A moment matching-based loop shaping design with closed-loop pole placement

In this paper, moment matching-based loop shaping design for finite-dimensional linear systems is considered. First, the time-domain moment matching model reduction problem with complex-conjugated pole-zero placement is revisited. We explicitly calculate the free parameters such that the reduced order model, achieving moment-matching at complex-conjugated interpolation points, has pairs of complex-conjugated poles and zeros placed in desired locations. Then, we recast the problem of closed-loop pole placement in terms of moment-matching, with the moments equal to -1 and 0, respectively. Consequently, the free parameters of a model achieving both moment matching at complex-conjugated points and closed-loop pole placement at prescribed locations are determined. Furthermore, we combine the classical loop shaping method with closed-loop pole placement via moment matching to design a robust controller for stable, minimum-phase, proper systems. We illustrate the proposed moment matching-based loop shaping approach on a benchmark example.