Nonlinear Analysis for Chemical Processes Based on Incremental Dissipativity

Many chemical processes exhibit strong nonlinear dynamic behaviours which may present significant challenges to process operation and control, including input and output multiplicities. Input multiplicity refers to the phenomenon where different inputs (control action) result in the same steady state process output, which is commonly encountered in biochemical reactors. A process with input multiplicity is not invertible and thus is difficult to control as a feedback controller essentially attempts to invert the process model. A process with output multiplicity may produce different steady-state output depending on its initial state, which is often observed in exothermic reactors and obviously leads to a difficulty in achieving the desired output. The work provides a link between these properties of nonlinear chemical processes and the concept of incrementally dissipative systems in nonlinear system theory. The quantitative analysis of the above two phenomena is proposed. Furthermore, a test of the feasibility of controlling nonlinear chemical processes using linear controllers is developed. Such a test is of practical significance because it is often attempted to control nonlinear chemical processes using linear controllers in control practice due to the simplicity in control system design. As the concept of dissipativity can be linked to thermodynamics, the dissipativity based analysis can be potentially related to process design and provides more insights into integrated process design and control. INTRODUCTION Operability analysis determines whether a process can be controlled effectively using a feedback control system. Upon the realization of the importance of simultaneous process design and control, such analysis plays an important role in the early stages of process design to reveal any potential operability problems, such as poor disturbance rejection, difficulty in changing operating conditions, or even plant stability. One of the most commonly researched methodologies for the analysis is the simultaneous optimization approach, which allows seamlessly integration of process and control design (Perkins & Walsh, 1996, Bahri et al., 1997). However, its implementation can be a challenging task, highly dependent on the size and complexity of the problem and by the limitations of the available computational algorithms (Sakizlis et al., 2004). As alternatives, a vast varieties of operability analysis based on open-loop models were proposed. These methods can be used without the knowledge of the closed-loop controllers structure, hence removing the arbitrary, time-consuming nature of simulation based approaches commonly applied in industry. However, many open-loop operability analysis methods are only applicable to linear processes. These include operability analysis methods developed based on non-minimum phase elements (Holt & Morari, 1985a, Holt & Morari, 1985b), condition numbers (Barton et al., 1991), process resilience indices (Cao et al., 1996, Morari, 1983) and relative gain array (RGA) (Bristol, 1966). Only a few methods are available for nonlinear processes. The process