Piezoelectric-Actuator Hysteresis Compensation in Student-Built Engineering Education Micropositioning Stages: A Capacitive-Sensor Evaluation Linking Drive-Voltage Sweep to Nanopositioning Repeatability Bounds

Student-built micropositioning stages that use piezoelectric actuators are common in engineering education laboratories, yet their nanopositioning performance is routinely overstated because hysteresis in the actuator is neither characterised nor compensated. The treatment is methodological and theoretical: no observational data are reported. A Preisach-type hysteresis operator is combined with a capacitive-sensor noise model to derive closed-form expressions for the repeatability floor as a function of sweep amplitude, sensor resolution and compensation residual. First, the repeatability bound scales linearly with the uncompensated hysteresis fraction and inversely with the square root of the number of sweep segments, so that doubling sensor resolution yields only a factor-of-√2 improvement unless the compensation residual is simultaneously reduced. Second, a compensation-residual threshold exists below which further sensor refinement yields no repeatability gain; this threshold is derived explicitly. Third, the framework predicts that student-built stages operating without compensation cannot achieve sub-100 nm repeatability for sweep amplitudes above 20 V, a bound consistent with the educational literature. The contribution is a design-oriented evaluation protocol that allows instructors and students to predict repeatability limits before construction, and to allocate resources between actuator linearisation and sensor quality.