Abstract
This paper presents an analytical approach for solving the weighting
matrices selection problem of a linear quadratic regulator (LQR) for the
trajectory tracking application of a magnetic levitation system. One of
the challenging problems in the design of LQR for tracking applications is
the choice of Q and R matrices. Conventionally, the weights of a LQR
controller are chosen based on a trial and error approach to determine the
optimum state feedback controller gains. However, it is often time
consuming and tedious to tune the controller gains via a trial and error
method. To address this problem, by utilizing the relation between the
algebraic Riccati equation (ARE) and the Lagrangian optimization
principle, an analytical methodology for selecting the elements of Q and R
matrices has been formulated. The novelty of the methodology is the
emphasis on the synthesis of time domain design specifications for the
formulation of the cost function of LQR, which directly translates the
system requirement into a cost function so that the optimal performance
can be obtained via a systematic approach. The efficacy of the proposed
methodology is tested on the benchmark Quanser magnetic levitation system
and a detailed simulation and experimental results are presented.
Experimental results prove that the proposed methodology not only provides
a systematic way of selecting the weighting matrices but also
significantly improves the tracking performance of the system.
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