Nonlinear Error Compensation for Pressure Sensors Over Full Temperature Range
Pressure sensors often exhibit significant nonlinearity across a wide temperature range, causing errors up to 0.5%FS. To achieve higher accuracy, compensation algorithms must account for both the inherent nonlinearity of the sensor element and the temperature dependence of its output. This article describes two practical approaches: polynomial fitting and neural network models, both utilizing temperature and pressure as dual inputs.
Polynomial fitting is a classical compensation technique. First, a calibration process collects sensor output values at known pressure points across multiple temperature levels (e.g., -40°C to 125°C). A two-dimensional polynomial model is then constructed, typically of the form: compensated pressure = a0 + a1*V + a2*T + a3*V² + a4*V*T + a5*T² + ... where V is the raw sensor voltage and T is the temperature reading. The coefficients are determined using least-squares regression on the calibration data. Once trained, this model can reduce the maximum error to below 0.1%FS by correcting the nonlinear behavior across the full temperature range.
For more complex nonlinearities, neural networks offer superior flexibility. A feedforward network with one hidden layer (e.g., 10-20 neurons) is sufficient. Inputs are raw pressure signal and temperature; output is the compensated pressure. The network is trained on the same calibration dataset using backpropagation. After training, the model accurately maps the nonlinear relationship, achieving similar or better accuracy than polynomial fitting, especially when the sensor's response is highly irregular or when higher-order interactions exist between temperature and pressure.
Implementation requires careful data collection with a precision reference pressure source and temperature chamber. The chosen model is embedded into the sensor's microcontroller or signal processing unit. After compensation, the full-scale error is validated across all temperature and pressure points. With proper calibration and model selection, both methods can elevate sensor performance from 0.5%FS to 0.1%FS, meeting stringent industrial requirements.