Model reference adaptive control of large structural systems

Attention is given to model reference adaptive control procedures that do not require explicit parameter identification for large structural systems. Even though such applications have been shown to be feasible for multivariable systems, provided there exists a feedback gain matrix that makes the resulting input/output transfer function strictly positive real, it is shown here that this constraint is overly restrictive and that only positive realness is required. Subsequent consideration of a simply supported beam reveals that if actuators and sensors are collocated, then the positive realness constraint will be satisfied and the model reference adaptive control will then indeed be suitable for velocity following when only velocity sensors are available and for both position and velocity following when velocity plus scaled position outputs are measured. For both cases, all states are guaranteed to be stable, regardless of system dimension.