Editing Proportional–integral–derivative controller (section)

==Limitations==
While PID controllers are applicable to many control problems, and often perform satisfactorily without any improvements or only coarse tuning, they can perform poorly in some applications and do not in general provide [[optimal control|''optimal'' control]]. The fundamental difficulty with PID control is that it is a feedback control system, with ''constant'' parameters, and no direct knowledge of the process, and thus overall performance is reactive and a compromise. While PID control is the best controller for an [[state observer|observer]] without a model of the process, better performance can be obtained by overtly modeling the actor of the process without resorting to an observer.

PID controllers, when used alone, can give poor performance when the PID loop gains must be reduced so that the control system does not overshoot, oscillate or [[hunting oscillation|hunt]] about the control setpoint value. They also have difficulties in the presence of non-linearities, may trade-off regulation versus response time, do not react to changing process behavior (say, the process changes after it has warmed up), and have lag in responding to large disturbances.

The most significant improvement is to incorporate [[feed-forward control]] with knowledge about the system, and using the PID only to control error. Alternatively, PIDs can be modified in more minor ways, such as by changing the parameters (either gain scheduling in different use cases or adaptively modifying them based on performance), improving measurement (higher sampling rate, precision, and accuracy, and low-pass filtering if necessary), or cascading multiple PID controllers.

===Linearity and symmetry===
PID controllers work best when the loop to be controlled is linear and symmetric. Thus, their performance in non-linear and asymmetric systems is degraded.

A non-linear valve, for instance, in a flow control application, will result in variable loop sensitivity, requiring dampened action to prevent instability. One solution is the use of the valve's non-linear characteristic in the control algorithm to compensate for this.

An asymmetric application, for example, is temperature control in [[HVAC control system|HVAC systems]] using only active heating (via a heating element), where there is only passive cooling available. When it is desired to lower the controlled temperature the heating output is off, but there is no active cooling due to control output. Any overshoot of rising temperature can therefore only be corrected slowly; it cannot be forced downward by the control output. In this case the PID controller could be tuned to be over-damped, to prevent or reduce overshoot, but this reduces performance by increasing the settling time of a rising temperature to the set point. The inherent degradation of control quality in this application could be solved by application of active cooling.

===Noise in derivative term===
A problem with the derivative term is that it amplifies higher frequency measurement or process [[noise]] that can cause large amounts of change in the output. It is often helpful to filter the measurements with a [[low-pass filter]] in order to remove higher-frequency noise components. As low-pass filtering and derivative control can cancel each other out, the amount of filtering is limited. Therefore, low noise instrumentation can be important. A nonlinear [[median filter]] may be used, which improves the filtering efficiency and practical performance.<ref>[http://eprints.gla.ac.uk/3815/1/IEEE_CS_PID_01580152.pdf Li, Y. and Ang, K.H. and Chong, G.C.Y. (2006) PID control system analysis and design - Problems, remedies, and future directions]. IEEE Control Systems Magazine, 26 (1). pp. 32-41. {{ISSN|0272-1708}}</ref> In some cases, the differential band can be turned off with little loss of control. This is equivalent to using the PID controller as a [[#PI controller|PI controller]].