2.1 System Inputs

Real inputs contain randomness (for example, noise). They are unpredictable.

Response of any system can be determined for known inputs. It is common practice to study the response of the system to step, impulse, and sinusoidal inputs, and sometimes to ramp and stochastic inputs. In addition to mathematical simplicity, there are other reasons for considering the manner in which the plant reacts to these input signals. For example, an arbitrary forcing function can approximated by a series of impulses, a series of step functions, etc. Refer to Fig.(2) for various idealized inputs.

  • Step input:
    Step inputs are useful to simulate sudden changes (startup, jump loading, etc). Example for a step change in input is making a sudden change in flow rate by increasing the valve opening. A practical application of the step response is the prediction of the plant behavior when a pump fails.

  • Sinusoidal input:
    A simple forcing function that varies continually and that has a zero mean value is a sinusoid. This function somewhat resembles the variations in ambient temperature during a day’s operation.

    Sinusoidal inputs are used to test frequency response.

  • Ramp input:

    Ramp inputs are used to simulate transitions between setpoints.

  • Impulse input:

    Impulses are used to simulate shock conditions