Non-minimum Phase Model Research Articles

Non-minimum phase plant control using fuzzy sliding mode

A new fuzzy logic based approach is proposed for the control of nonminimum phase systems. In this approach, a variable structure controller can be designed using fuzzy logic and linguistic control rules implementation. Simulation results of a nonminimum phase model using a fuzzy sliding mode controller are presented.

Estimation of glottal waves based on nonminimum phase models

Research on the glottal wave has been widely carried out because the characteristic of glottal wave generated by the vibration of a glottis greatly influences the quality of synthesized voice. Since it has been known that the waveforms of the glottal wave are asymmetric triangles with rounded corners, sound sources which parametrically express the glottal wave have been proposed. In these sound models, the characteristics of glottal waves in various cases must be known. In order to estimate the glottal wave from the observed voice signal, the inverse-filter method, in which an inverse filter with an inverse characteristic of the voice transfer function is used, has been widely developed. However, since the voice path transfer function and glottal wave are independently estimated in this method, error occurs and it is not an easy task to eliminate the error. This paper proposes a novel algorithm which simultaneously estimates the voice path transfer function and characteristic of the glottal wave. In this algorithm, the voice generation process is expressed by a nonminimum phase model including the characteristic of glottal wave, and the glottal wave is estimated by obtaining the parameters of the transfer function. In order to estimate the glottal wave, not only an estimation of the parameters of the transfer function but also an unknown driving input signal must be known. However, since the inverse system of the transfer function becomes unstable in this method based on the nonminimum phase model, an approximate inverse system is adopted. Then, when the characteristic of the voice path is given by an all-pole model, the glottal wave can be estimated. The nonminimum phase model by this method can be used for voice synthesis based on the glottal wave. The glottal wave was estimated by simulation and observing the sound of vowels, and it was found that this estimation algorithm was effective. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(9): 59–69, 1997

Estimation of glottal waves based on nonminimum phase models

Research on the glottal wave has been widely carried out because the characteristic of glottal wave generated by the vibration of a glottis greatly influences the quality of synthesized voice. Since it has been known that the waveforms of the glottal wave are asymmetric triangles with rounded corners, sound sources which parametrically express the glottal wave have been proposed. In these sound models, the characteristics of glottal waves in various cases must be known. In order to estimate the glottal wave from the observed voice signal, the inverse-filter method, in which an inverse filter with an inverse characteristic of the voice transfer function is used, has been widely developed. However, since the voice path transfer function and glottal wave are independently estimated in this method, error occurs and it is not an easy task to eliminate the error. This paper proposes a novel algorithm which simultaneously estimates the voice path transfer function and characteristic of the glottal wave. In this algorithm, the voice generation process is expressed by a nonminimum phase model including the characteristic of glottal wave, and the glottal wave is estimated by obtaining the parameters of the transfer function. In order to estimate the glottal wave, not only an estimation of the parameters of the transfer function but also an unknown driving input signal must be known. However, since the inverse system of the transfer function becomes unstable in this method based on the nonminimum phase model, an approximate inverse system is adopted. Then, when the characteristic of the voice path is given by an all-pole model, the glottal wave can be estimated. The nonminimum phase model by this method can be used for voice synthesis based on the glottal wave. The glottal wave was estimated by simulation and observing the sound of vowels, and it was found that this estimation algorithm was effective. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(9): 59–69, 1997

H∞ control for flutter suppression of a laminated plate with self-sensing actuators

Active flutter suppression system of a composite plate wing model is designed using a reduced order model. The analysis for a laminated composite wing with segmented piezoelectric sensor/actuator pairs is conducted by the Ritz solution technique. Unsteady aerodynamic forces calculated by doublet lattice method are approximated as the transfer functions of the Laplace variable by the minimum state method. Among the aerodynamic states obtained from rational function approximation, only one aerodynamic state is included in the plant model for feedback purpose. The neglected aerodynamic states are regarded as modeling error. The control system uses the integrated and collocated piezoelectric self-sensing actuator pairs so as to prohibit the non-minimum phase model and the spillover due to the unmodeled dynamics. Based on the mixed-sensitivityH∞ control method, the control parameters are determined. Using a simple wing model, the performance of the controlled system is shown in the frequency and time domain respectively. The electric current and the power requirement for aeroelastic control are also predicted.

Maximum likelihood estimation of the parameters of nonminimum phase and noncausal ARMA models

The well-known prediction-error-based maximum likelihood (PEML) method can only handle minimum phase ARMA models. This paper presents a new method known as the back-filtering-based maximum likelihood (BFML) method, which can handle nonminimum phase and noncausal ARMA models. The BFML method is identical to the PEML method in the case of a minimum phase ARMA model, and it turns out that the BFML method incorporates a noncausal ARMA filter with poles outside the unit circle for estimation of the parameters of a causal, nonminimum phase ARMA model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Non-Gaussian autoregressive moving average processes.

Non-Gaussian stationary autoregressive moving average sequences are considered. Under conditions concerning smoothness and positivity of the density function of the independent random variables generating the sequence, asymptotically efficient methods for the estimation of unknown coefficients of the model are described. The main interest is in nonminimum-phase models.

Optimal guidance for high-order and acceleration constrained missile

Explicit formulas of optimal guidance for a linear, time-invariant, arbitrary-order, and acceleration constrained missile are derived. These formulas are given in terms of the missile's transfer function and acceleration constraint. Optimal, full-state feedback guidance laws are synthesized and compared to first-order approximation and the proportional navigation for minimum and nonminimum missile dynamics. Simulations on a third-order missile model show the relative gain from using the full-order guidance law vs the acceleration constraint as well as some robustness tests. HE optimal control theory has been used to derive modern/optimal guidance laws which have improved performance. The improved performance of these homing laws is achieved by a consideration of the detailed dynamics of the threat (target) and the interceptor (missile). However, it comes at the expense of increased complexity in realization (cost), sensitivity to knowledge of various parameters, etc. An extensive study of literature on guidance laws in general, and optimal guidance laws in particular, is performed by Pastrick et al.1 In various references,2'6 optimal guidance laws are derived for first- and second-order missiles, respectively. In our previous paper,7 the structure of optimal guidance laws for a linear, arbitrary high-order missile was considered. Mainly, we derived the closed-loop, general structure formulas of the guidance law. Further, we studied the behavior of the gains for minimum and nonminimum phase missiles and compared the performance of some sub-optimal approximations of the guidance laws. The effect of the acceleration constraint, which is imposed by the structural or aerodynamic limitations, on guidance laws and performance for a first-order missile is systematicall y treated by Anderson.8 In this paper we derive an optimal/moder n guidance law, on collision course, for a linear, time-invariant, arbitrary order and acceleration constrained missile. It is shown that, for a minimum phase missile, the optimal guidance law is the guidance law for an unconstrained missile with saturation on the commanded acceleration. However, for a nonminimum phase missile, this is only a suboptimal guidance law, and the optimal controller is more complicated. In the paper comparison of the proportional navigation, first-order approximation, and full-order guidance laws is performed on a third-order minimum and nonminimum phase model of a missile. The comparison is performed on a common basis. Moreover, the robustness of these guidance laws is subject to an analysis, namely, the sensitivity to uncertainty/ variation in parameters, radome refraction slope, and acceleration constraint is checked for minimum and nonminimum phase air frames. The main conclusions are that, for a minimum phase missile, the full-order guidance law does not give improved performance with respect to the first-order approximation,

Slowing propagation error caused by finite register sizes in unstable systems

When doing simulations one of the worst problems that can occur is an unstable system model. These unstable models often appear in systems identification problems where the system has a non-minimum phase model. This situation leads to an unstable inverse system. The instability means that the system model must be redefined, even though the non-minimum phase model is most accurate. Or a method for deconvolution will be chosen that assumes the system is minimum phase, even though it is not. Often these inaccurate fixes or assumptions are not necessary. Cases where short strings of data are being processed can use the unstable inverse and produce good results. By using the superposition feature of linear systems it is possible to increase the useful run time of these unstable deconvolvers.

Nonminimum phase non-Gaussian autoregressive processes.

The structure of non-Gaussian autoregressive schemes is described. Asymptotically efficient methods for the estimation of the coefficients of the models are described under appropriate conditions, some of which relate to smoothness and positivity of the density function f of the independent random variables generating the process. The principal interest is in nonminimum phase models.

A Robust Pole Placement Algorithm for Adaptive Control

Publisher Summary This chapter describes a robust pole placement algorithm for adaptive control. Pole placement controllers have become popular with designers of adaptive control systems. They require only moderate computation effort, and will cope with nonminimum phase models and unknown transport lags. The computation can, however, be ill-conditioned. Ill-conditioning occurs when the plant model has dipoles. They may be inherent in the plant or can arise in the model when the model is over-parameterized. Common poles in the plant models occur in simulation studies when the A and B polynomials are over-parameterized. Advocates of pole placement have, however, maintained that as real plant is of infinite dimension, common poles will rarely arise in practice.

Internal model control of coupled distillation columns

AbstractAn experimental evaluation of methods to analyze process resilience based on internal model control (IMC) has been performed. A pilot plant consisting of two coupled distillation columns was instrumented for control studies using an LSI 11/23 microcomputer. Two alternative sets of inputs were chosen and the two full 7 (all outputs) × 4 (all inputs) transfer matrix models of the pilot plant were identified. From these models, a large number of potential 3 × 3 control structures were first screened for different levels of achievable control performance using the newly developed tools for resilience analysis. Without the need for simulation and with minimal computational effort these new techniques allow prediction of the effect of nonminimum phase characteristics, input constraints, and model uncertainty on achievable closed‐loop performance. The resilience analysis results were found to be in agreement with qualitative physical intuition. To more fully investigate the usefulness and precision of the resilience analysis, three control structures for maintaining three product compositions from a distillation system were studied experimentally. The design and performance of IMC for this complex system is demonstrated and compared with single‐loop PID controllers combined with a dynamic decoupler.