Improved Selection of State-Weighting Matrices for LQR MIMO-Controller Design

M.A. Hopkins (USA)


LQR, controller, optimization, MIMO, cantilevered beam, Nelder-Mead


A technique is presented for improving the selection of weighting matrices for the MIMO LQR design method, starting from any nominal set of weights that result in a stable observer-based controller with desired in-band performance. The nominal controller need not have particularly good stability margins or sensitivity, but it should provide desired closed-loop properties within the control bandwidth, such as increased damping. The technique is based on a particular cost function in the frequency domain, together with the use of a well known cost-reduction technique, sometimes called downhill-simplex. The importance of the cost function described here is it guarantees that certain desirable properties are sought, or are maintained if they already exist, such as good stability margins and low output sensitivity. The technique is illustrated by iterating on the design of a 40th -order controller for an actual 2-input, 3 output doubly-cantilevered beam, to significantly improve the stability margins and the output sensitivity outside of the controller bandwidth.

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