A process control approach using steady state multivariate statistical models is presented. The goal of this control approach is to improve product quality when the quality measurements are not available on line, or they have long time delays. Principal Component Analysis (PCA) is used to compress information from the process measurements down to a lower dimensional score space, where a control goal is specified using the approach of Piovoso and Kosanovich (1992). A new statistical controller is designed to control the equivalent score space representation of the process. The issue of how to account for the correlation structure of input variables when closing a feedback loop around the PCA model is specifically addressed. A binary distillation column and the Tennessee Eastman process are used for demonstrating the new control approach.