Extended horizon controller

In the last decade several other multivariable controllers have been proposed. We will briefly discuss two of the most popular in the sections below. Other multivariable controllers that will not be discussed but are worthy of mention are minimum variance controllers (see Bergh and MacGregor, lEC Research, Vol. 26, 1987, p. 1558) and extended horizon controllers (see Ydstie, Kershenbaum, and Sargent, AIChE J., Vol. 31, 1985, p. 1771). 

Environmental factors should also be incorporated into a company s technical or research and development program. Since the planning horizons for new projects may now extend to 5 to 10 years, R D programs can be designed for ecific projects. These may include new process modifications or end-of-pipe control technologies. 

Extended Kalman filtering has been a popular method used in the literature to solve the dynamic data reconciliation problem (Muske and Edgar, 1998). As an alternative, the nonlinear dynamic data reconciliation problem with a weighted least squares objective function can be expressed as a moving horizon problem (Liebman et al., 1992), similar to that used for model predictive control discussed earlier. 

The interactions between units do, however, become significant over long periods of time processes with recycle exhibit a slow, core dynamic component that must be addressed in any effective process-wide control strategy. This chapter presented an approach for systematically exploiting this two-time-scale behavior in a well-coordinated hierarchical controller design. The proposed framework relies on the use of simple distributed controllers to address unit-level control objectives in the fast time scale and a multivariable supervisory controller to accomplish process-wide control objectives over an extended time horizon. 

Finally, we analyzed the control implications of the presence of impurities in a process, concluding that the control of impurity levels must be addressed over an extended time horizon using the flow rate of the purge stream as a manipulated input. To close the impurity-levels loop, one should resort either to an appropriately tuned linear controller (e.g., a PI controller with long reset time) or to a (nonlinear) model-based controller that uses (an inverse of) the reduced-order model of the slow dynamics - as developed in this chapter - to compute the necessary control action. 

Rawlings and Muske (1993) have shown that this idea can be extended to unstable processes. In addition to guaranteeing stability, their approach provides a computationally efficient method of on-line implementation. Their idea is to start with a finite control (decision) horizon but an infinite prediction (objective function) horizon, i.e., m < < and p = , and then use the principle of optimality and results from optimal control theory to substitute the infinite prediction horizon objective by a finite prediction horizon objective plus a terminal penalty term of the form... 

---