LTR Design of propertional integral observers

This paper applies the proportional-integral (PI) observer in connection with loop transfer recovery (LTR) design for continuous-time systems. We show that a PI observer makes it possible to obtain time recovery, i.e., exact recovery for t -+ -, under mild conditions. Based on an extension of the LQG/LTR method of proportional (P) observers, a systematic LTR design method is derived for the PI observer. Our recovery design method allows time recovery and frequency (normal) recovery to be done independently. Furthermore, we give explicit expressions for the recovery error when asymptotic recovery cannot be obtained. A design example demonstrates the advantages of time recovery in the nonminimum phase case.