness of the rectifier system. This study handles these problems in the framework of the structured singular value, which helps to reduce the influence of model parameter perturbation, caused by measurement error and operation condition change, on the robustness. However, the conventional μ-synthesis robust controls only reflect tracking and anti-disturbance performance by weighting functions and ignoring the dynamic response performance. Herein, a direct current control (DCC) scheme based on improved μ-synthesis is proposed. A desired closed-loop transfer function is introduced to the conventional μ-synthesis control structure to ameliorate the performance of the dynamic response. Furthermore, considering the external disturbances on the system control output, a suitable weighting function is used to restrict the external disturbance. The input–output relationship of the generalised open-loop plant can thus be constructed accordingly. The proposed control scheme is compared with the widely applied proportional–integral-based DCC scheme and the conventional μ-synthesis DCC scheme. Hardware-in-the-loop experiment results show promising dynamic performance as well as stronger robustness against parameter perturbation and external disturbances.

Practical Estimation of Accuracy in Power Hardware-in-the-Loop Simulation Using Impedance Measurements

Power hardware-in-the-loop (PHIL) simulation is a technique whereby actual power hardware is interfaced to a virtual surrounding system, simulated in real-time, through PHIL interfaces making use of power amplifiers and/or actuators. While PHIL simulation affords many advantages for flexible testing of power hardware, the accuracy of the experiment can be degraded through the non-ideal aspects of the PHIL interface, including distortion in the frequency domain, delays, and disturbances. This paper presents a practical method to estimate a subset of the closed-loop transfer function accuracy metrics of a PHIL experiment based on impedance measurements from the experiment. The method of assessing the impacts of the PHIL interfaces is demonstrated through application to an experiment in which two simulated systems are coupled through two PHIL interfaces with high bandwidth power amplifiers, enabling comparison of results with those from the ideal system.

Optimal fractional‐order controller design using direct synthesis method

In this study, an optimal fractional-order controller is proposed for a type of fractional-order model utilising the direct synthesis method. In that respect, the fractional counterpart of the second-order integer transfer function is selected as a closed-loop reference transfer function. The stability region of the fractional-order closed-loop reference transfer function is given via a theorem and related lemmas. Considering that a unity feedback loop is used, the parameters of the fractional-order closed-loop reference transfer function are specified based on the integral square error performance index within the specified stability region using a genetic algorithm. The time-domain characteristics of the optimal fractional-order closed-loop reference transfer function are compared with those of the optimal second-order integer closed-loop reference transfer function. The fractional- and integer-order controllers that are designed based on optimal closed-loop reference transfer functions are implemented on a real-time system. The performance of the fractional-order controller outperforms that of the integer counterpart on the integral square error criterion. Moreover, the simulation and practical results are consistent with each other.

Centralized PI controller design method for MIMO processes based on frequency response approximation

A simple method of controller design for multi-input multi-output (MIMO) processes have been proposed in frequency domain. The intensive calculation for the inverse of the process transfer function matrix is simplified to a great extent by evaluating the process transfer function matrix at a low frequency point. The desired closed loop transfer functions are derived for the process using a single tuning parameter for each diagonal element of the process transfer function matrix which represents the desired closed loop time constant. Centralized PI controllers are then designed using a model matching technique by evaluating the transfer functions at a low frequency point. The PI controllers provide acceptable performances for lag dominated as well as time-delay dominated processes and is also applicable to high-dimensional processes. The proposed method is extended for the non-square MIMO processes using two approaches one of which squares up the process transfer function matrix to apply the proposed technique while the other is based on pseudo-inverse evaluation of the process transfer function matrix at a low frequency point.

Subsystem identification of feedback and feedforward systems with time delay

We present an algorithm for identifying discrete-time feedback-and-feedforward subsystems with time delay that are interconnected in closed loop with a known subsystem. This frequency-domain algorithm uses only measured input and output data from a closed-loop discrete-time system, which is single input and single output. No internal signals are assumed to be measured. The orders of the unknown feedback and feedforward transfer functions are assumed to be known. We use a two-candidate-pool multi-convex-optimization approach to identify not only the feedback and feedforward transfer functions but also the feedback and feedforward time delay. The algorithm guarantees asymptotic stability of the identified closed-loop transfer function. The main analytic result shows that if the data noise is sufficiently small and the cardinality of the feedback-candidate-pool set is sufficiently large, then the identified feedforward and feedback delays are equal to the true delays, and the parameters of the identified feedforward and feedback transfer functions are arbitrarily close to the true parameters. This subsystem identification algorithm has application to modeling human-in-the-loop behavior. To demonstrate this application, we apply the new subsystem identification algorithm to data obtained from a human-in-the-loop control experiment in order to model the humans’ feedback and feedforward (with delay) control behavior.

Thermoacoustics and combustion instability analysis for multi-burner combustors

This paper presents a low-order thermoacoustic model for multi-burner combustors and proposes a control theoretic approach to linear combustion instability analysis in frequency domain, taking acoustic and flame interaction effects among burners into account under a non-zero mean flow condition. Our thermoacoustic model can deal with can-annular and annular combustors in a unified way and is given as a multi-input multi-output transfer function matrix from heat fluctuation input vector to velocity fluctuation output vector. We also propose a flame transfer function matrix description where off-diagonal components describe the effects of a local acoustic field of one burner location on the flame response at another burner location. The discrete rotational symmetry of burner arrangement in a combustor makes it possible to diagonalize both the aforementioned thermoacoustic and flame transfer function matrices analytically from a spatial discrete-time Fourier transformation. The decoupled thermoacoustic transfer function matrix provides a characterization of acoustic resonances, particularly the longitudinal-azimuthal coupled modes unique to multi-burner combustors. In addition, from the Bloch wave interpretation, we find general patterns in the mode shape of a multi-burner combustor and its relations to the mode shape of a single-burner combustor. Furthermore, from a diagonalized closed loop transfer function matrix, a simple combustion instability condition for a multi-burner combustor is developed. This stability condition shows how a single-burner combustor and a multi-burner combustor are different quantitatively, when it comes to combustion instability. Numerical examples are presented to validate our thermoacoustic model against three-dimensional FEM results, and to illustrate our developments and findings.

Sampled-Data Modeling for PCM and ZVS Controlled Critical Conduction Mode (CrCM) Active Clamp Flyback (ACF) Converter at Variable Switching Frequency

Critical conduction mode (CrCM) active clamp flyback (ACF) converter is regarded as a good candidate for low power adaptor applications. However, the most adopted control strategy of variable-frequency peak current mode (VF-PCM) and discrete zero voltage switch (ZVS) control makes it difficult to get the accurate small signal model. Therefore, by using sampled-data modeling method, this paper proposes an exact small signal model of CrCM ACF converter for the first time. In the modeling process, the influence of discrete-ZVS control is firstly considered. The conduction time of power switch is regarded as the control signal, which is different from constant-frequency converter. The total current close-loop transfer function is simplified by the linear combination of single VF-PCM and discrete-ZVS control model. After considering the sampling effect and the modulator gain from the derived sampled-data model respectively, the control-to-output transfer function of CrCM ACF converter is developed. The analytical results are analyzed by comparing with single VF-PCM and the widely used average model. Finally, to validate the accuracy of the proposed model, a 65W 20V output CrCM ACF converter is simulated and measured. The verification shown that the proposed sampled-data model is basically agreement with the simulation and experimental results.

Stability and Accuracy Analysis of Real-Time Hybrid Simulation (RTHS) with Incomplete Boundary Conditions and Actuator Delay

The main purpose of this paper is to examine the effects of incomplete boundary conditions and actuator delay on the dynamic responses of seismically excited civil structures. A set of constraint equations representing the reserved interface degrees-of-freedom (DOFs) and the delay are introduced to form a mechanical model of real-time hybrid simulation (RTHS) (referred to as RTHS-I&A) for a multi-degree-of-freedom (MDOF) system based on dynamic substructure method (DSM). Then, the RTHS-I&A system is modeled by a discrete closed-loop transfer function based on discrete control theory, using a selected integration algorithm, and the stability of the system is investigated by examining the poles of the function. Three typical cases with different structural properties are utilized to investigate the effects of incomplete boundary conditions and actuator delay. The results show that both incomplete boundary conditions and actuator delay greatly affect the dynamic responses of structures, and the combination of the two factors will amplify their influence especially on the nodes at the interface. The numerical model of RTHS-I&A proposed in this paper is quite useful for evaluating the responses of structures with different interface conditions and loading schemes that are preliminarily designed before a physical testing is conducted, and provides guidance for future relevant researches.

Analytical Design of Multi-loop Fractional IMC-PID-Filter Controllers for MIMO System Using Equivalent NIOPDT Models

In this paper, a multiloop fractional IMC-PID-filter controller design is proposed for 2x2 multivariable systems (two-input two-output (TITO) system). The MIMO system is decomposed by an inverted decoupler into independent loops (SISO systems) and they are approximated to equivalent new fractional order models known as non integer order plus time delay (NIOPTD). The fractional property of the suggested controller is imposed by choosing the Bode’s ideal closed loop transfer function as the reference model for each loop. The design method is based on the internal model control (IMC) paradigm. Finally, an illustrative example of MIMO process is provided and a comparative study is conducted out to demonstrate the advantages of the proposed method where the simulation results show the superior performance obtained by a multi-loop fractional IMC-PID-filter controllers in comparison with fractional PI/PID controllers based on simplified decoupling smith predictor (Fractional-SDSP and Classical-SDSP) structure as well as classical decentralized PID controllers using root locus method.

Predictor-based fractional disturbance rejection control for LTI fractional-order systems with input delay

In this paper, a predictor-based fractional disturbance rejection control (PFDRC) scheme is proposed for processes subject to input delay. The proposed scheme can be generally applied to open-loop stable, integrative, and unstable integer-order processes, but it can be particularly utilized for open-loop stable fractional-order systems. A closed-loop reference model is formulated based on Bode’s ideal transfer function. The primary control design objective is to enable the output of input-delay process to follow the closed-loop reference model. Towards this end, the closed-loop transfer function of the PFDRC must take the same structure as that of the reference model. Meanwhile, the adverse effects of the input delay must be mitigated. To meet the latter, a filtered Smith predictor (FSP) is employed to provide a prediction of delay-less output response. To address the former, process dynamics are treated as a common disturbance; then, a fractional-order extended state observer (FESO) is introduced to estimate the delay-less output response and also the total disturbance (i.e. external disturbance and system uncertainties). The PFDRC feedback controller is easily derived by the gain crossover frequency of Bode’s ideal transfer function which facilitates the tuning process. The convergence analysis of the FESO is carried out in terms of BIBO stability. The effectiveness of the proposed control scheme is verified through three illustrative examples from the literature.

Improved Application of Third-Order LADRC in Wind Power Inverter

In wind power systems, LCL inverters have technical problems. First of all, they are non-linear systems and are no longer adapted to the superposition principle; secondly, the coupling is great; finally, it is easy to be interfered by the outside world, and the interference mainly comes from voltage fluctuations and nonlinear loads on the grid. Therefore, it is difficult to control the output result, and then the improved linear active disturbance rejection control (LADRC) is applied. The main improvement of the improved LADRC lies in the linear extended state observer (LESO). Introducing the total disturbance differential signal in LESO, and in order to improve the ability to suppress high-frequency noise, a series of first-order inertia link was applied. The analysis method in this article is mainly frequency domain analysis, under the condition of obtaining LADRC closed-loop transfer function and frequency band characteristics, theoretical analysis of LADRC tracking estimation ability, disturbance suppression ability, and stability. A large number of experimental simulation results verified the superiority of improving LADRC. The main manifestation is that the improved LADRC not only has a fast response speed but also has a strong ability to suppress disturbances and has a good noise suppression effect in high frequency bands.

Analytical Prediction and Minimization of Deadtime-Related Harmonics in Permanent Magnet Synchronous Motor

The current, torque, and speed harmonics caused by deadtime effect in voltage source inverter (VSI)-fed permanent magnet synchronous motor (PMSM) usually lead to undesired torque ripple and extra electrical loss, etc. In this article, a mathematical model is proposed to predict the deadtime-related harmonics in VSI-fed field-oriented control PMSM, and a deadtime-related harmonic minimization method is proposed based on proportional-integral (PI) controllers tuning and under the premise of keeping the same control strategy. The expressions of current, torque, and speed harmonics caused by deadtime effects are obtained based on the complex amplitude expression of the voltage error harmonic and the derivation of the closed-loop transfer function from the deadtime-related voltage error to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d–q</i> axis current. Based on the derived expressions, optimization objective functions are built to search the optimal PI parameters for minimizing deadtime-related harmonics and reducing the torque ripple. The optimization constraint functions can be adjusted for transient performance requirements, so the transient performance can keep good even if the deadtime-related harmonics are minimized with the optimal PI parameters. Both simulation analysis and experimental data verify the correctness of the analytical prediction and the validity of the deadtime-related harmonic minimization method.

Passivity-Based Design of Repetitive Controller for $LCL$-Type Grid-Connected Inverters Suitable for Microgrid Applications

A repetitive controller (RC) is one of the most promising candidates for harmonic compensation when designing the current controller of grid-connected inverters. The discrete-time closed-loop transfer function based frequency response method can be used to shape RC, which is applicable for a single inverter connecting to well-known inductive-impedance grids, but cannot guarantee the stability in the case of capacitive-impedance grids or complex systems, such as microgrids. To address this issue, this article presents a new passivity-based design method for an RC for LCL-type grid-connected inverters with either inverter-side or grid-side current control. With the proposed design guidelines, the output admittance of the RC-controlled inverter is tuned to be passive in all frequencies, so that it can be plug and play connected to a grid regardless of grid impedance. Meanwhile, thanks to infinite gains of an RC at the fundamental frequency and its multiples as the high-quality grid injected current in accordance with IEC 61000-3-4 standard is ensured even in the presence of distorted grid conditions. Finally, experimental results with an established lab prototype are provided to verify the effectiveness of the proposed approach.

Decoupled Average Current Control of Coupled Inductor Single-Input Dual-Output Buck Converter

Multiple-output dc–dc converters are compact and cost effective as compared to multiple parallel dc–dc converters. This article focuses on a coupled-inductor single-input dual-output (CI-SIDO) buck converter. For the CI-SIDO converter, achieving independent regulation of output voltages and maintaining good dynamic performance are difficult due to cross-regulation and cross-coupling problems. In addition, tuning of controller parameters is challenging. Thus, this article proposes a decoupled average current control (ACC) to suppress cross-coupling and cross-regulation in CI-SIDO buck. It also demonstrates the method of decoupling of inductor currents and the stability issue that exists in ACC of CI-SIDO buck. The analysis shows that decoupling of inductor currents makes the design of controllers independent and simplifies the closed-loop transfer functions. Based on the conditions of decoupling and stability, a systematic design procedure for a Type-II compensator is developed. The proposed control method is compared with the voltage-mode control by using MATLAB/Simulink results. The comparison shows that the proposed ACC exhibits better dynamic performance. Finally, the proposed method is validated using experimental results.

Proportional-Derivative Voltage Control With Active Damping for DC/DC Boost Converters via Current Sensorless Approach

This brief presents an advanced proportional-derivative (PD) voltage control mechanism for DC/DC boost converters suffering from the parameter and load variations. The proposed controller eliminates the requirement for current feedback by designing the first-order observer estimating the voltage derivative without the use of converter parameters, which corresponds to the first contribution. As another contribution, a specific feedback gain structure for PD-loop and the active damping component guarantees the first-order closed-loop transfer function from the reference to the output voltage by the stable pole-zero cancellation. A prototype bi-directional 3-kW boost converter experimentally validates the closed-loop performance of the proposed technique.