<p>Active magnetic bearings (AMBs) enable contactless support and are attractive for precision mechanisms in particle-sensitive environments. This work presents a complete discrete-time linear–quadratic–Gaussian (LQG) control pipeline on a field-programmable gate array (FPGA) for a low-speed robotic joint using a three-degree-of-freedom active magnetic bearing (two radial axes and one axial levitator). A translational physics-based model explicitly captures bias currents and nominal air gaps, followed by equilibrium linearization and zero-order-hold discretization at 2 kHz. The estimator–controller (<i>linear–quadratic regulator</i>, LQR, plus Kalman filter) is implemented in fixed-point logic with sub-200 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\upmu $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">μ</mi> </math></EquationSource> </InlineEquation>s end-to-end latency. Experiments on a dedicated testbed compare the proposed LQG against a tuned proportional–integral–derivative (PID) controller and an observer-based pole-placement baseline under identical sensing and actuation. In the radial loop, LQG reduces startup settling time by approximately 44% and integrated absolute error by approximately 36.5%, with overshoot below 0.5% and actuator limits respected; recovery to a <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\pm 5\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>±</mo> <mn>5</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> band under external disturbances is about 13% faster. A nonlinear plant robustness map indicates stable, non-overshooting behavior under <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\pm 20\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>±</mo> <mn>20</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> variations of magnetic and electrical parameters. Particle measurements during continuous operation remain below the International Organization for Standardization (ISO) Class 5 thresholds, supporting the suitability of the proposed joint for cleanroom robotics.</p>

FPGA-Based LQG Control of a Low-Speed Active Magnetic Bearing Joint: Implementation and Validation

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2026年5月5日

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Walter Torrestiana González,
Leopoldo González González,
Emmanuel González Mendoza,
Luis Bautista Cruz

摘要

Active magnetic bearings (AMBs) enable contactless support and are attractive for precision mechanisms in particle-sensitive environments. This work presents a complete discrete-time linear–quadratic–Gaussian (LQG) control pipeline on a field-programmable gate array (FPGA) for a low-speed robotic joint using a three-degree-of-freedom active magnetic bearing (two radial axes and one axial levitator). A translational physics-based model explicitly captures bias currents and nominal air gaps, followed by equilibrium linearization and zero-order-hold discretization at 2 kHz. The estimator–controller (linear–quadratic regulator, LQR, plus Kalman filter) is implemented in fixed-point logic with sub-200 $\upmu $ $μ$ s end-to-end latency. Experiments on a dedicated testbed compare the proposed LQG against a tuned proportional–integral–derivative (PID) controller and an observer-based pole-placement baseline under identical sensing and actuation. In the radial loop, LQG reduces startup settling time by approximately 44% and integrated absolute error by approximately 36.5%, with overshoot below 0.5% and actuator limits respected; recovery to a $\pm 5\%$ $\pm 5 %$ band under external disturbances is about 13% faster. A nonlinear plant robustness map indicates stable, non-overshooting behavior under $\pm 20\%$ $\pm 20 %$ variations of magnetic and electrical parameters. Particle measurements during continuous operation remain below the International Organization for Standardization (ISO) Class 5 thresholds, supporting the suitability of the proposed joint for cleanroom robotics.