Graphical Determination of Optimum Trajectories for Third-Order Systems

The present paper explains the use of two phase planes in the graphical determination of optimum trajectories for third-order systems, depending on the sign of a single control function. The control function is defined on these planes by means of different contours. Accordingly, the control signal is known at the different points on these planes. Once the control signal is found, the state trajectory is determined. Most of the arbitrary initial states are treated and, in particular, the cases of separate steps in each of the error and its first as well as second time derivatives. This work also explains the use of the graphical solution in obtaining the maximum error and switching times.

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The two-dimensional laminar jet in parallel streaming flow

Journal of Fluid Mechanics ◽

10.1017/s0022112067000461 ◽

1967 ◽

Vol 27 (3) ◽

pp. 431-443 ◽

Cited By ~ 8

Author(s):

I. Wygnanski

Keyword(s):

Order Term ◽

Asymptotic Series ◽

Maximum Error ◽

Approximate Determination ◽

Two Dimensional ◽

Direct Expansion ◽

Third Order ◽

Laminar Jet ◽

External Stream

Solutions to the problem of a two-dimensional, laminar jet of incompressible fluid issuing into a uniform stream in the direction of the main flow are considered. Two co-ordinate-type expansions are developed. A direct expansion, when suitably transformed, predicts approximately the velocity along the plane of symmetry of the jet for all values of the abscissa, with a maximum error of 7·6% far downstream from the origin. This error is established by comparison with a second, asymptotic expansion valid only at large values of the abscissa. The two expansions are subsequently joined, permitting an approximate determination of a constant which multiplies a third-order term in the asymptotic series and which initially remained unknown even after satisfying all boundary conditions imposed on these series.The decay of velocity excess along the plane of symmetry of the jet is accelerated by the presence of the external stream.

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Determination of the Maximum Error for Pole Placement for a Nonlinear Third-Order Process

Process Control Design for Industrial Applications ◽

10.1002/9781119407461.app2 ◽

2017 ◽

pp. 249-256

Keyword(s):

Maximum Error ◽

Pole Placement ◽

Order Process ◽

Third Order

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Surface active agents. Determination of anionic surface active agents. Potentiometric two-phase titration method

10.3403/03165095u ◽

2015 ◽

Keyword(s):

Titration Method ◽

Two Phase ◽

Surface Active Agents ◽

Surface Active ◽

Anionic Surface

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Surface active agents. Determination of anionic surface active agents. Potentiometric two-phase titration method

10.3403/03165095 ◽

2004 ◽

Keyword(s):

Titration Method ◽

Two Phase ◽

Surface Active Agents ◽

Surface Active ◽

Anionic Surface

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Evaluating the efficiency of closed two-phase thermosyphons based on experimental determination of temperatures in the characteristic cross sections of the working area

Tyumen State University Herald Physical and Mathematical Modeling Oil Gas Energy ◽

10.21684/2411-7978-2019-5-1-41-54 ◽

2019 ◽

Vol 5 (1) ◽

pp. 41-54

Author(s):

Vyacheslav I. Maksimov ◽

Atlant E. Nurpeiis

Keyword(s):

Experimental Determination ◽

Cross Sections ◽

Two Phase

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Determination of specific interfacial areas in swirled two-phase flow

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19830842 ◽

1983 ◽

Vol 48 (3) ◽

pp. 842-853

Author(s):

Kurt Winkler ◽

František Kaštánek ◽

Jan Kratochvíl

Keyword(s):

Interfacial Area ◽

Liquid Volume ◽

Upward Flow ◽

Two Phase ◽

Flow Rates ◽

Mist Flow ◽

Interfacial Areas ◽

Correlation Parameters ◽

Flow Components

Specific gas-liquid interfacial area in flow tubes 70 mm in diameter of the length 725 and 1 450 mm resp. containing various swirl bodies were measured for concurrent upward flow in the ranges of average gas (air) velocities 11 to 35 ms-1 and liquid flow rates 13 to 80 m3 m-2 h-1 using the method of CO2 absorption into NaOH solutions. Two different flow regimes were observed: slug flow swirled annular-mist flow. In the latter case the determination was carried out separately for the film and spray flow components, respectively. The obtained specific areas range between 500 to 20 000 m3 m-2. Correlation parameters are energy dissipation criteria, related to the geometrical reactor volume and to the static liquid volume in the reactor.

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Interphase distribution of 2-furylethylenes

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19851642 ◽

1985 ◽

Vol 50 (8) ◽

pp. 1642-1647 ◽

Cited By ~ 2

Author(s):

Štefan Baláž ◽

Anton Kuchár ◽

Ernest Šturdík ◽

Michal Rosenberg ◽

Ladislav Štibrányi ◽

...

Keyword(s):

Partition Coefficient ◽

Partition Coefficients ◽

Transport Rate ◽

Phase System ◽

Two Phase ◽

Interphase Distribution ◽

Distribution Kinetics ◽

System 1 ◽

Kinetics Of

The distribution kinetics of 35 2-furylethylene derivatives in two-phase system 1-octanol-water was investigated. The transport rate parameters in direction water-1-octanol (l1) and backwards (l2) are partition coefficient P = l1/l2 dependent according to equations l1 = logP - log(βP + 1) + const., l2 = -log(βP + 1) + const., const. = -5.600, β = 0.261. Importance of this finding for assesment of distribution of compounds under investigation in biosystems and also the suitability of the presented method for determination of partition coefficients are discussed.

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Determination of cross-sectional void fraction in a two-phase water flow through a PVC pipe

IOP Conference Series Earth and Environmental Science ◽

10.1088/1755-1315/655/1/012024 ◽

2021 ◽

Vol 655 (1) ◽

pp. 012024

Author(s):

O.H. Ajesi ◽

M.B. Latif ◽

S.T. Gbenu ◽

C. A. Onumejor ◽

M. K. Fasasi ◽

...

Keyword(s):

Water Flow ◽

Void Fraction ◽

Two Phase ◽

Cross Sectional ◽

Flow Through ◽

Pvc Pipe ◽

Phase Water

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Implementation of an FPGA-Based Current Control and SVPWM ASIC with Asymmetric Five-Segment Switching Scheme for AC Motor Drives

Energies ◽

10.3390/en14051462 ◽

2021 ◽

Vol 14 (5) ◽

pp. 1462

Author(s):

Ming-Fa Tsai ◽

Chung-Shi Tseng ◽

Po-Jen Cheng

Keyword(s):

Discrete Time ◽

Control Function ◽

Current Control ◽

Motor Drives ◽

Modulation Scheme ◽

Time Interval ◽

Switching Scheme ◽

Two Phase ◽

Ac Motor ◽

Ac Motor Drives

This paper presents the design and implementation of an application-specific integrated circuit (ASIC) for a discrete-time current control and space-vector pulse-width modulation (SVPWM) with asymmetric five-segment switching scheme for AC motor drives. As compared to a conventional three-phase symmetric seven-segment switching SVPWM scheme, the proposed method involves five-segment two-phase switching in each switching period, so the inverter switching times and power loss can be reduced by 33%. In addition, the produced PWM signal is asymmetric with respect to the center-symmetric triangular carrier wave, and the voltage command signal from the discrete-time current control output can be given in each half period of the PWM switching time interval, hence increasing the system bandwidth and allowing the motor drive system with better dynamic response. For the verification of the proposed SVPWM modulation scheme, the current control function in the stationary reference frame is also included in the design of the ASIC. The design is firstly verified by using PSIM simulation tool. Then, a DE0-nano field programmable gate array (FPGA) control board is employed to drive a 300W permanent-magnet synchronous motor (PMSM) for the experimental verification of the ASIC.

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