On defining the partial control problem: concepts and examples

Abstract

Many complex chemical processes having a large number of process variables and poorly understood models can be controlled reasonably well by controlling only a small subset of process variables using an equally small number of manipulated uariables. This is the central premise of this article and is referred to as partial control. Knowing4 or unknowingly, this idea has been and continues to be applied to successfully control numerous complex industrial processes. Despite its widespread use, partial control has never been explicitly formulated. The partial control problem is defined. A number of terms is introduced such as process variable dominance, modelable responses, practicaldegrees of freedom, and sufficiency of partial control. The new framework allows incorporation of both engineering-based decisions and more rigorous theoretical tools to achieve the goals of partial control. A number of practical examples illustrate the applicability of these concepts. IntroductionThe chemical and petrochemical industry is characterized by processes which can be classified as highly complex. This complexity arises from several sources:Process model uncertainty: The development of detailed and accurate models for chemical processes is rarely possible or prohibitively expensive. For example, the kinetics and mechanisms of many chemical reactions are often far too complex to allow an exact mathematical description. As a consequence, the model of the chemical process, which is based on this imperfect understanding of the kinetics, is inherently imperfect and has a large uncertainty associated with it. Inherent process nonlinearity:The steady state and dynamic behavior of chemical processes is generally highly nonlinear, implying the potential existence of complex behavior such as multiple steady states, instabilities, and limit cycles. Linear models are rarely suitable for describing these processes except in an unrealistically narrow operating regime.Correspondence concerning this article should be addressed to M. V. Kotharr. 2456December 2000 ProceAs constraints: The manipulated variables are limited in magnitude due to equipment limitations such as pump and compressor throughput limits and actuator limits. On the other hand, the process states and outputs are constrained to lie between prespecified limits of their reference values; these limits are arising due to stringent product specifications dictated by market demands, safety limits, or environmental regulations on effluent concentrations. The need for minimizing material and energy costs has led to the use of multiple material recycle loops and complex energy management networks. As a result, chemical processes have evolved into highly integrated, and, at times, unmanageable, monolithic systems. Large-scale qstem aspects:The total number of controlled and manipulated process variables is generally large and typically, the former is significantly larger than the latter. It is important to have a methodology to decide which of the large number of process and state varia...

Dominant Variables for Partial Control. 1. A Thermodynamic Method for Their Identification

“…Before we attempt to answer this question, a brief review of partial control will be given. For more details see Shinnar, Arbel et al, , and Kothare et al Partial control hinges on the observation that many process systems seem to have a few independent variables that tend to dominate the dynamic behavior of the entire system. The temperature in an exothermic reactor and sensitive tray temperatures in distillation columns have already been mentioned as good examples.…”

“…While the proposed method appears efficient in the identification of dominant variables, there are two remaining issues that need to be discussed. First is the issue of sufficiency (Kothare et al 4 ) dealing with how many control loops must be closed to achieve stability and a satisfactory level of partial control. Sufficiency is closely tied to the nature and specificity of the economic objectives.…”

“…The formal description of partial control was first put forward by Shinnar and recently illustrated by Arbel et al , through extensive case studies on an industrial-scale fluidized-bed catalytic cracker (FCC). Formal definitions of the terms used to describe partial control systems have been provided by Kothare et al However, despite the widespread use of partial control and the early introduction of the ideas behind it, there have been few papers published on the subject. The reason is most likely due to the technique's empirical and heuristic nature.…”

Dynamic considerations in the synthesis of self‐optimizing control structures

“…3,4,5 In particular, integrated processes have long been recognized to exhibit a dynamic behavior that spans multiple time scales. Many authors 6,7,8,9,10 have indirectly assumed this time scale multiplicity to propose tiered control structures, featuring at least two levels of control action: a primary layer addressing inventory and temperature control at the unit level and providing stability in operation, and a supervisory layer, acting over a slower time scale, that targets the control objectives at the plant level, such as product purity and production rate.…”

Fault Detection and Diagnosis in Chemical Processes Using Sparse Principal Component Selection

“…Many works try to select key variables for reducing dimension of data and seek a subset that contains the most important information for process monitoring. Kothare et al (2000) pointed out that a combination of mathematical criteria, physical insight and engineering judgment is required for choosing such variables. Peng et al (2005) put forward a new feature selection algorithm, called minimal-redundancy-maximal-relevance criterion (mℝMℝ).…”