Establishment of Strictly Positive Real Condition for Tuning MIMO Feedforward Control

The two-degree-of-freedom structure enables us to achieve stabilization and tracking independently using feedback (FB) and feedforward (FF) controls, respectively. The latter usually undergoes a model uncertainty, which is resolved by online tuning. A tuning law guarantees zero convergence of the output error for any target signals, under a certain strictly positive real (SPR) condition; however, it is noticeably restrictive. This study proposes a method for guaranteeing the SPR condition by designing an FF filter and modifying the error signal for tuning in the multi-input multi-output case. The proposed method is illustrated through a numerical example.