State-space Model Of Mechanical Systems

State-space model of mechanical systems:

A transfer function model is another way of representing a mathematical model of a linear, time-invariant system. For the present mechanical system, the transfer function model can be obtained as follows: Taking the Laplace transform of each term of Equation above gives

If we set the initial conditions equal to zero, or set y(0) = 0,dy(0)/dt = 0, and u(0) = 0, the Laplace transform of Equation above can be written as

Taking the ratio of Y(s) to U(s), we find the transfer function of the system to be

Such a transfer-function representation of a mathematical model is used very frequently in control engineering. It should be noted, however, that transfer-function models apply only to linear, time-invariant systems, since the transfer functions are defined only for such systems.

For obtaining a state-space model of this system we shall first compare the differential equation for this system,

Referring to the equations,

We have,