Closed-loop Transfer Function Research Articles

Research on control parameter optimization of LCC-HVDC system based on zero-pole optimal position distribution

The proportional-integral (PI) control is widely adopted as the leading controllers of the line-commutated converter high-voltage direct current transmission system (LCC-HVDC), while unreasonable coefficients setting will result in the DC system instability and aggravate system dynamic performance. In order to improve the overall response performance of the system, a tuning method of the controller parameters guided by the linearized zero-pole transfer function of the DC system is proposed. Firstly, the small signal analysis method is used to formulate the closed-loop transfer function model at the stable operating point. According to the position of zero and pole, the objective function which can quantitatively reflect the dynamic and steady state characteristics of the DC system is derived. Furthermore, combined with the particle swarm optimization (PSO) intelligent optimization algorithm, the multi-group control parameters of the system are optimized. Finally, by comparing the time domain numerical simulation results before and after parameter optimization, it is verified that the proposed tuning method can effectively improve the dynamic and steady-state characteristics of the DC system.

Closed-loop identification of stabilized models using dual input–output parameterization

This paper introduces a dual input–output parameterization (dual IOP) for the identification of linear time-invariant systems from closed-loop data. It draws inspiration from the recent input–output parameterization developed to synthesize a stabilizing controller. The controller is parameterized in terms of closed-loop transfer functions, from the external disturbances to the input and output of the system, constrained to lie in a given subspace. Analogously, the dual IOP method parameterizes the unknown plant with analogous closed-loop transfer functions, also referred to as dual parameters. In this case, these closed-loop transfer functions are constrained to lie in an affine subspace guaranteeing that the identified plant is stabilized by the known controller. Compared with existing closed-loop identification techniques guaranteeing closed-loop stability, such as the dual Youla parameterization, the dual IOP neither requires a doubly-coprime factorization of the controller nor a nominal plant that is stabilized by the controller. The dual IOP does not depend on the order and the state-space realization of the controller either, as in the dual system-level parameterization. Simulation shows that the dual IOP outperforms the existing benchmark methods.

Current coordinated distribution and voltage optimization control for multi-VSGs system considering nonlinear and negative sequence loads

In a microgrid system where multiple virtual synchronous generators (VSGs) are interconnected through high impedance cables, the total output negative sequence and harmonic current of multiple VSGs cannot be coordinated based on the capacity of each power conversion system (PCS). In addition, there is significant distortion in the voltage at the point of common coupling (PCC). Because the impedance amplitude and impedance angle of the cable change with the harmonic frequency, the resistive virtual impedance reshaping method and fixed impedance angle virtual impedance reshaping method used in the current research cannot solve the harmonic current distribution problem. To solve the above problems, a multi-frequency points VSG impedance reshaping control strategy is proposed in this paper, which can adjust the resistive and inductive output impedance of each harmonic frequency independently. The strategy is based on the harmonic separation algorithm of LPF with Feedforward Compensation (FCLPF) and the voltage controller of Vector Proportional Integral (VPI) in fundamental dq rotation coordinate system, which effectively improve the flexibility and accuracy of harmonic impedance reshaping. Among them, FCLPF harmonic separation algorithm has the characteristics of target frequency bandpass and non-target frequency notch, and can eliminate the coupling interference of each harmonic virtual impedance when accumulating virtual impedance voltage references at various frequency points. The closed-loop transfer function of the multi-parallel VPI voltage controller has the characteristics of unit gain and zero phase shift at each harmonic frequency point, which means the static response error of virtual impedance voltage command can be almost completely eliminated. Under the proposed control strategy, the fundamental positive power can be allocated according to the droop coefficient, the fundamental negative current and harmonic current can be allocated according to the sum of the reshaped virtual impedance and the actual line impedance. Reshaping virtual impedance at each harmonic frequency to negative value can also compensate the harmonic voltage drop on the high impedance cable and improve the voltage quality at the PCC.

Time-domain instability mechanism for artificial boundary condition of semi-infinite medium described by discrete rational approximation

The use of discrete rational approximation functions to represent foundation dynamic impedance plays a crucial role in the time-domain analysis of soil-structure interaction regarding artificial boundary. In modeling, the rational approximation functions need to be transformed into time-domain recursive models for incorporation into time-history analysis. However, this method also suffers from uncertainties in parameter identification and instability in time-domain analysis when the time-domain recursive models of soil are coupled with upper structure. The stability issue in artificial boundary coupled time-domain computation has not been effectively addressed. This paper establishes the closed-loop transfer function of the coupled system and analyzes the causes of instability in the coupled system based on gain margin analysis. Different numerical simulations demonstrate that the major cause of artificial boundary system instability is the description errors of discrete rational approximation functions beyond the fitting frequency range.

Current sensorless model predictive control for LC-filtered voltage source inverters based on sliding mode observer

Abstract In recent years, model predictive control (MPC) has gained significant traction within the realm of LC-filtered voltage source inverters (VSIs). In order to reduce the number of current sensors in conventional MPC, this paper proposes a MPC scheme without current sensors for LC-filtered VSIs. Firstly, this paper analyzes the mathematical model of LC-filtered VSIs and specifies the predictive control strategy based on capacitive current. On the basis of considering only the fundamental wave components of the capacitance current, this paper establishes a new sliding mode observer to observe the capacitance current. In order to ensure the stability of the system, the stability of the proposed sliding mode observer is analyzed using Lyapunov stability criterion, and the influence of the sliding mode gain on the current and voltage observations is also analyzed according to the closed-loop transfer function, giving the design method of the sliding mode gain. In addition, the parameter sensitivities of the newly proposed method and the conventional method are analyzed in detail in this paper. The results show that the method proposed in this paper does not depend on the filter inductance and the observed capacitance current have smaller errors and stronger parameter robustness than the conventional method. The comparative experimental study verifies the feasibility of the control scheme proposed in this paper.

Improvement of the linear quadratic regulator control applied to a DC-DC boost converter driving a permanent magnet direct current motor

This article discusses a new robust control technique that enables the DC-DC boost converter driving a permanent magnet direct current (PMDC) motor to operate in high static and dynamic performances. The new technique is based on the design of a both linear quadratic regulator (LQR) and linear quadratic regulator-proportional integral (LQR-PI) type controllers, which have the advantage of eliminating oscillations, overshoots and fluctuations on different characteristics in steady-state system operation. In order to increase the output voltage, the LQR regulator is combined with a first-order system represented in the form of a closed-loop transfer function, the latter raising the output voltage to 24 volts, this voltage is enough to drive the permanent magnet direct current motor. The contribution of this paper is the creation of a robust control system represented in the form of a hybrid corrector able to regulate steady-state and transient disturbances and oscillations as well as to increase DC-DC boost converter output voltage for the PMDC motor to operate at rated voltage. The results of the three control techniques are validated by MATLAB Simulink.

Low order speed harmonic suppression in FOC-PMSM based on the closed-loop transfer mechanism of injected voltage

In the field oriented control (FOC) permanent magnet synchronous motor (PMSM) servo system, torque ripple impairs motor performance. Harmonic injection methods can suppress torque ripple by injecting additional voltage harmonic to offset the existing speed harmonic. However, since FOC is a closed-loop motion control strategy, the transfer path from injected voltage harmonic to speed harmonic is affected by FOC, especially in very low frequency. Due to the influence of FOC on the transfer function, the relation between the injected voltage harmonic and speed harmonic varies with operating conditions and motor control parameters. It causes the existing harmonic injection methods ineffective to suppress low order speed harmonics. To solve the problem, in this paper, the closed-loop transfer mechanism of injected voltage harmonics is analyzed and the closed-loop transfer function is derived. Based on the derived closed-loop transfer function, a low order speed harmonic suppression method is proposed. With the derived transfer function, the proposed method can adapt to the variations of the relation between low order injected voltage harmonic and speed harmonic under different operation conditions. Finally, the accuracy of the derived closed-loop transfer function and the effectiveness of the proposed low order speed harmonic suppression method are evaluated by experiment.

Research on the Current Control Strategy of a Brushless DC Motor Utilizing Infinite Mixed Sensitivity Norm

During the brushless DC (BLDC) motor working process, the system encounters inevitable uncertainties. These ambiguities stem from potential fluctuations, random occurrences, measurement inaccuracies, varying operational conditions, environmental shifts such as temperature alterations, among other factors. Uncertainties, an inherent aspect of any real control system, can be broadly classified into two categories: sensor signal uncertainties and discrepancies between the mathematical and actual models due to parameter perturbations. To mitigate the impact of sensor noise and parameter perturbations on the BLDC motor, a robust control strategy utilizing infinite norm mixed sensitivity based on PI control strategy (PI-H∞-MIX) is proposed in this paper. Firstly, the closed-loop control structure and transfer function model of the BLDC motor control system current loop are analyzed based on the current loop circuit topology, and then, the model parameters perturbation is analyzed, and the multiplicative uncertainty bound is given. In addition, the appropriate weighting function is selected to ensure the robustness of the system. In this case, the controller design problem is transformed into the H∞ standard control problem, and then, the system augmentation matrix is established, and the controller is solved by Matlab/Simulink. Finally, the performances of the traditional PI control strategy and the PI-H∞-MIX are compared and analyzed. The results show that (1) the proposed PI-H∞-MIX strategy can improve the control system robustness under the parameter perturbation condition effectively, and (2) the proposed PI-H∞-MIX strategy can suppress the noise signal of the sensor.

One-Step Ahead Control Using Online Interpolated Transfer Function for Supplementary Control of Air-Fuel Ratio in Thermal Power Plants

Recently, the environmental problem has become a global issue. The air to fuel ratio (AFR) in the combustion of thermal power plants directly influences pollutants and thermal efficiency. A research result was published showing that the AFR control performance of thermal power plants can be improved through supplementary control using dynamic matrix control (DMC). However, online optimization of DMC needs an extra computer server in implementation. This paper proposes a practical AFR control with one-step ahead control which does not use online optimization and can be implemented directly in existing distributed control system (DCS) of thermal power plants. Closed-loop transfer function models at three operating points are independently developed offline. Then, an online transfer function using interpolation of offline models is applied at each sampling step. A simple one-step ahead control with online transfer function is applied as a supplementary control of AFR. Simulations with two different type power plants, a 600 MW oil-fired drum-type power plant and a 1000 MW ultra supercritical (USC) coal-fired once-through type power plant, are performed to show the effectiveness of the proposed control structure. Simulation results show that the proposed supplementary control can effectively improve the conventional AFR control performance of power plants.

Design and analysis of root locus based controllers

The root locus method is the classical method for analyzing the variation of the position of the poles of a closed-loop control system transfer function in the complex plane. It is also the basis for guiding the design of various controllers. Starting from the nature of the root locus, this paper takes a standard form of closed-loop feedback control system as an example, and analyzes in detail the internal logic of designing a controller and compensator by the root locus method. At the same time, software such as MATLAB/Simulink, and Octave are used. The working principles and properties of the PD controller; the lead and lag compensator, their interconnections, advantages, and characteristics, as well as the adjustment of parameters to better suit practical needs, are sorted out. The PD controller improves the system response, the lead compensator eliminates the PD controller’s defects, and the lag compensator reduces the steady-state error of the system. It provides help for understanding the essence of controller design and provides design ideas for control problems in actual engineering.

Implementation of Bio-inspired Algorithms in Designing Optimized PID controller for Cuk Converter for Enhanced Performance: A Software based Approach

This paper represents the idea of implementing bio-inspired algorithms in designing an optimized PID controller to investigate the stability and improve the performance of the closed-loop CUK converter. Bio-inspired algorithms (BIA) such as Firefly Algorithm (FA), Particle Swarm Optimization (PSO) and, Artificial Bee Colony (ABC) are stochastic optimization techniques and have been increasingly applied to attain optimal solution for designing and optimizing power converters in current times. The closed-loop transfer function of the CUK converter has been developed by the State Space Average (SSA) technique. This paper assesses both the cases of converter stability when it is integrated with the conventional PID controller and the BIA-PID controllers (FA-PID, PSO-PID, ABC-PID) and eventually compares the outcomes from all the controllers. For examining the stability of the system, three objective functions (IAE, ITAE, and ISE) and various performance specifications such as percentage of overshoot, rise time, settling time, and peak amplitude are tabulated. MATLAB and Simulink are used to carry out the simulations meticulously. Hence, a comparative analysis is illustrated in this paper to state a clear-sighted evaluation of the performances.

Comment on “Optimal tuning of sigmoid PID controller using nonlinear sine cosine algorithm for the automatic voltage regulator system”

In this short note, the relative stability results (based on root locus and Bode analyses) reported in “Optimal tuning of sigmoid PID controller using nonlinear sine cosine algorithm for the automatic voltage regulator system” (Suid and Ahmad, 2022) are analyzed. It is shown that the use of closed-loop transfer functions (CLTFs) should be avoided in relative stability analysis since they may lead to less accurate stability results. The present study affirms that the results of relative stability analysis obtained using loop transfer functions (LTFs) are more reliable and accurate.

Implementation Methods of Controllers Designed by $H_\infty$ Loop Shaping

When the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> loop-shaping controller is implemented as a unity feedback system, its step responses are sometimes unsuitable for tracking control, typically, displaying large overshoots. In this paper, the implementation method is studied for tracking control with small overshoots. Three implementation methods that are described by a unity feedback system, a previous simple two-degrees-of-freedom(2DoF) system, and a new simple 2DoF system proposed in this paper are examined. For the closed-loop transfer function of each system, the unstable zeros are analyzed and an upper bound of the peak gains is presented. These results show that the two simple 2DoF systems have adequate properties for tracking control with small overshoots. The new 2DoF system has good features that the system is minimum phase if the plant is minimum phase, and that the resonance peak gain is one. Their tracking performances are compared in several numerical examples.

Observer-Based Order-Reduction Speed Control for Converter-Fed BLDC Motors With Current-Loop Adaptation

This research considers the speed control problem for brushless DC motors (BLDCMs) fed by a buck converter subject to the BLDCM parameter and load uncertainty. This study makes three important contributions that distinguish it from previous results: (a) the plant model-free observer estimates the first-and second-order time derivatives for BLDCM speed by incorporating the disturbance-observing mechanism as the subsystem, (b) the proposed control law leads to the first-order closed-loop transfer function from the converter current reference to the DCM speed using observer-based active damping injection, and (c) the analytic variable feedback gain implements converter current-loop adaptation based on the size of the current error. Experimental analysis demonstrates the actual advantages of the proposed technique using a 420 W BLDCM fed by a DC/DC buck converter.

VSC control strategy for HVDC compensating harmonic components

This paper proposes a voltage source converter (VSC) control strategy for the high voltage direct current (HVDC) transmission systems compensating the harmonic components. For VSC-HVDC AC system accounted for a relatively large share of the 5th, 7th, 11th, 13th and other low harmonics. A selective harmonic current control strategy based on vector proportional integral (VPI) regulator in dq coordinate system is proposed on the basis of PI control. In which, PI is used to control the DC component of the current error, while VPI is used to suppress the multiplicative fluctuations of the current error. Unlike the proportional-integral resonant (PIR) regulator, the VPI contains a second-order numerator that achieves the ideal 0° phase delay of the closed-loop transfer function of the control system at the set resonant frequency point, so its control accuracy for harmonic currents is better than that of the PIR. A two-terminal VSC-HVDC system is built using Simulink software, and current compensation simulations are performed for three control methods: conventional PI, PIR and PI parallel VPI schemes. The superior harmonic suppression performance of VPI is verified by comparing the harmonic content.

Stability Analysis of Phase Locked Loops for AC Microgrids With Hybrid Power Sources

Synchronous instability of the multiple distributed generations has been an important issue for microgrids. Therein, the phase locked loop (PLL) instability is one of the significant reason for synchronous instability of multi-inverter microgrids. Although this instability issue has been widely studied, it is ignored for microgrids with numerous inverters controlled through different controllers. To full this gap, this paper proposes a multi-inverter parallel microgrid stability analysis method based on PLL. Firstly, this paper establishes a PLL small signal model based on the droop control strategy and the P&Q control strategy. Furthermore, the whole PLL small signal analysis model of multi-inverter parallel microgrid is proposed by signal flow graph and Mason Gain Theorem, which is more convenient for power engineers. Eventually, the closed-loop transfer function of PLL is obtained. The proposed integrated small signal model can predict the synchronous stability regarding the PLL of the multi-inverter under grid-connected mode and the island mode. Finally, the simulation and experimental results can well validate the feasibility and effectiveness of the proposed stability analysis strategy based on PLL in the multi-inverter parallel microgrid. Therein, the simulation and experimental results illustrate that the proposed stability identification approach can provide an effective stability control parameter selection method.

A frequency-domain approach to model vertical crowd-structure interaction in lightweight footbridges

Load models that account for Human-Structure Interaction (HSI) may be preferable to accurately predict the dynamic response of lightweight footbridges subjected to pedestrian actions. Representing each person within a crowd may not be practical in engineering design calculations as time-variant models with a large number of degrees of freedom have to be managed. In addition, high computational time may be required to achieve the steady-state response. In this sense, this paper proposes a novel approach to calculate the vertical steady-state response of footbridges from a time-invariant coupled crowd-structure system. Considering the model of the structure and a feedback model of the crowd, a total closed-loop Transfer Function (TF) of the coupled system is derived. Based on this frequency-domain interacting methodology, a step-by-step procedure is set to asses the vibration serviceability of lightweight footbridges due to harmonic excitations through simple algebraic operations. The proposal is used to study a Fibre Reinforced Polymer footbridge subjected to two streams of walking pedestrians. For this structure, a good compromise between experimental and numerical results is obtained in terms of vertical vibrations and TFs. To further validate the proposed approach, a pre-stressed concrete laboratory facility is also analysed, obtaining a satisfactory agreement between the experimental and numerical TFs. Thus, the proposed approach allows to evaluate lightweight footbridges under crowd-induced loads considering HSI in a simple and accurate manner, which is clearly geared to practice.

Study on stability margin of ultra-low frequency oscillation in hydropower system

In recent years, the ultra-low frequency oscillation of power system caused by hydropower units has occurred frequently. It is very important to study the ultra-low frequency oscillation characteristics of hydropower stations for the stable operation of power system. It is worth further research on how to determine the system stability margin in engineering practice. Based on the established model of single machine system with load, the analysis of the characteristic equation of closed-loop transfer function of single machine system shows that the ultra-low frequency oscillation will occur when the ratio of proportional parameter to integral parameter is too small. Based on the single machine with load system model and the equivalent single machine with load model of multi machine system, the ultra-low frequency oscillation mode of the system is analyzed by eigenvalue analysis method. According to the requirements of the damping ratio index, the security domain of the system ultra-low frequency oscillation is constructed, and the risk and stability margin of the system ultra-low frequency oscillation are evaluated by the characteristic values of the system ultra-low frequency oscillation mode.

PESNet 3.0: A WRN-Based Communication Network With ±0.5 ns Synchronization Error for Large-Scale Modular Power Converters

Emerging large-scale silicon-carbide (SiC)-based modular power converters are pursuing high-performance distributed control systems (DCSs). In particular, fast-switching-enabled novel control schemes raise the need for minimal synchronization error (SE) of communication networks. This article presents the development of a proposed power electronics system network (PESNet) 3.0 that features a sub-nanosecond (ns) SE and gigabits-per-second data rate. The White Rabbit Network (WRN) technology, originally developed for particle accelerators, has been embedded in PESNet 3.0 and tailored to be suited for large-scale high-frequency modular power converters. A simplified node-to-node phase-locked loop (N2N-PLL) and an improved precision time protocol (PTP) model has been proposed to lock both the frequency and phase of two independent clocks on two adjacent nodes. Subsequently, the stability analysis of the N2N-PLL is carried out with its closed-loop transfer function verified by digital perturbation injection (DPI). Finally, the experimental validation of PESNet 3.0 is demonstrated at both controller and converter levels. The latter is on a first-of-it-kind 10-kV SiC-MOSFET-based modular converter prototype operating at 12-kV dc-link voltage, 10-kHz switching frequency, and above 100-V/ns slew rate, verifying ±0.5 ns SE at 5 Gb/s data rate.

Fixed-order H-infinity controller design for port-Hamiltonian systems

We present a new fixed-order H-infinity controller design method for potentially large-scale port-Hamiltonian (pH) plants. Our method computes controllers that are also pH (and thus passive) such that the resulting closed-loop systems is again passive, which ensures closed-loop stability simply from the structure of the plant and controller matrices. In this way, we can avoid computationally expensive eigenvalue computations that would otherwise be necessary. In combination with a sample-based objective function which allows us to avoid multiple evaluations of the H-infinity norm (which is typically the main computational burden in fixed-order H-infinity controller synthesis), this makes our method well-suited for plants with a high state–space dimension.In our numerical experiments, we show that applying a passivity-enforcing post-processing step after using well-established H-infinity synthesis methods often leads to a deteriorated H-infinity performance. By contrast, our method computes pH controllers, that are automatically passive and simultaneously aim to minimize the H-infinity norm of the closed-loop transfer function. Moreover, our experiments show that for large-scale plants, our method is significantly faster than the well-established fixed-order H-infinity controller synthesis methods.