Control Engineering

What is the simplest way precisely control the temperature of a resistive heater?
June 18, 2007

There are a fair number of ways to control a resistive heater, but not many combine both “precise” and “simple.” My favorite¹ is to combine the functions of sensor and heater in the same object. That is, use the resistive heater element as a sensor as well.

The basic resistive heating element consists of a more-or-less refractory metal wire conductor that dissipates electric energy as heat. A controlled current I passes through the wire, whose sole function is to present an electrical resistance R_e, impeding the current flow.

A current-carrying conductor can also be used as a temperature detector, since the resistance of most materials is temperature dependent. Specifically, for metals the resistance rises slightly as temperature rises. Temperature sensors based on this effect are called resistance temperature devices (RTDs).

Since both resistance heaters and RTDs consist of a wire carrying electric current, it doesn’t take too much imagination to want to combine them into one device that will heat up and report its temperature at the same time. The control issue is that everything is in flux. To change the temperature, you need to change the current, which changes the measurement parameters. How do you separate the sensor output from the control input?

You do it by realizing that the only thing that affects the wire’s resistance is temperature. Increasing the current through the wire does tend to increase its resistance, but only because increased current leads to increased dissipation, which raises the temperature. The resistance changes only when the temperature changes.

The classic way to separate resistance measurement from other confounding factors is to use a Wheatstone bridge. The bridge consists of four resistors wired in a diamond pattern. The resistors form the diamond’s sides. For our purposes, three of the resistors are fixed and the heating element serves as the fourth. Say, we put it in the lower-right position.

Ideally, you want the resistors on the left side to be approximately equal. Since they’re both fixed, there’s no reason to not make them exactly (within manufacturing tolerances) equal. Their value (R₀) should be much higher (say an order of magnitude) than that of the heating element (R_e)at the control temperature.

To control the temperature of a resistive heater, place it in a Wheatstone bridge and use the out-of-balance signal to control the current feeding the bridge.

To get negative feedback to control the current through the heating element, I like to start with an op-amp wired as a differential amplifier. (See last week’s Ask Charlie posting) The differential amplifier’s negative terminal goes to the right-hand diamond point, and the positive terminal to the left. The amplifier’s single-ended output goes to a power amplifier—which can be a simple junction power transistor—supplying the bridge’s excitation current. The amplifier gain should be keep the power transistor either cut off or saturated except when the bridge is very nearly balanced.

When power is initially applied to this rig, the heating element will be cold, making its resistance low. The voltage at the amplifier’s negative input will therefore be lower than that at the positive input. The amplifier’s output will be high, driving the transistor current into saturation.

As the heating element’s temperature rises, its resistance also rises. The voltage difference between the inputs drops until the power transistor comes out of saturation and the supply current begins to fall.

As the temperature continues to rise, the supply current continues to fall until equilibrium is reached where the current is just enough to maintain the temperature very near to, but slightly below, the set temperature. How close depends on the differential amplifier’s gain.

This electrical circuit reacts faster than the thermal system, so the control loop is quite stable, even with relatively high differential amplifier gain.

¹ Masi, C.G., "Temperature Control of a Tungsten Incandescent Lamp," Review of Scientific instruments, vol. 50, no. 2, February 1979, pp. 257-258.

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