Modeling and Multivariable Control of a High Precision Multidimensional Positioner
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A precision positioner using a novel concentrated-field permanent-magnet matrix is presented in this paper. This integrated multidimensional positioner is actuated by three novel planar motors, which are attached on the bottom of the positioner. It can generate all 6-DOF motions with only a single moving part. The integrated multi-dimensional positioner offers a unique combination of range and precision: a planar traveling range of 160 mm 160 mm with a position resolution of 30 nm and position noise of 10 nm rms. The repeatability of the positioner is as good as 30 nm. The maximum velocity achieved so far is 0.5 m/s with 5-m/s2 acceleration. With direct-quadrature (DQ) decomposition theory, the positioner is modelled as a multi-input multi-output (MIMO) electromagnetic system: it has six inputs (currents) and six outputs (displacements). After the state-space model of the system is derived, multivariable controllers are designed for this high-precision positioner. To eliminate the steady-state error, discrete time integrator combined Linear Quadratic Regulation (LQR) and reduced order Linear Quadratic Gaussian (LQG) control methodologies are applied and implemented. Finally, the experimental results are presented in this paper. Several experimental results verified the utility of this positioner in precision applications, such as semiconductor manufacturing.
