Verification of Controllers in the Presence of Uncertainty:  Application to Styrene Polymerization

Abstract

This paper describes a methodology for verifying the stability and performance of closed-loop nonlinear systems, as arise in chemical plants with process controllers, when the process model is incompletely known, with uncertainty both in the parameter values and in the form of the equations. A systematic way of generating and summarizing all possible behavior patterns of the system is described. Temporal logic is used to formalize the posing of and automatic answering of qualitative questions about the response of the system. The methodology is demonstrated for controller verification in the design of a CSTR for styrene polymerization.

Optimization and control of a continuous polymerization reactor

“…The polydispersity is a property that indicates the distribution of the polymer chain size in the product. Additionally, the intrinsic viscosity η measures indirectly the average molecular weight of the polymer produced (Gazi et al, 1996). Both molecular weight and polydispersity are strong indicators of polymer quality.…”

“…In this work, it is assumed that an online viscosimeter provides reliable measurements of the intrinsic viscosity η . The following correlation is used to simulate the measurement of the viscosity (Gazi et al, 1996): The polydispersity index (PD) is a property of the molecular weight distribution of the dead polymer, defined as:…”

“…The phenomenological model of this styrene reactor was first published in 1990 and, since then, it has been widely used as a benchmark for process control studies (Maner et al, 1996;Gazi et al, 1996;Kendi and Doyle, 1998;Prasad et al, 2002;Asteasuain et al, 2006;Sotomayor et al, 2007). Prasad et al (2002) implemented a nonlinear MPC strategy for the control of the properties of the polymer.…”

Diagnosis of Abnormal Situations in a Continuous Solution Polymerization Reactor

“…In this work, we simulated measurements of the intrinsic viscosity (h) using the following expression: [22] h ¼ 0:0012ðM w Þ 0:71…”

“…Process parameters and steady-state operational conditions are listed in Table 1 and 2, respectively, which are taken from Maner et al [21] For more details about the model, the interested reader is referred to the aforementioned references. This styrene polymerization reactor has, since the work of Hidalgo and Brosilow, [20] resulted in several citations, and has been used as a benchmark to test various PSE techniques (e.g., Gazi et al, [22] Maner et al, [21] Kendi and Doyle, [23] Russo and Bequette, [24] Prasad et al, [25] and Asteasuain et al [26] ). In these studies, the main motivation in selecting this process as a benchmark is its complexity and hence its similarity to an industrial problem.…”