Understanding a PID Controller

The PID temperature controller is the most sophisticated controller available. Three levels of tuning - Proportional, Integral, and Derivative - provide exceptional performance at a surprisingly low price. But what is it, really? Here is an article that will help you understand it!

TEMPERATURE

A relatively new type of temperature controller is called a "PID" controller which this article will attempt to describe in layman’s language. 

As we know, characteristics and performance of many devices change with a change in temperature making them difficult to use in a particular operation. The change in temperature is caused by a change in environment. To hold characteristics constant in a changing environment we must supply or remove heat to compensate for variations in ambient temperature. This is accomplished with temperature controllers. 

Most installations of temperature controllers supply heat, or remove heat (chill), to hold the temperature at a constant point somewhat above or below the ambient temperature. Electronic temperature controllers are most often used to vary the supply of an electric current through a resistance heater to accomplish this when the controlled temperature is to be above ambient. 

The controlled device or material can also be stabilized at some temperature below environment by controlling the flow of a refrigerant through a heat exchanger. Yet another type of low temperature control system (called buck and boost) supplies cooling to drop the temperature below the desired set point and then controls the temperature by supplying heat via a controller to get the exact temperature setting. This type of operation is needed when the desired set point is close to the ambient temperature. 

In an ideal world, once we set the temperature of an area or device, the temperature would remain the same over any length of time. Unfortunately we do not live in an ideal world. Thus, the need for temperature controllers. 

If one were to observe the temperature of a controlled item over a period of time it would be rare to always find that item at the exact target (set point) temperature. Temperature would vary above and below the set point most of the time. What we are concerned about, therefore, is the amount of variation. One of the newer temperature controller designs uses a sophisticated means of reducing this variation. This controller is known as a PID controller. 
 

PID CONTROLLER DEFINITIONS

In order to understand the operation of a PID (Proportional-Integral-Differential) controller we should review a few basic definitions. 

Derivative - is a value which expresses the rate of change of another value. For instance, the derivative of distance is speed. 

Acceleration - is the derivative of velocity with respect to time. 

Integral - is the opposite of a derivative. The integral of acceleration is velocity and the integral of velocity is distance. 

Proportional - means a value varying relative to another value. The output of a proportional controller is relative to (or a function of) the difference between the temperature being controlled and the set point. The controller will be full on at some temperature which is well below the set point (or desired temperature). It will be full off at some point above the set point. 

Bandwidth of a controller is the difference in degrees between the highest full-on point and the lowest full-off point. It is the band of temperature, or range of temperature, over which the output of the controller is proportional. The width and center point temperature of this band can be varied using adjustments on the controller. 
 

PID OPERATION

A graph of the output power versus temperature would be a level line at the full output level from ambient up to the beginning of the proportional control band (which is the temperature where the controller begins to provide less than full-on power). The graph of current output versus temperature then slopes downward (to the right, in a typical chart) through the set point and on downward to the full off temperature. It would then remain full-off (a level line, now, at zero output on the vertical scale) as the controlled temperature increases. In this range, it is out of control unless cooling is switched in. 

In a narrow bandwidth, the slope of the line in the bandwidth temperature range gets steeper as the bandwidth is decreased. It is steep because the amplifier in the controller has been cranked up to a higher gain or higher amplification setting. In this high gain condition, the slightest amount of error, or deviation between the controlled temperature and the set point, causes a large change in the output of the controller. In this condition, it is very sensitive and will therefore result in a very closely regulated temperature. Because it is more sensitive, it can also result in faster changes of power output ... so much so that it can overshoot the mark and then overshoot the mark again going back down. If the bandwidth is set too narrow, the temperature can violently oscillate around the set point causing undesired variations in the controller output. 

At the other end of the bandwidth adjustment, the bandwidth is quite wide. That is to say the temperature points at which the controller turns full on and the temperature at which it turns full off are quite far apart. The graph now changes so that the slope of the power output of the controller in the proportional range is not steep. At this point, the gain of the controller amplifier is set low. It takes quite a change in the signal to result in a change of the output. This results in slow corrections of temperature. There is little or no chance of overshooting and therefore the temperature is quite stable. But although the temperature is relatively stable it may be off of the set point because of the gain not being high enough to keep up with changes in the environment around the controlled temperature area. This situation may occur when an unexpected blast of cold air sweeps across the controlled area. 

The bandwidth, therefore, must be adjusted according to conditions in and around the controlled temperature area and other thermal dynamics such as lack of insulation and thermal conductivity which results in loss of heat at a certain rate. In a well insulated area, heat loss is low and the bandwidth can be set wide. In a condition where there may be considerable heat loss, the bandwidth can be set narrower. What you want to adjust the controller for is an optimum point between stability and response time ... between holding a stable temperature and making fast corrections. 

Now we know about proportional control. We also know about gain and stability. There is one more consideration and that is the ability to hold a given temperature set point. 

For a given constant power condition, heat loss through insulation will cause the actual temperature to be slightly less than it would be in a well insulated heated area. This difference is the "I" in PID. It can be manually corrected by changing the position of the proportional band center point (called offset) so the result is the temperature you want to hold. The problem is that if the heat loss conditions (insulation) change and the system begins to lose heat faster, then that changes the offset and you may not be there to manually correct it. To compensate for this, we monitor the change of that temperature point by watching the change in temperature of the sensor. We then take the derivative of that change (get a value for the rate of change in temperature - the "D" in PID ) which is then added to the Integral value to make an automatic correction.