Electronic Design

Hybrid Digital-Analog Proportional-Integral Temperature Controller

A classic scheme for precision temperature control is the proportional-integral or “P/I” algorithm. In this method, the heater control equation consists of two terms. One term (“P”) is proportional to the instantaneous error differential between sensor and setpoint temperatures. The other (“I”) is proportional to the time integral of the error. P/I controllers characteristically have reasonably good dynamic response due to the proportional feedback term, nominally zero steady-state error thanks to the error integration term, and relatively simple loop optimization because only three adjustments (setpoint, proportional gain, and integrator time-constant) are involved in the setup process.

The simplicity of the P/I feedback algorithm argues for a similarly simple analog-based controller design. But some temperature-control applications involve long time-constants (running to minutes and hours) and often must live in hostile (hot and contaminated) industrial environments. These gremlins combine to make analog long-time-constant circuits problematic, with their high impedances and nano-ampere signal currents. This is so because nasty ambients exaggerate the leakage and bias currents of op amps, integrator capacitors, and even circuit boards.

The controller shown in the figure achieves adequate time-constants without the delicate high-impedance analog circuits. It uses Xicor’s X9C1O3 digitally controlled potentiometers as feedback elements together with the Linear Technology LTC1040 sampled comparator.

Controller operation is based upon a positive-temperature-coefficient (3850 ppm/°C) platinum RTD sensor arranged in a standard ratiometric bridge with reference resistors R1, R3, and R5, and setpoint pot R4. Aiding controller stability and precision is high level (≈5 mA) bridge excitation. It produces a relatively large 1.7 mV/°C RTD output signal that competes well against noise pickup and thermal-EMF error sources. Typically, such a high RTD drive level would threaten to produce large and unacceptable sensor self-heating errors. But in this case, sensor excitation is pulsed (80 ms) under control of the LTC1040. This keeps average sensor dissipation duty factor low (≈1%) and self-heating error inconsequential.

On each measurement cycle, A1’s lower input pair samples the bridge output. Depending on the result of the comparison, they tend to drive the pin 4 output bit to 0 or 1, as the bridge reports an RTD-setpoint differential that’s negative or positive. Thus, the solid-state relay (SSR) and heater will most likely turn on when the temperature is low and off when it’s high.

To make the resulting on/off heater drive have an average duty-factor that’s nicely proportional to the magnitude of the temperature error signal and not just a simple “bang-bang” relationship, the bridge output voltage is summed with a triangular dither signal produced by P2. The combination of P2 and U2 causes P2 to output one full triangular dither waveform every 128 measurement cycles.

Thermal inertia of the heater and the thermal load averages over the heater cycle rate (1 Hz in this example). Consequently, suitable selection of the R6-C1 oscillator RC will avoid significant temperature ripple. R2 adjusts the amplitude of the P2 dither signal and thereby sets the effective controller P-term gain that relates heater duty factor to temperature error to get adequate control loop “stiffness” without oscillation.

Meanwhile, error integrator A2 + P1 also samples the temperature difference signal. The integration sampling frequency, and therefore the integrator time constant, is set by the choice of which U2 output bit is connected to P1’s clock. This arrangement causes the integrator to take one step in the direction of zero setpoint error every 1, 2, 4, 8, 16, 32, 64, or 128 heater dither cycles. As a result, it gradually converges on zero temperature error.

Selecting the right U2 bit sets the integrator time constant anywhere from one minute to more than two hours, and can thus accommodate even the longest generally encountered control-loop thermal time delays.

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