Kalman filter based calibration of precision motion control

A method is described and validated for the automatic calibration of analog sine-wave quadrature sensors, such as optical encoders, embedded in a functioning system. The algorithm uses a Kalman filter to estimate the true position of the direct-drive actuated joint using a model of it's dynamics, an applied actuator command, and measurements from the uncalibrated sensor. From the estimated true position, a lookup table is constructed which corrects sensor errors. Our results indicate that this method achieves accuracies typical of interferometric calibration , without requiring an external measurement device. The accuracy is surprisingly robust to modeling errors. The need for precision position sensors is driven by a variety of industries that require precision motion. Typically , a rotary electromagnetic motor actuates either a rotary or linear motion stage using some sort of gearing arrangement. If the gearing ratio between the motor and the motion stage is high, then a relatively low resolution rotary position sensor at the motor will result in high resolution motion measurements at the motion stage. New technological demands in diverse fields, such as multi-chip semiconductor modules and biomedical genetics research, have motivated the development of small, direct-drive motion systems with very high positioning resolution. The lack of gearing in these systems implies that higher resolution position sensors are needed to achieve the higher positioning precision. Sensors with analog quadrature outputs are of particular interest for high-precision positioning because their analog nature allows a degree of interpolation between the quadrature phases. However, this type of sensor suffers from nonlinear effects which are difficult to calibrate out. A new technique for the in-situ calibration of analog quadrature position sensors is developed in this paper. The analog rotary incremental optical encoder is used to test this technique; however the calibration technique is applicable to many other analog quadrature sensors. The two analog encoder outputs, called may be approximated as quadrature-phase sinusoids which are periodic with the encoder disk line interval. If we define a normalized intra-line distance, , over the interval , then this ideal encoder output model may be a b , () τ 0.5 0.5 , – [) expressed as (1) The intra-line position, , may be inferred from the encoder outputs by solving (1) for : (2) where atan2 (the two argument arctangent function) is used to avoid quadrant ambiguity when estimating from. In a typical digital control system using an analog encoder, the analog encoder …