Phase Variable Form

Phase variable form is a state-space representation of a dynamical system in which the state variables are selected as a system output and its successive time derivatives, providing a structured description of system dynamics. For a linear time-invariant system, the variables are arranged in a chain, while the highest derivative is expressed using the lower-order states and the input, producing a companion, or controllable canonical, form. Engineers use phase variable form to convert transfer functions into state-space models, analyze controllability and stability, and design feedback controllers or observers. It also provides a systematic basis for simulation and system realization.

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JoVE Core - Chemistry

Phase Diagrams

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2020

A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...

Single Phase Inverter

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2023

Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT. DC power is unidirectional and flows in one direction, whereas, AC current alternates directions at a frequency of 50-60 Hz. Most common electronic devices are designed to run off of AC power; therefore an input DC source must be inverted to AC. Inverters convert DC voltage to AC through switching action that repeatedly flips the polarity of the input DC source at the output or load side for part of...

Manipulating an Independent Variable through Embodiment

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2023

Source: Laboratories of Gary Lewandowski, Dave Strohmetz, and Natalie Ciarocco—Monmouth University In any experiment, the researcher attempts to manipulate participants in one group to have different thoughts, experiences, or feelings than the other groups in the study. Some manipulations are overt, while others can be quite subtle. Embodiment is a growing research area focused on the theory that subtle physical experiences can unconsciously influence a person’s thoughts. For example if a...

Single Phase Rectifiers

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2023

Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT. A DC power supply is generally considered to be a device that supplies DC, or unidirectional, voltage and current. Batteries are one such power supply, however, they are limited in terms of lifetime and expense. An alternative method to providing unidirectional power is to transform AC line power to DC power using a rectifier. A rectifier is a device that passes current in one direction, and blocks...

Variables and Equations of State

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2026

The physical state of a pure substance can be defined by certain state variables such as volume (V), pressure (p), temperature (T), and amount of substance (n). When two gases are separated by a movable wall, the gas with the higher pressure naturally compresses the gas with the lower pressure. This causes the high-pressure gas to expand and the low-pressure gas to compress until both gases achieve mechanical equilibrium. At this point, their pressures equalize, and the movement of the wall...

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