Non Linear Hysteresis Compensation Models in Temperature Transducer Calibration
Generalized Prandtl-Ishlinskii play operators linearize directional thermal hysteresis loops, cutting transducer calibration uncertainty from 90 mK down to 13 mK.
Bouc-Wen Model
Phenomenological Representation
Differential equations describe the non-linear relationship between restoring force and displacement in systems experiencing hysteresis. With the bouc-wen model, a smooth curve represents the transition between elastic and plastic deformation in mechanical structures. This mathematical framework is widely used to simulate the behavior of damping devices and structural joints under cyclic loading.
Parameter Identification
Numerical coefficients in the formula determine the shape and width of the hysteretic loop. When the bouc-wen model is used for sensor compensation, these parameters are identified through experimental data fitting. Adjusting the power terms allows the curve to match the hardening or softening behavior of the material.
This versatility makes the model suitable for representing piezo-electric actuators and seismic dampers.
Algorithmic Efficiency
Simplicity in the computational structure allows for real-time implementation in control systems. Because the bouc-wen model relies on a single first-order differential equation, it consumes less processing power than more complex operator-based models. Real-time feedback loops use this efficiency to correct position errors in precision stages during high-speed operations.
Physical Limitation
Challenges exist regarding the thermodynamic consistency of the calculated output. The bouc-wen model sometimes predicts small energy gains during minor loops, which violates the second law of thermodynamics. Engineers must verify that the chosen parameters do not produce these non-physical results in the intended operating range of the sensor.