Passivity Based Operability Analysis for Unstable Processes
The integration of process design and control has been recognised as being important to design modern plants that are both economical and easy to operate. The operability analysis based on open-loop models is very useful in revealing controllability problems in early stages of process design. While controllability of unstable processes is often a bigger concern to chemical engineers, most existing open-loop analysis methods can only be used for stable processes. In this paper, an operability analysis for both stable and unstable processes is developed.
Passive systems are stable and easy to control. The degree of passivity of a process can be used to infer its operability. The operability of a non-minimum phase stable process can be determined by its Input Feedforward Passivity (IFP) index. This index implies the upper limit of the controller gain, thus the achievable performance of the closed-loop system. The operability of an unstable process can be determined by its Output Feedback Passivity (OFP) index, which implies the lower bound of the controller gain that should be provided to ensure stability. In a more complex non-minimum phase unstable process, both IFP and OFP indices should be examined. As IFP and OFP indices are correlated with each other, it is often hard to estimate both indices simultaneously. By using coprime factorization, both IFP and OFP indices can be obtained via the feedforward passification technique. This in turn will determine the achievable performance bound and the stability bound of the closed-loop system. This approach is illustrated using case studies.