<P> where K p (\ displaystyle K_ (\ text (p))), K i (\ displaystyle K_ (\ text (i))), and K d (\ displaystyle K_ (\ text (d))), all non-negative, denote the coefficients for the proportional, integral, and derivative terms respectively (sometimes denoted P, I, and D). </P> <P> In the standard form of the equation (see later in article), K i (\ displaystyle K_ (\ text (i))) and K d (\ displaystyle K_ (\ text (d))) are respectively replaced by K p / T i (\ displaystyle K_ (\ text (p)) / T_ (\ text (i))) and K p T d (\ displaystyle K_ (\ text (p)) T_ (\ text (d))); the advantage of this being that T i (\ displaystyle T_ (\ text (i))) and T d (\ displaystyle T_ (\ text (d))) have some understandable physical meaning, as they represent the integration time and the derivative time respectively . </P> <P> Although a PID controller has three control terms, some applications use only one or two terms to provide the appropriate control . This is achieved by setting the unused parameters to zero and is called a PI, PD, P or I controller in the absence of the other control actions . PI controllers are fairly common, since derivative action is sensitive to measurement noise, whereas the absence of an integral term may prevent the system from reaching its target value . </P> <P> The use of the PID algorithm does not guarantee optimal control of the system or its control stability (See § Limitations of PID control, below .). Situations may occur where there are excessive delays: the measurement of the process value is delayed, or the control action does not apply quickly enough . In these cases lead--lag compensation is required to be effective . The response of the controller can be described in terms of its responsiveness to an error, the degree to which the system overshoots a setpoint, and the degree of any system oscillation . But the PID controller is broadly applicable, since it relies only on the response of the measured process variable, not on knowledge or a model of the underlying process . </P>

What is steady state error in pid controller