Loop Shifting for Systems with Adobe Input Delay

Abstract

This paper presents the first complete solution to the loop shifting problem for systems with multiple loop delay channelss. The loop shifting is a technique aiming at reducing the stabilization and various performance problems for dead-time systems to equivalent problems for delay-free systems. While well understood in the single-delay case, the approach has not been fully extended to systems with multiple delays yet. Existing solutions offered so far only partial results, which only resolve the stabilization issue. We show that the effect of delayed control channel on the “delay-free” performance channel should be compensated to complete the procedure. This results in a novel form of the dead-time compensator, in which an interchannel feedforward term is present alongside the conventional internal feedback. We also argue that a reshape of the regulated signal is required to pull the delay out of the system. An energy preserving reshape is proposed, which facilitates the H2 analysis. Applications of this approach to some classes of robust stability problems are discussed.