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In many linear quadratic (LQ) optimal regulator problems, the tuning of design parameters such as weighting coefficients in the criterion function depends on trial-and-error simulations. In this note, an LQ optimal regulator is used to prevent tumbling from power-assisted carts. The cart has two actuators: a DC servomotor that drives the cart, where power assistance is realized by impedance control of the motor; and a linear motor actuator to prevent the conveyed objects from tumbling. This note mainly discusses a systematic LQ optimal regulator design method for the latter actuator. The relationships between the feedback gain tuning of the tumble prevention actuator and controlled object responses were examined by simulation. Actual feedback gains were then determined by gain scheduling of the gains obtained a priori based on the relationships, control specifications and constraints. The effectiveness of the design method was verified by simulation examples.

Tuning of LQ Feedback Gains for Power-Assisted Cart to Prevent Tumbling of Conveyed Objects