In this paper we shall extend the applications of iterative identification
and control design to partially unknown unstable plants. We show that by em
ployong a two step approach, where an unstable plant is first stabilized by
a parallel feedback stabilizer, it is possible to design systematically an
overall closed-loop system that has good step responses with little oversh
oots by using the iterative identification and control design methodology.
Furthermore, this approach easily preserves the simplicity of an IMC design
through tuning the overall designed closed-loop bandwidth with a single de
sign parameter. Specifically, similarly to situations where the plant is st
able (apart from possibly including a simple integrator), we can design a s
ystem with a small initial overall designed closed-loop bandwidth (after th
e plant is stabilized by a known parallel feedback stabilizer) such that hi
gh frequency unmodelled dynamics of the plant are not overly excited. Throu
gh iterative applications of a control-relevant closed-loop system identifi
cation procedure and the standard IMC design method to the stabilized plant
, the overall designed closed-loop bandwidth of the system can be widened p
rogressively while maintaining good step responses with little overshoots.
Two simulation examples are employed to illustrate the method. These exampl
es show that, irrespective of the presence of adverse unstable real pole-ze
ro structures, the expected results are achievable by the method described.