 An example would be a valve for cooling water, where the fail-safe mode, in the case of loss of signal, would be 100% opening of the valve; therefore 0% controller output needs to cause 100% valve opening.The overall control function
formula_6

where formula_7, formula_8, and formula_9, all non-negative, denote the coefficients for the proportional, integral, and derivative terms respectively (sometimes denoted "P", "I", and "D").In the "standard form" of the equation (see later in article), formula_8 and formula_9 are respectively replaced by formula_12 and formula_13; the advantage of this being that formula_14 and formula_15 have some understandable physical meaning, as they represent the integration time and the derivative time respectively.