Research on System Stability with Extended Small Gain Theory Based on Transfer Function

2011 ◽  
pp. 600-605
Author(s):  
Yuqiang Jin ◽  
Qiang Ma
Keyword(s):  
Transfer Function ◽  
System Stability ◽  
Small Gain

A simulation study of nonideal mixing effect on the dynamic response of an exothermic CSTR with Cholette’s model

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Chane-Yuan Yang ◽  
Yu-Shu Chien ◽  
Jun-Hong Chou
Keyword(s):  
Transfer Function ◽  
Dynamic Response ◽  
The Other ◽  
System Stability ◽  
Mixing Effect ◽  
Characteristic Roots ◽  
Mixing Parameter ◽  
Perfect Mixing ◽  
And Control ◽  
Inverse Response

Abstract The study of nonideal mixing effect on the dynamic behaviors of CSTRs has very rarely been published in the literature. In this work, Cholette’s model is employed to explore the nonideal mixing effect on the dynamic response of a nonisothermal CSTR. The analysis shows that the mixing parameter n (the fraction of the feed entering the zone of perfect mixing) and m (the fraction of the total volume of the reactor), indeed affect the characteristic roots of transfer function of a real CSTR, which determine the system stability. On the other hand, the inverse response and overshoot response are also affected by the nonideal mixing in a nonisothemal CSTR. These results are of much help for the design and control of a real CSTR.

scholarly journals Unified SISO Loop Gain Modeling, Measurement, and Stability Analysis of Three-Phase Voltage Source Converters

2021 ◽  
Author(s):  
Jianheng Lin
Keyword(s):  
Stability Analysis ◽  
Transfer Function ◽  
Power Systems ◽  
Linear Time ◽  
System Stability ◽  
Voltage Source ◽  
Domain Modeling ◽  
Loop Gain ◽  
Single Input Single Output ◽  
Three Phase

Frequency-domain modeling is an effective technique in the dynamic analysis of power electronic converters-based power systems. In this paper, a unified single-input single-output (SISO) loop gain modeling for the three-phase grid-tied VSCs under both symmetric and asymmetric ac grids is presented, which facilitates the physical measurement and stability analysis. Based on the linear-time-periodic (LTP) modeling technique, the harmonic admittance model of the three-phase grid-tied VSC is developed in the stationary (<i>αβ</i>)-frame. Instead of the transfer function matrix, the frequency-coupling effects are modeled by the transfer function vector, which simplifies the modeling process. According to the idea of mathematical induction, a two-by-two recursive admittance matrix (RAM) model that can accurately capture the coupling dynamics introduced by the power grid is derived. The RAM has an analytical form and is easy to include harmonic coupling components of arbitrary order. Furthermore, the RAM is converted to its equivalent SISO models following the concept of loop gain. The system stability is thus assessed by the SISO stability criteria (e.g., Nyquist stability criterion). In addition, the loop gain allows the traditional SISO perturbation and measurement scheme to be used for detecting the stability margin information. Finally, simulation results verify the feasibility and correctness of the theoretical analysis presented above.

scholarly journals A Critical Analysis of Non-ideal Quasi Z Source Inverter Considering with Parasitic Resistances

2019 ◽  
Vol 8 (4) ◽  
pp. 2061-2069
Keyword(s):  
Transfer Function ◽  
Controller Design ◽  
System Stability ◽  
Transfer Function Model ◽  
Small Signal ◽  
Signal Model ◽  
Function Model ◽  
Passive Components ◽  
Control Transfer ◽  
Conduction Mode

This paper describes the perfect small signal mathematical modeling of a non-ideal quasi-Z-source inverter (q-ZSI) by considering the parasitic resistances of capacitors and inductors. In this work, the detailed transfer function model of the system is derived mathematically by using state-space averaging method under continuous conduction mode (CCM). The deduced transfer function model exhibits the non-minimum phase of a system in the capacitor voltage-to-control transfer function due to the presence of Right-Half-Plane (RHP) zeros. The RHP zeros could impose a limitation on the controller design. Therefore, the effect of parasitic resistances of passive elements on system dynamics is analyzed with the frequency response plots such as Bode plot, Root locus and Pole-Zero maps. This analysis helps to frame the guidelines for selecting the pertinent values of passive components and their parasitic resistances. The system stability and dynamic response of the presented small signal model are compared with circuit model and validated in Mat lab/Simulink environment

Identifying the Optimal Controller Strategy for DC Motors

2017 ◽  
Vol 6 (4) ◽  
pp. 252
Author(s):  
M. R. Qader
Keyword(s):  
Transfer Function ◽  
Angular Rate ◽  
Linear Quadratic Regulator ◽  
System Stability ◽  
Step Response ◽  
Phase Lag ◽  
Linear Quadratic ◽  
Loop Control ◽  
Dc Motors ◽  
Tuning Methods

<p class="Default"><span>The aim of this study is to design a control strategy for the angular rate (speed) of a DC motor by varying the terminal voltage. This paper describes various designs for the control of direct current (DC) motors. We derive a transfer function for the system and connect it to a controller as feedback, taking the applied voltage as the system input and the angular velocity as the output. Different strategies combining proportional, integral, and derivative controllers along with phase lag compensators and lead integral compensators are investigated alongside the linear quadratic regulator. For each controller transfer function, the step response, root locus, and bode plot are analysed to ascertain the behaviour of the system, and the results are compared to identify the optimal strategy. It is found that the linear quadratic controller provides the best overall performance in terms of steady-state error, response time, and system stability. The purpose of the study that took place was to design the most appropriate controller for the steadiness of DC motors. Throughout this study, analytical means like tuning methods, loop control, and stability criteria were adopted. The reason for this was to suffice the preconditions and obligations. Furthermore, for the sake of verifying the legitimacy of the controller results, modelling by MATLAB and Simulink was practiced on every controller.</span></p>

scholarly journals Unified SISO Loop Gain Modeling, Measurement, and Stability Analysis of Three-Phase Voltage Source Converters

2021 ◽  
Author(s):  
Jianheng Lin
Keyword(s):  
Stability Analysis ◽  
Transfer Function ◽  
Power Systems ◽  
Linear Time ◽  
System Stability ◽  
Voltage Source ◽  
Domain Modeling ◽  
Loop Gain ◽  
Single Input Single Output ◽  
Three Phase

Frequency-domain modeling is an effective technique in the dynamic analysis of power electronic converters-based power systems. In this paper, a unified single-input single-output (SISO) loop gain modeling for the three-phase grid-tied VSCs under both symmetric and asymmetric ac grids is presented, which facilitates the physical measurement and stability analysis. Based on the linear-time-periodic (LTP) modeling technique, the harmonic admittance model of the three-phase grid-tied VSC is developed in the stationary (<i>αβ</i>)-frame. Instead of the transfer function matrix, the frequency-coupling effects are modeled by the transfer function vector, which simplifies the modeling process. According to the idea of mathematical induction, a two-by-two recursive admittance matrix (RAM) model that can accurately capture the coupling dynamics introduced by the power grid is derived. The RAM has an analytical form and is easy to include harmonic coupling components of arbitrary order. Furthermore, the RAM is converted to its equivalent SISO models following the concept of loop gain. The system stability is thus assessed by the SISO stability criteria (e.g., Nyquist stability criterion). In addition, the loop gain allows the traditional SISO perturbation and measurement scheme to be used for detecting the stability margin information. Finally, simulation results verify the feasibility and correctness of the theoretical analysis presented above.

scholarly journals Determining the effect of fuzziness in the parameters of a linear dynamic system on its stability

2021 ◽  
Vol 2 (4 (110)) ◽  
pp. 15-21
Author(s):  
Mykhailo Horbiychuk ◽  
Nataliia Lazoriv ◽  
Lidiia Feshanych
Keyword(s):  
Transfer Function ◽  
Mathematical Models ◽  
Dynamic System ◽  
Control Systems ◽  
Linear Dynamic System ◽  
System Stability ◽  
Design Stage ◽  
Automated Control ◽  
Margin Of Stability ◽  
Linear Dynamic

This paper considers a relevant issue related to the influence exerted by the fuzziness in linear dynamic system parameters on its stability. It is known that the properties of automated control systems can change under the influence of parametric disturbances. To describe the change in such properties of the system, the concept of roughness is used. It should be noted that taking into consideration the fuzziness in the parameters of mathematical models could make it possible at the design stage to assess all the risks that may arise as a result of an uncontrolled change in the parameters of dynamic systems during their operation. To prevent negative consequences due to variance in the parameters of mathematical models, automated control systems are designed on the basis of the requirement for ensuring a certain margin of stability of the system in terms of its amplitude and phase. At the same time, it remains an open question whether such a system would satisfy the conditions of roughness. Parameters of the mathematical model of a system are considered as fuzzy quantities that have a triangular membership function. This function is inconvenient for practical use, so it is approximated by the Gaussian function. That has made it possible to obtain formulas for calculating the characteristic polynomial and the transfer function of the open system, taking into consideration the fuzziness of their parameters. When investigating the system according to Mikhailov’s criterion, it was established that the dynamic system retains stability in the case when the parameters of the characteristic equation are considered as fuzzy quantities. It has been determined that the quality of the system significantly deteriorated in terms of its stability that could make it enter a non-steady state. When using the Nyquist criterion, it was established that taking into consideration the fuzziness in the parameters of the transfer function did not affect the stability of the closed system but there was a noticeable decrease in the system stability reserve both in terms of phase and amplitude. The relative decrease in the margin of stability for amplitude was 16 %, and for phase ‒ 17.4 %.

scholarly journals POSSIBILITIES OF CYBER-PHYSICAL APPROACH TO STUDYING FREQUENCY PROPERTIES OF CLOSED SYSTEM WITH INCOMPLETE INFORMATION ABOUT CONTROL OBJECT MODEL

2021 ◽  
Vol 2021 (4) ◽  
pp. 21-34
Author(s):  
Elena Georgievna Krushel ◽  
Ekaterina Sergeevna Potafeeva ◽  
Tatyana Petrovna Ogar ◽  
Ilya Viktorovich Stepanchenko ◽  
Ivan Mikhailovich Kharitonov
Keyword(s):  
Transfer Function ◽  
Incomplete Information ◽  
Closed System ◽  
Control Object ◽  
Optimization Procedure ◽  
Frequency Characteristics ◽  
System Stability ◽  
Object Model ◽  
Physical Approach ◽  
Frequency Properties

The article considers a method of reducing the time spent on the experimental study of the frequency properties of an object with an unknown mathematical model by using the cyber-physical approach to the automation of the experiment. Nonparametric estimates of unknown frequency characteristics of an object are received from experimental data on the reaction of the object's output to the input harmonic signal in the form of a mixture of sinusoidal signals of different frequencies. To divide the output signal into components corresponding to each frequency, a computer technology is used that implements an optimization procedure for finding the values of both real and imaginary frequency characteristics, according to the frequencies represented in the harmonic input signal. The method is also suitable for accelerated evaluation of the frequency characteristics of an object with an unknown delay. There are considered the aspects of frequency properties estimation in the problem of closed system stability analysis, which is supposed to control an object with incomplete information about its model using a series-connected proportional-integral controller. The results of quick estimating the frequency characteristics of the object are used to identify the parameters of its transfer function. To solve the parameterization problem, there are used automation tools for calculating the transfer function according to data on the points of frequency characteristics implemented as part of the open-access computer mathematics system Scilab. There is given an example illustrating the possibilities of developing a control system using a reduced-order object model, as one of the applications of the results of parametric identification of the transfer function

Comparison of robust optimal QFT controller with TFC and MFC controller in a multi-input multi-output system

2020 ◽  
Vol 1 (1) ◽  
pp. 151-161
Author(s):  
Mohammad Reza Gharib ◽  
Keyword(s):  
Transfer Function ◽  
Degrees Of Freedom ◽  
System Stability ◽  
Optimization Process ◽  
Tracking Problem ◽  
Robust Controller ◽  
Robot Controller ◽  
Process System ◽  
Output System ◽  
Nonlinear Plant

This paper suggests a practical approach for the development of a stable robot controller using the Quantitative Feedback Principle (QFT). Robot manipulators have a multivariable nonlinear transfer function, the implementation of the QFT method includes, first the conversion of their nonlinear plant into a group of linear and uncertain plant set, and then an ideal robust controller for each set has been designed. To demonstrate the effectiveness of our algorithm, we show the implementation of the two degrees of freedom manipulator. In the approach provided, the controller has been designed directly by specifying and optimizing the transfer function coefficients using a genetic algorithm. The consistency and limitations of the method are considered to be the restrictions of the problem in the optimization process. System stability and tracking problem are perceived to be the limitations of the system in the optimization process. Non-linear simulations on the tracking problem are carried out and the results illustrate the performance of the controllers. Finally, the controller constructed based on the QFT approach is compared with the TFC and MFC (Fuzzy) controllers and it is shown that the QFT methodology indicates a controller that has increased control efficiency.

scholarly journals Improving Power System Stability Using Transfer Function: A Comparative Analysis

2017 ◽  
Vol 7 (5) ◽  
pp. 1946-1952
Author(s):  
G. Shahgholian ◽  
A. Fattollahi
Keyword(s):  
Transfer Function ◽  
Power System ◽  
Closed Loop ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
System Stability ◽  
Closed Loop System ◽  
Simulation Results ◽  
Single Machine Infinite Bus ◽  
Signal Dynamic

In this paper, a small-signal dynamic model of a single-machine infinite-bus (SMIB) power system that includes IEEE type-ST1 excitation system and PSS based on transfer function structure is presented. The changes in the operating condition of a power system on dynamic performance have been examined. The dynamic performance of the closed-loop system is analyzed base on its eigenvalues. The effectiveness of the parameters changes on dynamic stability is verified by simulation results. Three types of PSS have been considered for analysis: (a) the derivative PSS, (b) the lead-lag PSS or conventional PSS, and (c) the proportional-integral-derivative PSS. The objective function is formulated to increase the damping ratio of the electromechanical mode eigenvalues. Simulation results show that the PID-PSS performs better for less overshoot and less settling time compared with the CPSS and DPSS under different load operation and the significant system parameter variation conditions.

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