Null-space-based steady-state tracking error compensation of simple adaptive control with parallel feedforward compensator and its application to rotation control

In the design of simple adaptive control (SAC) using almost strictly positive real (ASPR), the feedback control system is stabilized by the output feedback with a high gain. Although ASPR is not, however, generally satisfied, it is achieved by introducing a parallel feedforward compensator (PFC). When SAC is designed for the augmented system which consists of an actual plant and PFC, not the actual plant output but the augmented system output converges to the reference input because of the influence of PFC. To resolve the problem, an extension method of the conventional SAC is proposed. In the proposed method, based on the null-space of an augmented plant, an exogenous input, which is independent of the augmented system output, is newly introduced. Because the exogenous input is designed so that PFC output is to be 0, the actual plant output is the same as the augmented system output in the steady state, and as a result, the actual plant output converges to the reference input. From a practical application point of view, the proposed method can easily improve the control performance of the conventional SAC with a PFC. In the proposed method, an exogenous input generated as the feedback signal of PFC output is only added to the conventional SAC control input. Therefore, the proposed method can be applied to various field in which the SAC method has been implemented, e.g., process control, mechanical systems, power systems, robotics, and others. In the present study, the effectiveness of the proposed method is also demonstrated through experiments for a motor control.