Complex Coefficient Transfer Function Research Articles

An Angle-Compensating, Complex-Coefficient PI Controller Used for Decoupling Control of a Permanent-Magnet Synchronous Motor

An asymmetric, cross-coupling effect, as well as digital control delays, in a permanent-magnet synchronous motor (PMSM) will deteriorate its current-control performance in the high-speed range, especially for electric motors used in electric vehicles (EVs) with features such as high-power density and a low carrier/modulation frequency ratio. In this paper, an angle-compensating, complex-coefficient, proportional-integrator (ACCC-PI) controller is proposed, which aims to provide an excellent decoupling performance even with considerable digital control delay. Firstly, the current open and closed loop complex-coefficient transfer functions were established in the synchronous rotation coordinate system. The proposed method, along with existing ones, were then evaluated and theoretically compared. On this basis, the parameter-tuning method of the ACCC-PI controller was presented. Finally, simulation and experimental results proved the correctness of the theoretical analysis and the proposed method.

Implementation of Cross-Coupling Terms in Proportional-Resonant Current Control Schemes for Improving Current Tracking Performance

The proportional-integrator (PI) controller in the synchronous reference frame (dq-frame) and the proportional-resonant (PR) controller in the stationary reference frame (αβ-frame) are two typical linear current control schemes for three-phase voltage source converters. It is generally believed that the plant model is mathematically uncoupled in αβ-frame. Hence, the decoupling control required to attenuate the axis cross-coupling effect in dq-frame is regarded as not necessary in αβ-frame. However, detailed analysis with complex coefficient transfer functions reveals differences in the control performance between the fully decoupled PI control scheme in dq-frame and the PR control scheme in αβ-frame. When regulating sinusoidal currents in αβ-frame, the α-axis and β-axis current references are strongly correlated with each other, which implies a cross-coupling effect equivalent to that of dq-frame. In analogy to the dq-frame decoupling control, cross-coupling terms can be employed together with the conventional PR control scheme. It can bring the benefit of improving the transient response of current tracking and reducing the sensitivity of the resonant controller to frequency variation, especially for low-switching-frequency applications with limited current control bandwidth. Furthermore, the cross-coupling terms based on reference current feed-forward are proposed to improve the performance of both positive- and negative-sequence current control. Experimental results are shown to validate the analysis and the performance of the proposed control scheme.

The Impact of VSFPWM on DQ Current Control and a Compensation Method

The variable switching frequency pulsewidth modulation (VSFPWM) is varying the carrier frequency of pulsewidth modulation (PWM) based on the prediction model to reduce the switching losses and lower the electromagnetic interference (EMI). However, it may cause some deterioration in digital dq current control of voltage source converters. This article takes the L -type grid-connected converter as the research object, and first presents the generation mechanism of the varying time delay caused by VSFPWM. In the case of proportional-integral current regulator implemented with VSFPWM, the varying time delay is accompanied by the frame rotation, which causes a varying phase lag in output voltages, degrading the system performance. Subsequently, an analytical method based on complex coefficient transfer functions is developed to provide an accurate explanation of the relation between the VSFPWM and the corresponding impacts. A compensation method is then proposed to eliminate the varying phase lag of output voltages when the VSFPWM is employed, improving the steady state and dynamic performance of dq current control. Finally, the simulation and experimental results are presented to verify the analysis and the effectiveness of the proposed compensation method.

Guest Editorial: Special Section on Complex Vector Theory and Its Application in Power Electronic Systems

Complex space vectors have for decades proven their usefulness for modeling, analysis, and control design in electric power engineering. One fundamental benefit is that they allow two variables—the d and q components of the vector—to be expressed in a single-input–single-output (SISO) notation. Symmetric three-phase systems and dynamic elements can be modeled using complex-coefficient transfer functions. Various extensions, primarily the corresponding two-row real space vectors and two-by-two transfer function matrices—giving a multi-input–multi-output (MIMO) model—allow asymmetric systems and elements to be modeled as well.

An Analytical Design of a Complex Coefficient Transfer Function with Flat Passband Characteristics and Finite Transmission Zeros at Two Frequencies

An Analytical Design of a Complex Coefficient Transfer Function with Flat Passband Characteristics and Finite Transmission Zeros at Two Frequencies

An Analytical Design of a Complex Coefficient Transfer Function with Finite Transmission Zeros at D. C.

An Analytical Design of a Complex Coefficient Transfer Function with Finite Transmission Zeros at D. C.

DQ Current Control of Voltage Source Converters With a Decoupling Method Based on Preprocessed Reference Current Feed-forward

Axes cross-coupling in dq-frame will deteriorate the current control performance, especially for applications with low switching/sampling frequency. Decoupling methods based on inductor current state feedback and complex vector proportional-integrator controllers are usually performed to solve this problem. In this paper, an alternative decoupling method based on preprocessed reference current feed-forward is proposed, which can provide excellent decoupling performance even with considerable control delay. The current control of grid-connected voltage source converters is analyzed with complex-coefficient transfer functions. It is revealed that the decoupling performance of current control schemes is closely related to the symmetry of current closed-loop transfer function bode diagrams. The current closed-loop transfer function should show a standard symmetrical bode diagram with respect to 0 Hz, if axes cross-coupling is well decoupled. A quantitative index named cross-coupling function is then proposed to analyze and comprehensively compare the decoupling performance of the proposed method and existing ones in terms of the influence of the control delay, inductance estimation error, grid frequency deviation, and voltage disturbance. Experimental tests are implemented to validate the performance of the proposed method and comparison results.

Study on stability and rotating speed stable region of magnetically suspended rigid rotors using extended Nyquist criterion and gain-stable region theory

This paper presents a novel and simple method to analyze the absolute stability and the rotor speed stable region of a magnetically suspended rotor (MSR). At the beginning of the paper, a complex variable is introduced to describe the movement of the MSR and a complex coefficient transfer function is obtained accordingly. The equivalent stability relationship between this new variable and the two traditional deflection angles is also demonstrated in a simple way. The detailed characteristics of the open-loop MSR system with time delay are studied carefully based on the characteristics of its Nyquist curve. A sufficient and necessary condition of absolute stability is then deduced by using an extended complex Nyquist stability criterion for MSRs. Based on the relationship between the rotor speed and gain-stable region proposed in this paper, the rotor speed stable region can be solved simply and directly. The usefulness and effectiveness of the proposed approaches are validated by examples and simulations.

Erratum: Design of a Direct Sampling Mixer with a Complex Coefficient Transfer Function [IEICE Transactions on Electronics E95.C (2012) , No. 6 pp. 999-1007

Erratum: Design of a Direct Sampling Mixer with a Complex Coefficient Transfer Function [IEICE Transactions on Electronics E95.C (2012) , No. 6 pp. 999-1007

Design of a Direct Sampling Mixer with a Complex Coefficient Transfer Function

The Direct Sampling Mixer (DSM) with a complex coefficient transfer function is demonstrated. The operation theory and the detail design methodology are discussed for the high order complex DSM, which can achieve large image rejection ratio by introducing the attenuation pole at the image frequency band. The proposed architecture was fabricated in a 65nm CMOS process. The measured results agree well with the theoretical calculation, which proves the validity of the proposed architecture and the design methodology. By using the proposed design method, it will be possible for circuit designers to design the DSM with large image rejection ratio without repeated lengthy simulations.

A realization of a real filter based on a complex filter

In this paper, we investigate a method of using active RC circuits to realize a complex coefficient transfer function with bandpass characteristics that can be obtained by shifting the poles of a real coefficient low-pass transfer function in the direction of the frequency axis. Complex signals and the signal path were divided into real and imaginary parts, and the imaginary resistance component was simulated by a leapfrog configuration method. We configured a complex active RC filter using a small number of operational amplifiers and attempted to construct a high-frequency filter by compensating the finite gain bandwidth product. Finally, a sixth-order bandpass filter was configured and experiments were performed. The element sensitivity was estimated using a computer and the validity of the proposed method was shown. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(8): 87–94, 1997

Complex reference networks to realize transfer functions with arbitrary transmission zeros

This paper proposes a method of realizing arbitrary complex coefficient transfer functions with complex double resistively terminated lossless filters as the reference network for complex wave digital filters (CWDFs). For this purpose, the Darlington synthesis method, which is known for realizing arbitrary real coefficient transfer functions, is expanded into the complex domain. Furthermore, a new construction method for a digital adapter without a delay-free loop is presented. Finally, a complex coefficient transfer function using some realization method is constructed and the validity of the proposed method is confirmed. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(2): 12–23, 1997

Realization of two transfer functions with complex coefficients by a transfer function with hypercomplex coefficients

AbstractThis paper shows that two complex coefficient transfer functions can be realized by a single hypercomplex coefficient network, utilizing all four outputs of the hypercomplex network. the realization is considered for the case where the two arbitrary complex coefficient transfer functions do and do not have a common denominator. It is shown that the transfer functions can be realized by the hypercomplex coefficient network of the same order in the former case and by the hypercomplex coefficient network with the half‐order in the latter case. the realization of the transfer functions with the common denominator is interesting, but the general method to derive the transfer functions is not known.From such a viewpoint, this paper proposes the discrete‐type Kautz approximation with the positive frequency as the domain of approximation, including the optimal pole determination algorithm. By this approach, two complex coefficient transfer functions with an n‐th‐order common denominator are derived from the two 2n‐th‐order real or complex coefficient transfer functions. the method can be considered as one that simultaneously approximates the amplitude and the phase. the proposed approximation method is an approximation only for the positive frequency domain, and the property of the analytic signal that the negative frequency component is zero can be utilized. As a result, the method proposed in this paper has the advantages that the degree of freedom in the filter design is enhanced and the sampling frequency can be halved. In addition, the network structure can be simplified.

Complex coefficient reference networks with transmission zeros on imaginary axis

AbstractThis paper considers the complex coefficient transfer function with transmission zeros on the imaginary axis and presents a method to realize such a transfer function by a reactance network including imaginary resistors with double resistor termination. Using the obtained network and the reference network for the complex‐wave digital filter, the complex digital filter with transmission zeros on the imaginary axis can easily be extended, which is important in practice.In this paper, Brune's method modified by Belevitch as well as Fujisawa's method extended by Morimoto et al. are improved and the realizability condition is relaxed. Then, several construction examples are shown and the features of construction methods are compared and discussed.

Implementation of real coefficient two-dimensional denominator-separable digital filters based on decomposition techniques

In the paper, the implementation of two-dimensional digital filters is dealt with for the processing of real sequences. The approach is based on decomposition techniques to obtain separable one-dimensional polynomials from a two-dimensional polynomial, and then one-dimensional techniques are used to express the one-dimensional transfer functions as a sum of two reduced-order transfer functions with complex coefficients. Thus, new realisation structures are obtained for the equivalent reduced-order complex-coefficient transfer functions for the processing of real sequences. The authors concentrate more on two-dimensional denominator-separable digital filters and also confine themselves to the parallel-form structures as the emphasis is now on low data throughput delay and high parallelism due to recent advances in VLSI technology. All these structures consist only of one-dimensional first-order minimum-norm sections. Thus, these structures possess low round-off noise and freedom from overflow limit cycles. A comparison of different structures is made based on data throughput delay, efficiency in multiprocessor environment and round-off noise properties.