The fisrt part of this article was printed in CONTROL's May 2009 edition. Part two is included in June 2009 and part three in July 2009. Below is the complete article.
By F. Greg Shinskey
For the last two decades, model predictive control (MPC) has been promoted for multivariable processes, particularly in petroleum refineries. Yet its performance hardly justifies its promises, and economic payout is spotty at best. A. G. Kern in his article, “Outlook for Multivariable Predictive Control,” in the October 2008 issue of Hydrocarbon Processing cites “lackluster performance” of MPCs. In the March 2006 issue of the same magazine, Y. Z. Friedman in “Where Has Engineering Judgment Gone?” suggests that these “applications have not been successful.” This author is currently involved with a major refinery, proceeding from one distillation column to the next, replacing disappointing MPC systems with structured advanced regulatory controls (ARC), achieving substantial economic benefit and operator acceptance. The purpose of this article is to analyze some of the factors limiting MPC performance and demonstrate how ARC systems overcome them.
Most refineries require quality control over both top and bottom products to minimize energy consumed in separating their components. Product compositions are historically inferred from temperatures a few trays removed from where the product is withdrawn. This location is selected to minimize influence from off-key components and to increase sensitivity to manipulated variables. Ultimately, product compositions are usually measured in an on-line analyzer. The analyzer may have a sample interval of 10 minutes or more, along with sampling-line delay and lags associated with capacity in the reflux drum and column base. The temperature measurements—although less accurate—are far more responsive than the analyzers, both to disturbances and to manipulated flows. As a result, it’s common practice to control compositions by adjusting temperature set points in cascade, either using PID controllers or with a multivariable MPC (Figure 1). This structure has been published in handbooks and papers over the years, and can be considered standard practice.
Figure 1 (above). The MPC is shown setting TCs that manipulate reflux and boilup.
As shown, the typical column has five pairs of manipulated and controlled variables―two product flows, reflux, reboiler heat and condenser cooling―used to control two levels, pressure and two temperatures. Analyzers report the overhead vapor and bottom compositions, y and x respectively. Condenser cooling is most often used to control pressure, in this example by partially flooding the condenser with condensate by means of the hot-vapor-bypass valve. The assignment of level controllers to manipulate the flow of their respective products is most common, leaving temperatures to be controlled by reflux and boilup. Disturbance variables are feed rate, composition and enthalpy, and coolant temperature.
The structure represented by Figure 1 just happens to be the least controllable of all possible single-loop configurations, as well as the most obvious. The principal difficulty is that the manipulation of reflux and boilup has almost the same effect on both temperatures. In other words, increasing steam flow will raise the top temperature almost as much as it raises the bottom temperature, and increasing reflux flow will lower both by similar amounts. In most columns, these temperature loops are therefore tightly coupled, and no amount of clever set point adjustment by the MPC can break through that tight coupling. The reflux-boilup control structure is marginally stable, presenting the MPC with what is known as an ill-conditioned matrix (See A. Hugo’s “Limitations of Model Predictive Controllers,” in the January 2000 issue of Hydrocarbon Processing.) The result is a tendency for the two temperature controllers to cycle against one another. While multivariable MPC has decoupling built into it, the coupling here is between the inner temperature loops, and the MPC is unable to defeat it from the outside.
Loop Interaction in Distillation
While there are five manipulated and controlled variables, their interaction exists in two distinct dynamic domains. For example, changing reflux flow causes the level in the reflux drum to begin moving immediately, while the top temperature may take several minutes before responding at all. The period of oscillation of a typical temperature loop on a column is about 10 to 40 minutes, while that of the level and pressure loops is more like one to two minutes. As a result, imbalances in the vapor and liquid traffic in the column appear as variations in liquid levels and pressure long before they affect temperatures, and these effects can be used to detect and counteract disturbances.
Being slower, the temperature loops can’t upset levels or pressure significantly, so interaction in this direction is minimal. The principal interaction problem exists between the two slow temperature (composition) loops. Their very similar dynamics makes each especially sensitive to oscillations developing in the other loop at the same period—a resonant effect. The two different sets of dynamics allow interaction between the temperature loops to be analyzed alone as a 2x2 system, assuming level and pressure loops closed as necessary.
The severity of the temperature-loop interaction varies greatly from one column to another, but may be estimated by comparing the relationship between the two product compositions as we hold a particular manipulated variable (MV) constant. The ideal case of regulation is where holding a particular MV constant results in one of the product compositions remaining nearly constant regardless of changes in the other MVs. This is not really achievable, so we are left to choose the best of the available MVs for regulation of the two compositions.