Minimum Phase Transfer Function Research Articles

状態フィードバックによる擬似インナー化制御

In this paper, we will propose the method of pseudo innerizing by state feedback for a given strictly proper transfer function matrix. The method is an extended result for transfer function matrices which have proper left-inverse, and a generalization of inverted interactorizing for minimum phase transfer function matrices. Numerical examples will be also shown to illustrate the presented method.

Causality in Continuous Wavelet Transform Without Spectral Matrix Factorization: Theory and Application

This paper proposes a continuous wavelet transform causality method that dispenses with minimum-phase spectral density matrix factorization. Extant methods based on minimum-phase function are computationally intensive and those utilizing discrete wavelet transform also fail to unfold causal effects over time and frequency. The proposed method circumvents the need for minimum-phase transfer functions and is able to localize causality in time and frequency suitably. We study the ability of the proposed method using simulated data and find that it performs excellently in identifying the causal islands. We then use the method to analyze the time---frequency causal effects in the relationship between the US financial stress and economic activity and find that financial stress has been causing economic activity particularly during the unwinding financial and economic distress and not the other way around.

Combining differential evolution and particle swarm optimization to tune and realize fractional-order controllers

In recent years, several research works proposed fractional-order controllers as means to improve the performances of common proportional, integral and derivative controllers. However, the design and tuning methods for these new controllers are still at their infancy. As a contribute for filling this gap, this article proposes a two-step design approach. First, differential evolution determines the fractional integral and derivative actions satisfying the required time-domain performance specifications. Second, particle swarm optimization determines rational approximations of the irrational fractional operators as low-order, stable, minimum-phase transfer functions with poles interlacing zeros. Extensive time- and frequency-domain simulations validate the efficiency of the proposed approach.

Time-domain simulation and waveform reconstruction for shielding effectiveness of materials against electromagnetic pulse

Shielding effectiveness (SE) of materials of current testing standards is often carried out by using continuous-wave measurement and amplitude-frequency characteristics curve is used to characterize the results. However, with in-depth study of high-power electromagnetic pulse (EMP) interference, it was discovered that only by frequency-domain SE of materials cannot be completely characterized by shielding performance of time-domain pulsed-field. And there is no uniform testing methods and standards of SE of materials against EMP. In this paper, the method of minimum phase transfer function is used to reconstruct shielded time-domain waveform based on the analysis of the waveform reconstruction method. Pulse of plane waves through an infinite planar material is simulated by using CST simulation software. The reconstructed waveform and simulation waveform is compared. The results show that the waveform reconstruction method based on the minimum phase can be well estimated EMP waveform through the infinite planar materials.

The Combined Effect of Missile IMU Shift, Model Following and Add-on SAC on the Autopilot Response

Proper location of the missile's inertial measurement unit renders the transfer function from the control surfaces to the acceleration measurement minimum-phase. Usually the poles and zeros of the missile actuators and rate gyros lie in the open left half plane. In this case the minimum-phase transfer function implies minimum-phase autopilot. Missile autopilots are designed to guarantee stability and performance throughout the flight envelope. The stability and performance are conflicting objectives. The final design is a compromise between stability margins and autopilot agility. In this paper the presented control architecture has the potential to resolve the conflict between robust stability and robust performance. The performance of the missile autopilot resulted from the combined effect of IMU location and reference model following can be further improved by using a simple Add-On adaptive control algorithm. The paper demonstrates the improved performance via example. The simple adaptive control (SAC) algorithm used in the paper involves the synthesis of parallel feedforward which guarantees that the controlled plant is almost strictly positive real (ASPR).

Second-Order Systems With Acceleration Measurements

Accelerometers are often used to measure the output of second-order systems, such as structural vibrations. Conditions under which these systems are well-posed are obtained. We also establish conditions under which these systems have minimum-phase transfer functions.

Pole-Zero, Zero-Pole Canceling Input Shapers

This paper presents the development of an input-shaper/time-delay filter, which exploits knowledge of the zeros of a minimum-phase transfer function to reduce the output-transition time for a rest-to-rest maneuver problem, compared to the traditional zero vibration (ZV) input shaper. The maneuver time of the robust input shaper presented in this work will correspondingly have a smaller maneuver time compared to the zero vibration derivative (ZVD) input-shaper. The shaped profile is changing with time even after the completion of the maneuver similar to postactuation controllers. All the traditional technique for addressing multiple modes and desensitizing the filter over a specified domain of uncertainties are applicable to the technique presented in this paper.

Force Control of a Constrained One-Link Flexible Arm with Internal Damping

In this paper, the contact force control of a constrained one-link flexible arm is fully investigated using a linear distributed parameter model including the internal damping of Kelvin-Voight type. To overcome the inherent limitations caused by the non-minimum phase nature of the noncollocation of the joint torque input and the contact force output, a minimum phase transfer function is deduced by using the feedback and the output redefinition. A PD controller is then designed to accomplish the regulation of the contact force. Therefore, asymptotic tracking of a desired contact force trajectory with internal stability can be achieved. With the infinite product of transcendental functions, exact solutions of the noncollocated infinite-dimensional closed-loop force control system can be obtained so that it is free from spillover problems with stability robustness to parameter uncertainties. Numerical simulations are provided to verify the effectiveness of the proposed approach.

Conditions for a Class of Rational Approximants of Fractional Differentiators/Integrators to Enjoy the Interlacing Property

AbstractFractional-order controllers are based on fractional differentiators and integrators, which extend classical integral or derivative actions to improve performance and robustness of feedback loops. The fractional (irrational) operators are usually realized by continued fractions leading to rational approximations. Stable and minimum-phase transfer functions, with interlaced distribution of real zeros and poles, are also requested as suitable approximations. This paper proves that two classes of continued-fractions-based approximations have negative zeros and poles enjoying the interlacing property, for any fractional order v, with |v| < 1, and for any degree, m, of the approximating transfer function.

Stable equivalent models with minimum phase transfer functions in the dynamic aggregation of voltage regulators

The dynamic aggregation is a step of the calculation of coherency-based dynamic equivalents. If the dynamic aggregation of voltage regulators is solved as an unconstrained optimization problem, negative time constants may appear in the solution, which characterize unstable equivalent models and/or nonminimum phase equivalent transfer functions. The squared-variable transformation is considered to solve this problem. The solutions of the dynamic aggregation problem of voltage regulator models obtained with both the original formulation and the squared-variable transformation are compared. A criterion is also proposed to select the best equivalent voltage regulator model for each coherent group. The New England system, including salient-pole synchronous machines with subtransient effects and excitation system models, is considered in the studies.

A real-time kepstrum approach to speech enhancement and noise cancellation

This paper introduces the kepstrum method of identification of acoustic transfer functions and its real-time application in techniques such as speech enhancement and noise cancellation. By using kepstrum (known elsewhere as complex cepstrum) analysis, we will show that the kepstrum method is reliable and applicable to real-time processing by providing an efficient kepstrum processing technique with a fast processing time using fast Fourier-transforms (FFTs). Furthermore, it will be shown that its application to speech enhancement methods gives several favourable effects such as: (1) application flexibility by enabling invertibility, which gives a stable minimum phase transfer function on application of the inverse of a room impulse response, (2) processing robustness by using it as building blocks and (3) computational simplicity by highly reduced weights in an adaptive algorithm when it is used with a cascaded adaptive filter. Accordingly, we will show that the kepstrum approach contributes to speech enhancement and noise cancellation with an improved performance in signal-to-noise ratio (SNR) by using only two microphones with a small physical dimension in size. Experiments on a 20 cm broadside two-microphone acoustic beamformer configuration are implemented in real-time in an indoor office.

A Study on Pre-Inverse Adaptive System Based on Estimation of Minimum-Phase and Allpass Transfer Function

In this paper, we discuss a pre-inverse adaptive system in which the adaptive filter is located before the unknown system. We then propose an adaptive system that does not require a replica of the unknown system, as in the case of the filtered-x adaptive system. With the proposed method, we can therefore avoid the instability that arises from error in the replica of the unknown system. In the proposed method, the inverse transfer function of the minimum-phase part of the unknown system is estimated by an adaptive exponential filter. The inverse transfer function of the allpass part of the unknown system is estimated by an adaptive transversal filter, whose inverse can be easily realized by reversing the order of the weights. Finally, a numerical verification of the analytical results, the convergence performance of the adaptive systems, and a performance comparison with the filtered-x adaptive system are obtained by computer simulation

Partial Fraction Decomposition and Correlation Sequence in 2D Systems

In this paper, results of the one-dimensional (1D) digital filtering are extended to the two-dimensional (2D) case. It introduces a technique and an algorithm for the computation of the product H(z1,z2)H(z1-1z2-1). The technique is used to find a minimum phase transfer function of a 2D system such that the previous product matches a given correlation sequence. The algorithm requires less arithmetic operations than the traditional methods. The former is based on a matrix formulation of the product, which is used to investigate the 2D partial fraction decomposition (PFD) and stability.

ACHIEVING MINIMUM PHASE TRANSFER FUNCTION FOR A NONCOLLOCATED SINGLE‐LINK FLEXIBLE MANIPULATOR

ABSTRACTA noncollocated system has the potential of providing more precise tracking, improved disturbance rejection and increased bandwidth at the sensor location, but is considerably more difficult to stabilize than a collocated system due to its nonminimum phase nature. For a flexible manipulator, the problem becomes even more complicated because the system is inherently infinite dimensional. In this paper, a single‐link flexible manipulator having a tip payload and a noncollocated actuator and sensor is investigated using a linear distributed parameter model. With the joint torque as the input and the joint angle plus a weighted value of tip deflection as the measured output, an exact transfer function involving transcendental functions is derived. Using the methods of infinite product expansion, the root locus, and the asymptotic property of the roots of the transcendental equation, a necessary and sufficient condition in terms of the weighting factor of tip deflection is obtained such that the transfer function does not have any open right‐half plane zeros. This condition depends neither on the physical properties of the link nor on the mass properties of the tip payload. In order to correct the misinterpretation which has occurred in some closely‐related works concerning the stability of the infinite‐dimensional zero‐dynamics, the equivalence of the zeros of the transfer function and the eigenvalues of zero‐dynamics is also verified. Numerical results for the closed‐loop performance of a single‐link flexible arm using collocated and noncollocated PD controllers are given to show the efficacy of the proposed minimum phase transfer function approach.

On the identification of certain rational transfer functions from truncated autocovariance sequences

Let H(z)=/spl Sigma//sub k=0//sup /spl infin// H/sub k/z/sup -k/ be a q/spl times/p rational causal minimum phase transfer function, and let (R/sub n/)/sub n/spl isin/Z/ be the autocovariance sequence associated to the spectral density H(z)H/sup T/ (z/sup -1/). In this paper, the authors address the identification problem of H(z) from the truncated autocovariance sequence (R/sub n/)/sub n/spl ne/0/ for the case q>p.

Robust adaptive ship autopilot with wave filter and integral action

A stable minimum phase transfer function from rudder angle to yaw angle is used to design a globally convergent adaptive ship autopilot. First-order wave disturbances in yaw are filtered by applying a notch filter. Integral action is introduced by augmenting the plant. Global convergence is proven for the total system which includes the observer, the parameter update law, the feedback controller, the notch filter and the integral part of the controller. The simulation results showed that the performance is excellent, even with no a priori knowledge of the ship parameters. © 1998 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.

A Globally Stable Adaptive Ship Autopilot with Wave Filter using Only Yaw Angle Measurements

A stable minimum phase transfer function from rudder angle to yaw angle is used to design a globally stable adaptive ship autopilot. 1st-order wave disturbances in yaw are filtered by applying a notch filter. Integral action is introduced by using a reference model technique. Global stability is proven for the total system which include the yaw rate observer, the parameter update law, the feedback controller, the notch filter and the integral part of the controller. The simulation results showed that the performance is excellent, even with no a priori knowledge of the ship parameters.

Simultaneous stabilization using stable system inversion

This paper investigates the use of stable system inversion to design controllers for the simultaneous stabilization of multi-input multi-output systems. A parametrization of all simultaneously stabilizing controllers for systems admitting a stable inverse is developed. The controller is shown to have the structure of a generalized observer. For strictly proper systems, an intermediate step of the design requires solving a sequence of strong stabilization subproblems. For systems with components having identical stable minimum phase transfer functions, the design requires only a single model of the component in the controller. In systems where a stable inverse fails to exist, an interpolation scheme is proposed to develop a stabilizing controller.

A globally optimal minimax solution for spectral overbounding and factorization

In this paper, an algorithm is introduced to find a minimum phase transfer function of specified order whose magnitude tightly overbounds a specified real-valued nonparametric function of frequency. This method has direct application to transforming nonparametric uncertainty bounds (available from system identification experiments and/or plant modeling) into parametric representations required for modern robust control design software (i.e., a minimum-phase transfer function multiplied by a norm-bounded perturbation). >