How many state equations are there for energy storage elements?

There are three energy storage elements, so we expect three state equations. Try choosing i 1, i 2 and e 1 as state variables. Now we want equations for their derivatives. The voltage across the inductor L 2 is e 1 (which is one of our state variables)

How many energy storage elements are there?

There are three energy storage elements, so we expect three state equations. The energy storage elements are the spring, k 2, the mass, m, and the spring, k 1.

How many energy storage elements does a circuit have?

So, even having three energy storage elements (capacitors), the order of system is two. On the second circuit There are only 3 INDEPENDENT initial conditions. The initial current through L3, for example, can be determined by the initial currents I1 and I2. So, even having four energy storage elements, the order os system is three.

What is the state space model for an nth-order system?

The state space model for an nth-order system is a set of n 1st-order differential equations, called the state equations, and a set of p algebraic equations, called the output equations. The set of equations are written in a compact matrix-vector notation in the following manner:

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?