Python app for drawing Bode diagram asymptotes of transfer function for minimum and non-minimal phase systems

Mapping Intimacies ◽

10.22541/au.163765400.01884533/v1 ◽

2021 ◽

Author(s):

Magno Enrique Mendoza Meza

Keyword(s):

Transfer Function ◽

Phase Curve ◽

Phase System ◽

Minimum Phase ◽

Transport Delay ◽

Phase Systems ◽

Bode Diagram ◽

Response Method ◽

Quadratic Factor ◽

Minimal Phase

The purpose of this article is to introduce an application to draw the asymptotes of Bode diagram module and phase from each constituent elementary factors of any transfer function for minimum and non-minimal phase systems without transport delay. The Bode diagram is the most used tool in the frequency response method. Python was used to program the application to perform the operations as well as the Qt5 Design for the simple graphical interface for the application and all this in the Linux operating system. The application purpose is to assist students in learning the concept and drawing of Bode diagram. For students the non-minimum phase system Bode diagram is more difficult to draw than a minimum phase system due to the presence of zeros and/or poles on right half of s-plane. The phase asymptotes of a quadratic factor was closest to the real phase curve around the corresponding undamped natural frequency and this can be observed in the example showed in this article. This example must be used as a help and not a simply to solve a problem.

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Adaptive Inverse Control of Hydro Electric Unit Based on Wavelet Neural Networks

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.591-593.1200 ◽

2012 ◽

Vol 591-593 ◽

pp. 1200-1203

Author(s):

Zhong Liao ◽

Bin Yuan Ye

Keyword(s):

Neural Networks ◽

Control Method ◽

Phase System ◽

Minimum Phase ◽

Wavelet Neural Networks ◽

Adaptive Inverse Control ◽

New Approach ◽

Inverse Control ◽

Unit System ◽

Phase Systems

Due to the nonlinear, time-variable and non-minimum phase character of hydro electric unit system integrated with water, motor and power, a new adaptive inverse control method of hydro electric unit based on the function approximation ability of the wavelet analysis and the learning characteristic of neural network is presented. The algorithm and formulas and method of adaptive inverse control is studied. It approximates the model and its inversion of hydro electric unit by wavelet neural networks(WNN), and then through constructing an aim function of broad sense, which is effective to the nonlinear non-minimum phase system. Theory and simulation to for hydro electric unit system demonstrate that the control strategy can more effective improve the dynamic and stationary performance than those based on neural networks. It gives a new approach in control for hydro electric unit system besides offer a beneficial reference to the control of non-minimum phase systems.

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Application of Fractional PID Controller to Single and Multi-Variable Non-Minimum Phase Systems

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.b2805.078219 ◽

2019 ◽

Vol 8 (2) ◽

pp. 2801-2811 ◽

Cited By ~ 1

Keyword(s):

Pid Controller ◽

Optimization Method ◽

Phase System ◽

Minimum Phase ◽

Single Variable ◽

Zero Crossing ◽

Number Of Zeros ◽

Phase Systems ◽

Simulation Results ◽

Systems Simulation

A non-minimum phase system has the unique characteristic of undershoot or over and undershoot based on the number of zeros and the location of zeros in the systems. A fractional PID controller has the ability to capture more dynamics, as there are two more parameters to tune compared to a traditional PID controller. In this paper, a fractional PID controller is designed for single and multi-variable non-minimum phase systems. A simple optimization method for the tuning of a fractional PID controller has been applied. Six different single variable plants were simulated covering different cases of non-minimum phase systems. Simulation results showed that zero crossing is reduced to a greater extent by fractional PID controller as compared to traditional PID controller for single variable systems. This paper also provides experimental validations for design and tuning of a fractional PID controller for a multi-variable non-minimum phase quadruple-tank system. Fine tuned experimental results agree well with simulation results, thereby validating the applicability of the fractional PID controller for multi variable non-minimum phase systems.

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Frequency model of an essentially nonlinear steering drive with a digital microcontroller

Civil Aviation High TECHNOLOGIES ◽

10.26467/2079-0619-2020-23-3-52-62 ◽

2020 ◽

Vol 23 (3) ◽

pp. 52-62

Author(s):

S. V. Gryzin

Keyword(s):

Transfer Function ◽

Frequency Band ◽

Dynamic Characteristics ◽

Phase System ◽

Minimum Phase ◽

Stabilization System ◽

Bending Vibrations ◽

Frequency Model ◽

Simple Description ◽

The Stability

When designing a stabilization system for highly maneuverable unmanned aerial vehicles (UAVs), one of the relevant tasks is to study the operation of the steering drive in the frequency band corresponding to the flexural vibrations of the UAV body. To ensure the stability of the UAV stabilization system, quite conflicting requirements may be imposed on the dynamic characteristics of the drive. In particular, the requirement for a sharp suppression of the amplitude-frequency characteristic at the frequency of UAV bending vibrations with minimal phase distortions in the control band of the longitudinal and lateral channels of the stabilization system can significantly complicate the task of researching the stability of the UAV motion control system. The article discusses an electric drive prototype with a digital microcontroller, designed for a highly maneuverable UAV. Adaptive algorithms of the digital controller make it possible to provide the necessary phase delays in the control frequency band and at the same time almost completely suppress the harmonic components of the control signals at the frequencies of the bending vibrations of the UAV body. The algorithms are essentially nonlinear in nature and are based on a change in the gain of the direct circuit of the drive depending on the frequency of the input signal, which greatly complicates the calculation of the transfer function of the steering drive for use in the frequency model of the stabilization system. Generally, the steering drive is described by a linear minimum-phase system, presented as a transfer function of one of the typical blocks of the first or second order, but for the specified steering drive with given dynamic characteristics, this approach is untenable. As a result of the study, a method for obtaining a frequency model of the steering drive is proposed, which is implemented as a non-minimum phase system, the main property of which is the independence of the amplitude-frequency and phase-frequency characteristics. In the process of research, the results obtained on the proposed model are compared with the results of experiments on a drive prototype and its complete non-linear time model. The main advantage of the proposed frequency model is a fairly simple description of the steering drive in the frequency domain, convenient for use as part of the frequency model of the stabilization system in the study of problems of ensuring the stability of UAV flight.

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Analysis of Practical Non-minimum Phase Systems by Transfer Function Approach

2018 4th International Conference on Electrical Energy Systems (ICEES) ◽

10.1109/icees.2018.8442413 ◽

2018 ◽

Cited By ~ 1

Author(s):

Soumyadeep Bose ◽

Yogesh V. Hote ◽

Sandeep D. Hanwate

Keyword(s):

Transfer Function ◽

Function Approach ◽

Minimum Phase ◽

Phase Systems

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On Minimum Phase

at - Automatisierungstechnik ◽

10.1524/auto.2013.1002 ◽

2013 ◽

Vol 61 (12) ◽

pp. 805-817

Author(s):

Achim Ilchmann ◽

Fabian Wirth

Keyword(s):

Transfer Function ◽

Transfer Functions ◽

Main Tool ◽

Rational Functions ◽

Phase System ◽

Zero Dynamics ◽

Minimal Realization ◽

Minimum Phase ◽

Denominator Polynomial ◽

The Time Domain

Abstract We discuss the concept of `minimum phase' for scalar semi Hurwitz transfer functions. The latter are rational functions where the denominator polynomial has its roots in the closed left half complex plane. In the present note, minimum phase is defined in terms of the derivative of the argument function of the transfer function. The main tool to characterize minimum phase is the Hurwitz reflection. The factorization of a weakly stable transfer function into an all-pass and a minimum phase system leads to the result that any semi Hurwitz transfer function is minimum phase if, and only if, its numerator polynomial is semi Hurwitz. To characterize the zero dynamics, we use the Byrnes-Isidori form in the time domain and the internal loop form in the frequency domain. The uniqueness of both forms is shown. This is used to show in particular that asymptotic stable zero dynamics of a minimal realization of a transfer function yields minimum phase, but not vice versa.

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