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State-Space System Representation for Control Systems

By: Gabe

Mathematical System Structures

With the dynamic nature of real-world processes, the common mathematical equations of system models includes:

(a) dependencies on the additive influence of process variables

(b) dependencies on the rate of change of the variables.

These two features define what is generally called the plant dynamics.

These point to the fact that the behavior of a real process will not be described satisfactorily without including its past history and the way it deals with changes.

System models can typically be reduced to the form of differential equations (continuous-time), difference equations (discrete-time) or a combination of them (hybrid or sample-data systems).

These models relate plant inputs to desired plant outputs and they deal with a limited description of the system under analysis.

State-Space Equations

A very valuable and often employed technique for plant modeling is a state-variable representation.

State variables form a set of inner variables which is a complete set. It is a complete set in the sense that; if these variables are known at some time, then any system output, y(t), can be calculated at all times in the future, as a function of the state variables and the present and future values of the inputs.

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