Controllability Analysis for Unstable Processes

Abstract

We study the controllability of unstable processes, with emphasis on selection of measurements and manipulated variables, and the pairing, problem for dessatralized control. The well known pairing criteria based on the Niederlinski Index and the steady state Relative Gain Array (RGA) have been generalized to open loop unstable plants. Right Half Plane (RHP) zeros in individual transfer func-tion dements may make it practically impossible to stabilize the individual loops, and in such cases these pairing criteria are not very helpful. We have found RGA ≈ I in the bandwidth region to indicate good pairings also when paired elements have significant RHP zeros, but have found the Direct Nyquist Array (DNA) to perform poorly as an indicator of good pairings. In some cases it is preferable to avoid pairings giving narrow Gershgorin bands.