Dual control and prevention of the turn-off phenomenon in a class of MIMO systems

A recently developed methodology of adaptive dual control based upon sensitivity functions is applied here to a multi-variable input-output model. The plant has constant but unknown parameters. It represents a simplified linear version of the relationship between the vibration output and the higher harmonic control input for a helicopter. The cautious and the new dual controller are examined. In many instances, the cautious controller is seen to turn off. The new dual controller modifies the cautious control design by numerator and denominator correction terms which depend upon the sensitivity functions of the expected future cost and avoids the turn-off and burst phenomena. Monte-Carlo simulations and statistical tests of Significance indicate the superiority of the dual controller over the cautious and the heuristic certainty equivalence controllers.