Minimum Phase Condition Research Articles

Individual Channel Analysis of the Thyristor-Controlled Series Compensator Performance

The TCSC is the electronically-controlled counterpart of the conventional series bank of capacitors. A mature member of the FACTS technology, the TCSC has the ability to regulate power flows along the compensated line and to rapidly modulate its effective impedance. In this paper its performance is evaluated using Individual Channel Analysis and Design. Fundamental analysis is carried out to explain the generator dynamic behavior as affected by the TCSC. Moreover, a control system design for the system is presented, with particular emphasis in the closed-loop performance and stability and structural robustness assessment. It is formally shown that the incorporation of a TCSC operating in its capacitive range improves the dynamical performance of the synchronous machine by decreasing the electrical distance and therefore considerably reducing the awkward switchback characteristic exhibited by synchronous generators. It is also formally proven in the paper that the inductive operation should be avoided as it impairs system operation. In general, the TCSC inclusion brings on fragility into the global system, making it non-minimum phase and introducing adverse dynamics in the speed channel of the synchronous machine. Moreover, it is shown that the minimum-phase condition may also be present in cases featuring high capacitive compensation levels.

Optimization of local damping treatments for plate vibrations.

This work considers passive damping treatments that dynamically interact with plates over areas that are much smaller than a flexural wavelength. Each treatment is modeled as a frequency-dependent admittance presented to the plate at a point. The frequency-dependence is required to satisfy the causality and minimum phase conditions, which are implicitly enforced via a specialized Fourier series in frequency. The Fourier coefficients, as well as the positions of the attachments, are regarded as optimization parameters to be varied so as to globally decrease plate vibrations over a frequency band of interest. Various cost functions are considered, such as the sum of modal loss factors over the band as well as acoustic radiation efficiencies. Examples involving a simply supported plate excited by a point force illustrate the approach. [Work supported by ONR under Grant No. N000140810531.]

SLIDING SURFACE MATCHED CONDITION IN SLIDING MODE CONTROL

ABSTRACTIn this paper, the recently developed sliding surface matching condition (SSMC) is viewed from a new point that the mismatched uncertain term should satisfy the minimum‐phase condition for the nominal system. With this new viewpoint, SSMC is extended to a more general class of system with nonlinear uncertainties. Finally, a numerical example demonstrates the developed results.

Frequency domain interpretations of the invariance condition of sliding mode control theory

The sliding-surface design problem for unmatched uncertain systems is considered. In the literature, it has been shown that if a system with unmatched uncertainties satisfies an invariance condition, then there exists a linear switching surface such that the sliding-mode dynamics restricted to the switching surface are not only stable but completely invariant to unmatched uncertainties. Frequency domain interpretations of the invariance condition of the sliding-mode control theory are given. It is shown that a certain H∞-norm bound constraint should be satisfied in order to guarantee the invariance condition. It is also shown that the invariance condition is guaranteed for any unmatched uncertainties satisfying a certain minimum phase condition. These results can be used to efficiently design a sliding surface. Finally, the effectiveness of the results is verified via some numerical design examples.

Evaluation of performance of the echolocation model for the restoration of an acoustic image from a single‐emission echo

Using frequency‐modulated echolocation sound, bats can form a fine acoustic image of an object. The acoustic image is an impulse response, known as a reflected‐intensity distribution, which is composed of amplitude and phase spectra over a range of frequencies. However, bats detect only the amplitude spectrum due to the low‐time resolution of their peripheral auditory system, and the frequency range of emission is restricted. The amplitude spectrum varies with the changes in the configuration of the reflected‐intensity distribution, while the phase spectrum varies with the changes in its configuration and location. By introducing some reasonable constraints, we previously proposed a method for restoring an acoustic image from the echo produced by a single emission. The configuration is extrapolated from the amplitude spectrum of the restricted frequency range by using the continuity condition of the amplitude spectrum at the minimum frequency of the emission and the minimum phase condition. The location is estimated from the temporal changes of the amplitude spectra computed by the convolution of the Gaussian chirplet with a carrier frequency compatible with bat emission sweep rates. In this paper, the performance of this model is evaluated by measuring and analyzing the echo reflected from the object.

Dual-Mode Space-Temporal Simultaneous Processing Equalizer

A tapped delayed line adaptive array antenna (TDL-AAA) and a space-temporal simultaneous processing equalizer (ST-SPE) are proposed as simple space-temporal equalizers based on minimum mean square error (MMSE) criterion. The ST-SPE has a compact hardware with a small number of taps compared to that of the TDL-AAA. The ST-SPE can reduce the computational complexity of the space-temporal joint equalization and it works effectively under the minimum phase condition such as appeared at line-of-sight (LOS) propagation environments at a high antenna height base station. However the ST-SPE cannot work under a non-minimum phase condition caused under N-LOS (non-line-of-sight). On the other hand, the TDL-AAA whose reference signal is synchronized at the center tap (TDL-AAAC) can work even in the non-minimum phase condition. In this paper, we propose a dual-mode space-temporal simultaneous processing equalizer (Dual-mode ST-SPE) which has a simple configuration and also works in non-minimum phase condition. The Dual-mode ST-SPE can reduce the computational complexity compared to the TDL-AAAC.

최소 위상 조건을 적용한 음향 반사계수 측정

For the accurate measurement of acoustic properties of a surface, efforts have been made to reduce errors caused by external disturbance. If the reflection coefficient is considered as a transfer function between reflected wane and incident wave, the causality is required between them and the reflection coefficient should be of minimum phase. In this thesis, the minimum phase condition is applied to measure correct reflection coefficient. The reflection coefficient is approximated as a rational function In the Z domain by minimizing the sum square error. Then the minimum phase reflection coefficient is reconstructed using the distribution of poles and zeros of the reflection coefficient model.

A computational model of echolocation: Restoration of an acoustic image from a single-emission echo

Bats can form a fine acoustic image of an object using frequency-modulated echolocation sound. The acoustic image is an impulse response, known as a reflected-intensity distribution, which is composed of amplitude and phase spectra over a range of frequencies. However, bats detect only the amplitude spectrum due to the low-time resolution of their peripheral auditory system, and the frequency range of emission is restricted. The amplitude spectrum varies with the changes in the configuration of the reflected-intensity distribution, while the phase spectrum varies with the changes in its configuration and location. Here, by introducing some reasonable constraints, we propose a method for restoring an acoustic image from the echo produced by a single emission. The configuration is extrapolated from the amplitude spectrum of the restricted frequency range by using the continuity condition of the amplitude spectrum at the minimum frequency of the emission and the minimum phase condition. The determination of the location requires extracting the temporal changes of amplitude spectra. For this purpose, the Gaussian chirplets with a carrier frequency compatible with bat emission sweep rates was used. The location is estimated from the temporal changes of the amplitude spectra. This method can determine the acoustic images of objects.

An echolocation model for the restoration of an acoustic image from a single-emission echo

Bats can form a fine acoustic image of an object using frequency-modulated echolocation sound. The acoustic image is an impulse response, known as a reflected-intensity distribution, which is composed of amplitude and phase spectra over a range of frequencies. However, bats detect only the amplitude spectrum due to the low-time resolution of their peripheral auditory system, and the frequency range of emission is restricted. It is therefore necessary to restore the acoustic image from limited information. The amplitude spectrum varies with the changes in the configuration of the reflected-intensity distribution, while the phase spectrum varies with the changes in its configuration and location. Here, by introducing some reasonable constraints, a method is proposed for restoring an acoustic image from the echo. The configuration is extrapolated from the amplitude spectrum of the restricted frequency range by using the continuity condition of the amplitude spectrum at the minimum frequency of the emission and the minimum phase condition. The determination of the location requires extracting the amplitude spectra, which vary with its location. For this purpose, the Gaussian chirplets with a carrier frequency compatible with bat emission sweep rates were used. The location is estimated from the temporal changes of the amplitude spectra.

Robust Adaptive Output Feedback Control for a Class of Nonlinear Systems

In this paper, we consider a class of single input-single output nonlinear systems whose nominal model is feedback linearizable and satisfies a minimum-phase condition. The system model depends linearly on unknown parameters which belong to a known compact convex set, and includes asymptotically stable, nonlinear actuators. A semi-global adaptive output feedback controller is developed; this scheme guarantees that the output of the system tracks any bounded reference signal which possesses bounded derivatives and satisfies a persistence of excitation condition. The controller scheme consists of an adaptive state-feedback controller and a high-gain observer. It is established that when the speeds of the observer and actuator are sufficiently high, the adaptive output feedback controller recovers the performance achieved under state feedback. In addition, the special case of robust adaptive regulation is presented. Finally an example is given to illustrate the developed theory.

Interpretation and identification of minimum phase reflection coefficients

If the acoustic reflection coefficient is minimum phase, then the causality condition can be used to reconstruct its phase from its magnitude. Such reconstructions are useful when environmental conditions obscure the phase, which is vital to understanding the dynamics of the reflecting object. However, the reconstructions are usually impossible because one cannot be sure that the reflection coefficient is minimum phase. The present work addresses this difficulty by formulating a time-domain description of the minimum phase condition and by identifying classes of submerged objects that always create minimum phase reflection coefficients. Numerical examples are used to confirm the analytical findings and to illustrate their applicability to objects that reflect sound with a wide range of magnitudes.

Synthesis of fiber Bragg gratings for use in transmission

A method for designing fiber Bragg gratings with desired complex transmission coefficients is proposed. The transmission coefficient of a fiber grating satisfies the minimum-phase condition when the linear phase from the pure propagation is ignored. Therefore only a finite bandwidth is considered for the synthesis. The algorithm is based on a result of Krein and Nudel’man [Prob. Peredachi Inf.11, 37 (1975)]. A numerical algorithm is developed, and by numerical examples it is demonstrated that it is possible to realize gratings with specified complex transmission responses inside the considered bandwidth. The method is also applicable for thin-film filters.

Robust output tracking of constrained nonlinear systems

The problem of output tracking for constrained nonlinear systems in the presence of uncertainties is studied. The concepts of input/output (I/O) linearization, relative degree, hyporbolically minimum phase and matching condition arc reviewed. A sliding mode control (SMC) law is developed which achieves asymptotically tracking despite the uncertainties while maintaining the boundness of all signals inside the loop.

Adaptive deadbeat control of linear time-varying systems with disturbances

This paper studies the adaptive control problem of a linear time-varying system with bounded disturbances. It is assumed that the system is uniformly controllable with known orders, and that the system parameters are varying asymptotically slowly in the mean within a bounded set. Explicit knowledge of the bounded set is not required, and neither is the stability nor the minimum phase condition for the open loop plant. The work adopts the self-excitation and identification-stabilization time-splitting approaches, and uses a special design of monotonically increasing normalization factor in the estimation algorithm. It is shown that the closed loop signals are uniformly bounded as well for sufficiently small parameter variations.

An analysis/synthesis auditory filterbank based on an IIR implementation of the gammachirp.

This paper proposes a new auditory filterbank that enables signal resynthesis from dynamic representations produced by a level-dependent auditory filterbank. The filterbank is based on a new IIR implementation of the gammachirp, which has been shown to be an excellent candidate for asymmetric, level-dependent auditory filters. Initially, the gammachirp filter is shown to be decomposed into a combination of a gammatone filter and an asymmetric function. The asymmetric function is excellently simulated with a minimum-phase IIR filter, named the “asymmetric compensation filter”. Then, two filterbank structures are presented each based on the combination of a gammatone filterbank and a bank of asymmetric compensation filters controlled by a signal level estimation mechanism. The inverse filter of the asymmetric compensation filter is always stable because the minimum-phase condition is satisfied. When a bank of inverse filters is utilized after the gammachirp analysis filterbank and the idea of wavelet transform is applied, it is possible to resynthesize signals with small time-invariant errors and achieve a guaranteed precision. This feature has never been accomplished by conventional active auditory filterbanks. The proposed analysis/synthesis gammachirp filterbank is expected to be useful in various applications where human auditory filtering has to be modeled.

Model reference robust control of systems with significant unmodelled dynamics

In this paper, a recently proposed control design technique, model reference robust control (MRRC), is generalized to provide input–output robust control for a much wider class of SISO systems. A system under consideration may contain not only parametric uncertainties, disturbances, uncertain high-order nonlinearities associated with system output (including stable unmodelled dynamics of the output), but also multiplicative unmodelled dynamics of the input of the system. Input unmodelled dynamics may be unstable and of infinite dimension. Common assumptions such as the order of the system, or bounds on system parameters, or coefficients in size-bounding functions on uncertainties and unmodelled dynamics are not needed in this paper. The a priori information required to apply the proposed design procedure includes the relative degree of the overall system, closed-form expressions of bounding functions, and, for arbitrarily small error in tracking the output of any given reference model, the minimum phase condition. Under the proposed control, the output tracking error can be made arbitrarily small to achieve any specified tracking accuracy. The distinct feature of MRRC is that neither uncertainties nor unmodelled dynamics are required to be small. © 1997 by John Wiley & Sons, Ltd.

A weighted adaptive one‐step‐ahead minimum variance controller based on the ELS algorithm

This paper deals with the design of a weighted adaptive one-step-ahead minimum variance controller based on the extended least squares (ELS) algorithm for a discrete time stochastic system. The stability of the closed-loop system and the convergence rates of the general adaptive tracking and estimation errors are respectively established under strictly positive real and minimum phase conditions. The best possible convergence rate of the average error between the predicted and desired outputs is obtained given some identifying condition and the above-stated conditions. No modification of the adaptive controller is made. © 1997 by John Wiley & Sons, Ltd.

Characterization of in-building UHF wireless radio communication channels using spectral energy measurements

A simple, cost-effective means is developed to estimate the time-invariant wireless radio channel impulse response h(t) using only the magnitude of the channel transfer function, H(jw). The Hilbert transform is used to calculate the phase of H(jw) from its magnitude. Inverse discrete Fourier transformation (IDFT) of H(jw) yields h(t). The Hilbert transform relation is applicable provided H(jw) is a minimum phase transfer function. An experimental in-building wireless channel testbed was established, for which h(t) was determined over the 1000-2500 MHz range. Both line of sight (LOS) and non-LOS transmission was investigated. Good agreement was observed between values of h(t) calculated from measured values of H(jw) and from those based only on [H(jw)] and its Hilbert transform. Even when the minimum phase condition is violated, h(t) as calculated from [H(jw)] and its Hilbert transform provides a useful lower bound on the time-spread of h(t). The measurement of [H(jw)] is easily implemented using a signal source, receiving antenna, and spectrum analyzer. A personal computer and software are required to calculate the phase of H(jw) and its IDTF. Existing frequency-domain measurement schemes utilize a vector network analyzer to measure H(jw) (magnitude and phase angle). Such equipment is expensive, subject to transmitter-receiver crosstalk, and restrictive as to the relative locations of the transmitting and receiving antenna.

Adaptive output feedback control of nonlinear systems represented by input-output models

We consider a single-input-single-output nonlinear system which can be represented globally by an input-output model. The system is input-output linearizable by feedback and is required to satisfy a minimum phase condition. The nonlinearities are not required to satisfy any global growth condition. The model depends linearly on unknown parameters which belong to a known compact convex set. We design a semiglobal adaptive output feedback controller which ensures that the output of the system tracks any given reference signal which is bounded and has bounded derivatives up to the nth order, where n is the order of the system. The reference signal and its derivatives are assumed to belong to a known compact set. It is also assumed to be sufficiently rich to satisfy a persistence of excitation condition. The design process is simple. First we assume that the output and its derivatives are available for feedback and design the adaptive controller as a state feedback controller in appropriate coordinates. Then we saturate the controller outside a domain of interest and use a high-gain observer to estimate the derivatives of the output. We prove, via asymptotic analysis, that when the speed of the high-gain observer is sufficiently high, the adaptive output feedback controller recovers the performance achieved under the state feedback one.

Effect of spectral notches on robust waveform recovery methods for machinery diagnostics

Recovery of pulselike waveforms from vibration response measurements is often a goal in reciprocating machinery diagnostics. One such method, which makes use of inverse filtering, uses cepstral windowing in an attempt to make the procedure ‘‘robust.’’ It has been observed that, under certain conditions, the timing of the (cepstrally windowed) waveforms recovered from several consecutive machine cycles may occur at one of two distinct values. This behavior stems from a zero lying close to the unit circle in the response spectrum. Small changes in the measured response will cause such a zero to fluctuate between minimum and nonminimum phase conditions, resulting in corresponding phase differences of 2π between cycles. Subsequent cepstral windowing (smoothing) of the phase curves tends to ‘‘smear’’ this difference out over a broader frequency range, causing the recovered waveforms to be grouped into two distinctly different times, depending on whether π was added or subtracted at the frequency of the zero. The timing differences between these two groups is a function of the frequency of the zero, the characteristics of the transfer function, and the cepstral window width. Waveform recovery procedures that try to take this behavior into account have been investigated, and will be discussed. [Work supported by Robert Bosch GmbH.]