Adaptive Output Tracking Control System Design With SPR‐Based Adaptive PFC

ABSTRACT

Adaptive output feedback control based on an Almost Strictly Positive Real (ASPR) condition has been developed. In the control method based on the ASPR condition, its distinct feature is that an ASPR system can be stabilized by merely applying static output‐feedback control, which endows a simple structure of adaptive controllers. However, many practical systems do not satisfy the ASPR property; thus, it is significant to guarantee ASPR‐ness. One of the effective methods for rendering a system ASPR is to introduce a Parallel Feedforward Compensator (PFC). As its name suggests, a compensator is implemented into a controlled system in parallel and feedforward to make the resulting augmented system ASPR. In this paper, a new PFC design method with a Strictly Positive Real (SPR) property is developed. The output of a system with a relative degree of 1 can be represented in a canonical form, and the actual PFC output is designed based on this form. In addition, the stability of the control system is ensured subject to the SPR property of the ideal PFC, and the convergence of the actual error is analyzed. Then, a design guideline for improving control performance is provided. Finally, two types of simulations are done to verify the effectiveness of the proposed method. One of the two is performed for the non‐minimum phase systems to show the effectiveness toward non‐ASPR models, and the other is performed to verify the validity of the design guideline by setting different ideal ASPR models.