Can dependent energy storage elements be a state variable
In previous examples, state equations were obtained by a simple process of substitution, yet in the simple example above, further algebraic manipulation was required. This is a typical consequence of dependent energy storage elements and, as one might expect.
However, to put this discussion in perspective, every mathematical model falls short of reality, usually very far short; for example, the idea of a rigid body (which we used in.
A point to be taken from this discussion is that, if possible, energy-storage elements should be independent and have integral causality. But why? Why does it matter if an energy-storage element is dependent? If it is regarded as merely another modelling.The natural variables associated with the energy storing elements are commonly used as state variables, though alternate variables can be selected.
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6 FAQs about [Can dependent energy storage elements be a state variable]
What are state variables in energy storage?
The state variables are typically selected as the natural variables associated with the energy storage elements in the process, but alternate variables can also be used. The state equations of the system describe the time derivatives of the state variables. When the state equations are linear, they are expressed in a vector-matrix form.
What are the natural variables associated with energy storing elements?
The natural variables associated with the energy storing elements are commonly used as state variables, though alternate variables can be selected. The natural variables include, for example, capacitor voltage and inductor current in the electrical networks, and position and velocity of the inertial mass in the mechanical systems.
How many independent energy storing elements are in a state variable?
Generally we take no. Of state variable equal to number of independent energy storing elements ,
Which energy storage element does not give rise to a state variable?
Conversely, any energy storage element which must be described using a derivative operation will not require an independent initial condition and therefore will not give rise to a state variable; energy storage elements which have derivative causality are dependent.
Why do we need to know about dependent energy storage elements?
This is a typical consequence of dependent energy storage elements and, as one might expect, in more complex systems the algebraic manipulations can become formidable, even prohibitively so. It would be useful to know about dependent energy-storage elements before attempting to derive equations. How may we do so?
Why are energy storage elements not independent?
Because the two energy storage elements in this model are not independent. Because of the one-junction, the velocity or momentum of one determines the velocity or momentum of the other; given the masses of both bodies, knowing the energy of one is sufficient to determine the energy of the other.