The PID is by far the most prevalent controller in the process industry. Here we step back for a view of the basics of the proportional, integral, and derivative modes. These PID controller modes have distinct advantages and disadvantages and consequences if one mode dominates. Excessive proportional action causes a faltering or hesitation, excessive integral action causes overshoot, and excessive derivative action causes an oscillatory approach to setpoint. Here is a review of the basic functionality of each mode to achieve the best balance between modes.

Slide 1 in Basics-of-PID-Control-Figures.pdf shows the contribution of each mode to the output for a setpoint change. In this figure the proportional mode and derivative mode is acting on error (difference between setpoint and the process variable) rather than just the process variable. In the time period shown, there is no update from the process measurement so we can see more clearly the function of each mode without any feedback from the process.

**Proportional Mode Basics**

The proportional mode provides an immediate reaction to a change in the process variable. If the PID structure on proportional action on error, there is an immediate reaction to a setpoint change as well as shown in slide 1. The change in percent output is the change in percent setpoint multiplied by the controller gain. For a step change in setpoint, there is a step in the controller output from the proportional mode. This step will help get the process variable to setpoint sooner and in particular will eliminate the dead time from valve stiction and backlash. However, this step can be too large or disruptive to other loops for some applications. In particularly, operators get concerned about rapid changes. The use of a setpoint filter will slow down the change in output and the approach to setpoint reducing overshoot. The tradeoff is an increase in rise time (time to reach setpoint). If the setpoint filter time constant is set equal to the reset time, the PID effectively has a structure of proportional action on process variable rather than error.

The contribution from the proportional mode will decrease for a process variable increasing and approaching setpoint (reverse acting). This change counteracting the approach provides some anticipatory action and a sense of direction. If the proportional mode contribution is greater than the integral mode contribution, overshoot is minimized for controller gain settings that provide a fast non-oscillatory (critically damped) response. If the proportional action is too much there will be a faltering in the approach to setpoint and oscillations that could lead to overshoot. Thus, we have the interesting situation where too low of a gain can cause an overshoot by not counteracting the integral mode and too high of a gain can cause overshoot from oscillations.

If there is no change in the process variable or setpoint, the proportional mode ceases to change the output. Thus, a proportional only or proportional plus derivative controller will not cause a limit cycle from stiction or backlash in a self-regulating process.

Note that many analog controllers used proportional band instead of gain for the proportional mode tuning setting. Proportional band is the % change in the process variable needed to cause a 100% change in controller output. A 100% proportional band means a 100% change in process variable would cause a 100 % change in the controller output, which is a gain of 1. It is critical that users know the units of their controller gain setting and convert accordingly.

Gain = 100 % / Proportional Band

**Proportional Mode Advantages**

•· Minimize dead time from stiction and backlash

•· Minimize rise time

•· Minimize peak error

•· Minimize integrated error

Proportional Mode Disadvantages

•· Abrupt changes in output upset operators

•· Abrupt changes in output upset other loops

•· Amplification of noise

**Integral Mode Basics**

The integral mode integrates the error with respect to time. For a constant error as shown in slide 1, the result is a constant ramp rate. The integral mode will continue to increase the controller output even though the process variable is increasing and approaching setpoint (reverse acting) because the error is negative. Interaction action will not change sign until the process variable crosses setpoint. Consequently there is no anticipatory action or sense of direction of change. Integral action that exceeds proportional and derivative action will delay an output getting off of an output limit and will cause overshoot. Excessive integral action can also cause a runaway reaction by accelerating a temperature increasing and approaching setpoint.

If there is no change in the process variable or setpoint, the integral mode will continue to ramp since the error is never exactly zero. Thus, a controller with an active integral mode will cause a limit cycle from stiction in a self-regulating process and from backlash in an integrating process. The integral deadband parameter will suspend integral action when the PV is within the specified deadband. The enhanced PID developed for wireless will inherently suspend integral action if there is no PV update. In this case a small threshold sensitivity setting is used to prevent reaction to noise.

Note that many analog controllers used reset settings in repeats per minute instead of reset time for the integral mode tuning setting. Repeats per minute indicate the number of repeats of the proportional mode contribution in a minute. Today's reset time settings are minutes per repeat or seconds per repeat which gives the time to repeat the proportional mode contribution. Often the "per repeat" term is dropped giving a reset time setting in minutes or seconds.

Seconds per repeat = 60 / repeats per minute

**Integral Mode Advantages**

•· Eliminate offset

•· Minimize integrated error

•· Smooth movement of output

**Integral Mode Disadvantages**

•· Limit cycles

•· Overshoot

•· Runaway of open loop unstable reactors

**Derivative Mode Basics**

The derivative mode provides an output that is proportional to the rate of change of the error with respect to time. For a step change in error, the result would be a spike. A built-in derivative filter with a time constant that is a faction of the rate time, changes the spike to a kick with a moderated decay as shown in slide 1. Unless the trend chart update time is fast and time scale is short, the kick will look like a spike. When derivative action is used on PV instead of error, the kick or spike is eliminated since there is rarely a step change in the PV of loops where derivative is used (e.g. temperature). Derivative is not used in dead time dominant loops because the changes in the PV are abrupt due to the lack of a significant process time constant. If the full response occurs within one dead time, derivative action can do more harm than good. The most effective use of derivative action is the compensation (cancellation) of a secondary lag particularly in an integrating or runaway process.

Too much derivative action will cause an oscillatory approach to setpoint with a frequency faster than the natural frequency. These oscillations can persist after reaching setpoint.

Nearly all derivative tuning settings are given as a rate time in seconds or minutes. The effective rate time setting must never be greater than the effective reset time setting. The effective settings are for an ISA Standard Form. For PID with Series Form, an interaction factor as shown in Appendix K prevents the effective rate time from becoming larger than the reset time. The tuning methods developed prior to the 1990s were for the Series Form predominantly in use at the time. These tuning methods may set the rate time equal to the reset time. The use of these settings in an ISA Standard Form predominantly used today will result in severe oscillations.

The advantages and disadvantages of the derivative mode are similar to that of the proportional mode except the relative advantages is less and the relative disadvantages are greater for the derivative mode.

**Derivative Mode Advantages**

•· Minimize dead time from stiction and backlash

•· Minimize rise time

•· Minimize peak error

•· Minimize integrated error

**Derivative Mode Disadvantages**

•· Abrupt changes in output upset operators

•· Abrupt changes in output upset other loops

•· Amplification of noise

**Split Range Example**

I have had several reports from control rooms stating that a PID controller was doing the wrong thing. Consider the temperature control loop where the PV is 48 degrees, the SP is 52 degrees, and the output is split ranged between a water valve and a steam valve with the split range point at 50%. The operator looking at a faceplate as shown in Basics-of-PID-Control-Figures.pdf wants the steam valve to be open when in fact the water valve is open. He will ask the controller tuning to be corrected to make this happens which results in a technician or engineer adding more integral action to get the steam valve open. Integral action has no sense of direction and will help meet human expectations and deal with impatience when looking at digital displays. If the operator looked at the trajectory and understood dead time, he or she would realize the temperature was on a trajectory to overshoot setpoint and any change now takes on dead time to have an effect. The water valve should be open. Improvements in operator displays will show relative rate and direction of change and values one dead time into the future.