Abstract: Systematic methods to detect, verify, and repair a collinear model are presented. After detecting collinearity in a model or subsets of a model, a directional test is carried out to verify if the collinearity is real. The model can then be adjusted in either direction to making a near collinear model exactly collinear or less collinear, subject to model uncertainty bounds or other linear constraints. When doing the model adjustment, deviations from the original model are minimized and the directionality of the model is kept unchanged.

Abstract: Systematic methods to detect, verify, and repair a collinear model are presented. After detecting collinearity in a model or subsets of a model, a directional test is carried out to verify if the collinearity is real. The model can then be adjusted in either direction to making a near collinear model exactly collinear or less collinear, subject to model uncertainty bounds or other linear constraints. When doing the model adjustment, deviations from the original model are minimized and the directionality of the model is kept unchanged.

Abstract: A multivariable process controller controls a chemical, polymer or other physical process. Slow tuning and over-conservative controlled variable values are employed during step testing. While all controlled process variables are within safe limits, only one manipulated variable (MV) at a time is step changed. Several manipulated variables are moved when process variables exceed safe limits to ensure that the controlled process variables return to the safe range, such that suitable MV targets for step testing are able to be automatically discovered within a closed loop control environment. Thus, the step test is able to be conducted mostly unsupervised and/or remotely via a telephone or network connection. A new process perturbation approach simultaneously perturbs multiple or all of the process input variables in such a way that the process responses (process outputs) are maximized, while the process variables are maintained inside its predefined operating constraints.