Figure 1. In this simple controller circuit with thermocouple and load, you adjust the setpoint by setting a DC millivolt signal representing desired temperature.

This month, as promised, I’ll show the elements of a controller that can throttle back the power well ahead of the temperature reaching setpoint and provide a way to defeat temperature overshoot and cycling. Figure 1 shows the elements of a controller that would achieve this, along with a thermocouple and a controlled load.

## Proportional Control

How It Works.On the circuit on figure 1 you adjust the setpoint by setting a DC millivolt signal representing desired temperature. You read this on a scale or on a digital readout. Your control thermocouple (feedback) will match this value when the process comes up to the desired temperature.

The back-to-back (subtractive) connection of setpoint millivolts and thermocouple millivolts puts the difference (called the error signal, e) into the amplifier.

As connected in figure 1, the amplifier’s objective is to deliver enough power to the heater to bring the thermocouple temperature (therefore, millivolts) up to match the setpoint.

Potential Problem. If the amplifier gain is very high, the slightest error signal (minus or plus) at its input gives full heater power or no heater power. You are now back to on/off control; power does not go off until the temperature has reached setpoint. The result is large overshoot and temperature swings.

Solution. Reduce the amplifier gain (k) so that it takes an error (e) of say 70oF (40oC) to give full heater power at the output. Because it is a linear amplifier in terms of power, it then will give 50 percent power at a 35oF (20oC) error; 25 percent power at a 18oF (10oC) error, and so on.

The controller is now delivering corrective action (i.e., power) in proportion to deviation of temperature from setpoint. This is proportional control, where Power (P) = ke (that is, power equals amplifier gain times error).

The size of error needed to make the amplifier deliver 100 percent power is called the proportional band (70oF [40oC] in this example). It is sometimes expressed as a percentage of controller temperature range. So, if this controller has a range of say 32 to 1832oF (0 to 1,000oC) 70oF (40oC) represents a 4 percent proportional band. The gain (k) is defined as 100 divided by the proportional band (or, 100/4, which equals 25 in this example).

Avoid Overshoot and Temperature Swings. If you make the proportional band large enough (figure 2), the power will throttle back in good time to avoid overshoot and the temperature swings that come with it.

If the temperature could reach setpoint (giving zero deviation), the amplifier input would reach zero; therefore, so would the power. This does not happen. The temperature settles out somewhere below setpoint, and some intermediate level of power is delivered. This shortfall of temperature below setpoint is called offset.

It is no use reducing the proportional band to get more power and try to reduce the offset. You would soon break into temperature and power swings again (called control loop instability).

How to Eliminate Offset? Say the temperature settles at 356oF (180oC), or 36oF (20oC) below your setpoint of 392oF (200oC).

You could reset the setpoint 36oF (20oC) up at 428oF (220oC) to get the controlled temperature close to 392oF (200oC). Early controllers had a small knob called manual reset that achieves this without showing it as an extra 36oF (20oC) on the setpoint display. So, this 36oF (20oC) deviation is amplified into enough power to heat the zone to about 392oF.

Problem. There will be times when the zone needs say, twice that power to hold 392oF (200oC). One example is when you have a higher material throughput or a very cold material and environment. To put out twice the power, the amplifier needs twice the input, or a 72oF (40oC) offset. Simply setting the manual reset at 36oF (20oC) and leaving it there would take the temperature down again toward 356oF (180oC) during times when the zone needs more power.

So, are you going to keep resetting the setpoint and waiting around every time the heat demand changes? No. You need an automatic and continuous watch on the temperature and gentle corrections of the power aimed at keeping the deviation at zero.

Figure 2. This startup graph of a temperature control loop show that if you make the proportional band large enough, the power will throttle back in good time to avoid overshoot and the temperature swings that come with it.

## Integral Action

Instead, you give the amplifier a second job: integral action, which is sometimes called automatic reset. Let it watch the deviation, and so long as it persists, make the amplifier put out a gently increasing contribution until there is just enough power to reach setpoint, making the deviation (e) equal to 0.

The amplifier is designed to make the rate of power growth proportional to deviation. So, when temperature comes close to setpoint, the power is changing very slowly. When the temperature reaches setpoint, the power stops growing and holds at just the level needed to hold the temperature at setpoint. This is called integral action. With it, you now have a PI (proportional + integral) controller.

A simple definition of integral time is this: If the deviation stays equal at one proportional band, the contribution of integral action will grow to 100 percent power in one integral time (Ti).

## Derivative Action

Now, you give the amplifier a third job: derivative action, which is sometimes called rate action. Let it watch for changes of temperature and put out a contribution of power proportional to rate of change. For example, does the temperature change in a fast dive? Give a big power boost. Slow dive? Gentle boost. Fast rise? Big throttle back. The purpose is to resist and damp out unwanted changes and to speed up recovery from temperature disturbances.

A simple definition of derivative time is this: If the temperature dives at a rate of one proportional band in one derivative time (Td), the contribution of derivative action is 100 percent power. (And, its response would be minus 100 percent power for temperature climbing.)

You now have a PID (proportional + integral + derivative) controller, which is also called a three-term or three-mode controller. Among the parameters that you adjust to optimize (or tune) your controller are proportional band, integral time and derivative time. I'll pick up with tuning your PID controller in my next column. PH