• International Journal of Control, Automation, and Systems
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• v.4 no.1
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• pp.1-9
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• 2006

This paper presents the modeling and multivariable feedback control of a novel high-precision multi-dimensional positioning stage. This integrated 6-degree-of-freedom. (DOF) motion stage is levitated by three aerostatic bearings and actuated by 3 three-phase synchronous permanent-magnet planar motors (SPMPMs). It can generate all 6-DOF motions with only a single moving part. With the DQ decomposition theory, this positioning stage is modeled as a multi-input multi-output (MIMO) electromechanical system with six inputs (currents) and six outputs (displacements). To achieve high-precision positioning capability, discrete-time integrator-augmented linear-quadratic-regulator (LQR) and reduced-order linearquadratic-Gaussian (LQG) control methodologies are applied. Digital multivariable controllers are designed and implemented on the positioning system, and experimental results are also presented in this paper to demonstrate the stage's dynamic performance.

• International Journal of Control, Automation, and Systems
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• v.5 no.2
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• pp.161-169
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• 2007

The PLL equivalent augmented system incorporated with state feedback is proposed in this paper. The optimal value of filter time constant of loop filter in the phase-locked loop control system and the optimal state feedback gain designed by using linear quadratic regulator approach are derived. This approach allows the PLL control system to employ the large value of the phase-frequency gain $K_d$ and voltage control oscillator gain $K_o$. In designing, the structure of phase-locked loop control system will be rearranged to be a phase-locked loop equivalent augmented system by including the structure of loop filter into the process and by considering the voltage control oscillator as an additional integrator. The designed controller consisting of state feedback gain matrix K and integral gain $k_1$ is an optimal controller. The integral gain $k_1$ related to weighting matrices q and R will be an optimal value for assigning the filter time constant of loop filter. The experimental results in controlling the second-order lag pressure process using two types of loop filters show that the system response is fast without steady-state error, the output disturbance effect rejection is fast and the tracking to step changes is good.