Analysis and Control of Halbach Linear Motor for Nanopositioning

This paper presents control of a Halbach linear motor for nano-precision positioning. Using an FPGA based decoding scheme and sensor signal processing, a 0.23nm root-mean-square (RMS) sensor noise level has been obtained from a 4 micrometer period sinusoidal quadrature encoder. Disturbances to the linear motor are studied at nanometer scale. When the motor is supported by the air bearing without feedback control, the mechanical motion measured by the sensor shows substantial low frequency oscillation around 10Hz. Under a PID digital servo feedback control, the stage can be brought to a regulated state of 11.14nm RMS error at 10kHz sampling rate, otherwise not achieved by lower sampling rate. Although PID servo loop substantially reduces the 10Hz motion, a 60Hz vibration and its harmonics begin to dominate at nanometer level. It is suspected and confirmed by experiments to be due to the coupling of the DC power supply/amplifier and control computer to the AC power source. A robust repetitive control scheme is employed to reject the 60Hz disturbance and its harmonics and bring the regulated state to 1.78nm RMS value.