State equation independent energy storage element

How do you describe the flow of energy into a storage element?

The flow of energy into or out of a storage element occurs at a finite rate and is described by a differential equation relating the derivative of the energy storage variable (a state variable) to the other power variable of the element. We will first formulate the state equations to find state variables, V3g and iL.

What are the energy storage elements in RLC circuit?

There are two independent energy storages in RLC circuit, the capacitor which stores energy in an electric field and the inductor which stores energy in a magnetic field. The state variables are the energy storage variables of these two elements,V3g and iL. The energy storage elements of a system are what make the system dynamic.

What is a state equation?

In the standard form the mathematical description of the system is expressed as a set of n coupled first-order ordinary differential equations, known as the state equations, in which the time derivative of each state variable is expressed in terms of the state variables x1(t), . . . , xn(t) and the system inputs u1(t), . . . , ur(t).

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:

How do state variables determine the rate of change of energy?

The values of the state variables at anytime t specify the energy of each energy storage element within the system and therefore the total system energy and the time derivatives of the state variables determine the rate of change of the system energy.

Can a time-varying state-space control model predict stability and voltage?

A time-varying state-space control model was presented and used to predict the stability and voltages of the RLC series circuit results are shown to validate the method. We find that the effects of changing the resistances and capacitors on the systems are negligent, whereas changing the inductor causes the output to change.