Study of the stability and other properties of a class of second order variable magnitude 2-D digital transfer functions with 2-parameter denominator

2003 ◽  
Author(s):  
C.S. Gargour ◽  
V. Ramachandran
Keyword(s):  
Transfer Functions ◽  
Second Order ◽  
Order Variable ◽  
The Stability

Neural approximation-based adaptive variable impedance control of robots

2020 ◽  
Vol 42 (13) ◽  
pp. 2589-2598
Author(s):  
Xuexin Zhang ◽  
Tairen Sun ◽  
Dongning Deng
Keyword(s):  
Impedance Control ◽  
Second Order ◽  
Environment Interaction ◽  
Control Methods ◽  
Tracking Errors ◽  
The Neural Networks ◽  
Order Variable ◽  
Impedance Parameters ◽  
The Stability ◽  
Interaction Constraints

Variable impedance control improves compliance and robustness in robot-environment interaction through variation of the desired stiffness and the desired damping. This paper proposes neural approximation-based variable impedance controllers for robots in robot-environment interaction. Constraints on variable impedance parameters are given to ensure the exponential stability of the desired first- and second-order variable impedance dynamics. Adaptive neural network controllers are proposed to ensure the achievement of the desired first- and second-order variable impedance dynamics through convergence of variable impedance errors. In the neural networks, deadzone modifications are utilized to enhance robustness by turning off adaptation when auxiliary tracking errors enter the constructed small neighbourhoods of zero. The proposed variable impedance control methods in this paper guarantee the stability and achievement of the desired variable impedance dynamics. Theoretical analysis and simulation results validate the effectiveness of the proposed variable impedance control methods.

Stability of radical anions derived from substituted 5-nitrofurans investigated by ESR spectroscopy

1985 ◽  
Vol 50 (7) ◽  
pp. 1594-1601 ◽  
Author(s):  
Jiří Klíma ◽  
Larisa Baumane ◽  
Janis Stradinš ◽  
Jiří Volke ◽  
Romualds Gavars
Keyword(s):  
Radical Anion ◽  
High Stability ◽  
Esr Spectroscopy ◽  
Reaction Path ◽  
Order Reaction ◽  
Second Order ◽  
Radical Anions ◽  
Second Order Reaction ◽  
Unpaired Electron Density ◽  
The Stability

It has been found that the decay in dimethylformamide and dimethylformamide-water mixtures of radical anions in five of the investigated 5-nitrofurans is governed by a second-order reaction. Only the decay of the radical anion generated from 5-nitro-2-furfural III may be described by an equation including parallel first- and second-order reactions; this behaviour is evidently caused by the relatively high stability of the corresponding dianion, this being an intermediate in the reaction path. The presence of a larger conjugated system in the substituent in position 2 results in a decrease of the unpaired electron density in the nitro group and, consequently, an increase in the stability of the corresponding radical anions.

Analysis on the Performance of Deckwetness of Sandglass-type and Cylindrical Floating Bodies

2016 ◽  
Vol 60 (03) ◽  
pp. 145-155
Author(s):  
Ya-zhen Du ◽  
Wen-hua Wang ◽  
Lin-lin Wang ◽  
Yu-xin Yao ◽  
Hao Gao ◽  
...  
Keyword(s):  
Transfer Functions ◽  
Linear Response Theory ◽  
Second Order ◽  
Irregular Waves ◽  
Wave Loads ◽  
Floating Bodies ◽  
Drift Motion ◽  
First Order ◽  
Series Of Experiments ◽  
Deck Wetness

In this paper, the influence of the second-order slowly varying loads on the estimation of deck wetness is studied. A series of experiments related to classic cylindrical and new sandglass-type Floating Production, Storage, and Offloading Unit (FPSO) models are conducted. Due to the distinctive configuration design, the sand glass type FPSO model exhibits more excellent deck wetness performance than the cylindrical one in irregular waves. Based on wave potential theory, the first-order wave loads and the full quadratic transfer functions of second-order slowly varying loads are obtained by the frequency-domain numerical boundary element method. On this basis, the traditional spectral analysis only accounting for the first-order wave loads and time-domain numerical simulation considering both the first-order wave loads and nonlinear second-order slowly varying wave loads are employed to predict the numbers of occurrence of deck wetness per hour of the two floating models, respectively. By comparing the results of the two methods with experimental data, the shortcomings of traditional method based on linear response theory emerge and it is of great significance to consider the second-order slowly drift motion response in the analysis of deck wetness of the new sandglass-type FPSO.

Stability and resonance conditions of second-order fractional systems

2016 ◽  
Vol 24 (4) ◽  
pp. 659-672 ◽  
Author(s):  
Elena Ivanova ◽  
Xavier Moreau ◽  
Rachid Malti
Keyword(s):  
Second Order ◽  
Damping Factor ◽  
Fractional Differentiation ◽  
Resonance Amplitude ◽  
Fractional Systems ◽  
Integral Number ◽  
At Resonance ◽  
Fractional System ◽  
The Stability ◽  
Normalized Gain

The interest of studying fractional systems of second order in electrical and mechanical engineering is first illustrated in this paper. Then, the stability and resonance conditions are established for such systems in terms of a pseudo-damping factor and a fractional differentiation order. It is shown that a second-order fractional system might have a resonance amplitude either greater or less than one. Moreover, three abaci are given allowing the pseudo-damping factor and the differentiation order to be determined for, respectively, a desired normalized gain at resonance, a desired phase at resonance, and a desired normalized resonant frequency. Furthermore, it is shown numerically that the system root locus presents a discontinuity when the fractional differentiation order is an integral number.

scholarly journals PHASE PORTRAIT OF SECOND-ORDER DYNAMIC SYSTEMS

2018 ◽  
Vol 6 (3) ◽  
pp. 252-262 ◽  
Author(s):  
Kaloyan Yankov
Keyword(s):  
Phase Portrait ◽  
Plasma Renin ◽  
Higher Order ◽  
Second Order ◽  
Graphical Form ◽  
Time Behavior ◽  
Long Time ◽  
Phase Plane Method ◽  
The Stability ◽  
Higher Order Differential Equations

The phase portrait of the second and higher order differential equations presents in graphical form the behavior of the solution set without solving the equation. In this way, the stability of a dynamic system and its long-time behavior can be studied. The article explores the capabilities of Mathcad for analysis of systems by the phase plane method. A sequence of actions using Mathcad's operators to build phase portrait and phase trace analysis is proposed. The approach is illustrated by a model of plasma renin activity after treatment of experimental animals with nicardipine. The identified process is a differential equation of the second order. The algorithm is also applicable to systems of higher order.

An Evaluation of Stability Indices Using Sensitivity Functions for Active Magnetic Bearing Supported High-Speed Rotor

2006 ◽  
Vol 129 (2) ◽  
pp. 230-238 ◽  
Author(s):  
Naohiko Takahashi ◽  
Hiroyuki Fujiwara ◽  
Osami Matsushita ◽  
Makoto Ito ◽  
Yasuo Fukushima
Keyword(s):  
High Speed ◽  
Transfer Functions ◽  
Mimo System ◽  
Magnetic Bearing ◽  
Singular Value ◽  
Active Magnetic Bearing ◽  
Sensitivity Functions ◽  
Phase Lags ◽  
The Stability ◽  
Stability Indices

In active magnetic bearing (AMB) systems, stability is the most important factor for reliable operation. Rotor positions in radial direction are regulated by four-axis control in AMB, i.e., a radial system is to be treated as a multi-input multioutput (MIMO) system. One of the general indices representing the stability of a MIMO system is “maximum singular value” of a sensitivity function matrix, which needs full matrix elements for calculation. On the other hand, ISO 14839-3 employs “maximum gain” of the diagonal elements. In this concept, each control axis is considered as an independent single-input single-output (SISO) system and thus the stability indices can be determined with just four sensitivity functions. This paper discusses the stability indices using sensitivity functions as SISO systems with parallel/conical mode treatment and/or side-by-side treatment, and as a MIMO system with using maximum singular value; the paper also highlights the differences among these approaches. In addition, a conversion from usual x∕y axis form to forward/backward form is proposed, and the stability is evaluated in its converted form. For experimental demonstration, a test rig diverted from a high-speed compressor was used. The transfer functions were measured by exciting the control circuits with swept signals at rotor standstill and at its 30,000 revolutions/min rotational speed. For stability limit evaluation, the control loop gains were increased in one case, and in another case phase lags were inserted in the controller to lead the system close to unstable intentionally. In this experiment, the side-by-side assessment, which conforms to the ISO standard, indicates the least sensitive results, but the difference from the other assessments are not so great as to lead to inadequate evaluations. Converting the transfer functions to the forward/backward form decouples the mixed peaks due to gyroscopic effect in bode plot at rotation and gives much closer assessment to maximum singular value assessment. If large phase lags are inserted into the controller, the second bending mode is destabilized, but the sensitivity functions do not catch this instability. The ISO standard can be used practically in determining the stability of the AMB system, nevertheless it must be borne in mind that the sensitivity functions do not always highlight the instability in bending modes.

scholarly journals Research on Heat Transfer Dynamic Characteristics of Composite Layer Based on Laplace Transform

2019 ◽  
Author(s):  
Chunyu Xu ◽  
Junhua Lin ◽  
Wenhao Liu ◽  
Yuanbiao Zhang
Keyword(s):  
Heat Transfer ◽  
Composite Materials ◽  
Temperature Distribution ◽  
Transfer Function ◽  
Dynamic Characteristics ◽  
Transfer Functions ◽  
Composite Layer ◽  
Engineering Application ◽  
Second Order ◽  
Inverse Transformation

This paper predict and effectively control the temperature distribution of the steady-state and transient states of anisotropic four-layer composite materials online, knowing the density, specific heat, heat conductivity and thickness of the composite materials. Based on the transfer function, a mathematical model was established to study the dynamic characteristics of heat transfer of the composite materials. First of all, the Fourier heat transfer law was used to establish a one-dimensional Fourier heat conduction differential equation for each composite layer, and the Laplace transformation was carried out to obtain the system function. Then the approximate second-order transfer function of the system was obtained by Taylor expansion, and the Laplace inverse transformation was carried out to obtain the transfer function of the whole system in the time domain. Finally, the accuracy of the simplified analytical solutions of the first, second and third order approximate transfer functions was compared with computer simulation. The results showed that the second order approximate transfer functions can describe the dynamic process of heat transfer better than others. The research on the dynamic characteristics of heat transfer in the composite layer and the dynamic model of heat transfer in composite layer proposed in this paper have a reference value for practical engineering application. It can effectively predict the temperature distribution of composite layer material and reduce the cost of experimental measurement of heat transfer performance of materials.

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