Feedback Control Theory:First Order Transfer Function

First Order Transfer Function

First order transfer function in standard form may be written as

It should be noted that both for step and ramp inputs, a unity gain was used. If different gain is used, the solution will be multiplied by that factor. For a ramp in- put, there is a shift between the output and input. This is known as following error. The value of the following error depends on the transfer function, which for first order system described in this section is τ. Later we will describe how to calculate the steady state error without actually solving the differential (transfer function).

Throughout this book, the variables x, y are considered as input and output variables. From the equation, it will be clear whether they are in time or Laplace domain.

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