Consistent and Effective Nonlinearity Index and its Application on Model Predictive Controller Performance Deterioration

Abstract

Many control-relevant systems present the challenges of nonlinearity, directionality and ill-conditioning for the control systems, and exhibit poor controller performance. This study proposes a Nonlinearity Index to quantify the extent of nonlinearity of such systems. A dynamic nonlinear model of a pilot-scale distillation column operating near the azeotropic region was simulated using Aspen Plus Dynamics. A comparison of the results is made with the Nonlinearity Measure proposed by Du et al. Results show that a significant increase is exhibited in the proposed Nonlinearity Index values of the system as the system moves toward the azeotropic region. Prediction errors of the linear models are also shown to be correlated to the proposed index. Therefore, the proposed Nonlinearity Index is consistent with the existing indicators of nonlinearity, and thus its measurements of system nonlinearity are reliable. Controller performance for the system at higher values of the proposed index further presents its efficacy.

Low‐density polyethylene tubular reactor control using neural Wiener model predictive control

“…54 In addition, in order to assess the LDPE polymerization nonlinearity level, the calculation of nonlinearity index (NLI) is performed. 55 According to Uddin, Tufa, and Maulud, 55 any process with NLI larger than one represents a sufficient degree of nonlinearity for applying nonlinear model identification. In this case, the respective LDPE tubular reactor has produced NLI of 2.2, which justifies its nonlinear behavior.…”

Nonlinear Control of Fouling in Polyethylene Reactors

“…Finally, the rest of the data (15%) is used for the second validation after the training is completed. To evade ill-conditioned system modeling, all parameters are reformed by data scaling using eq below: x scaled = x − x ss x max − x min where x is the original value, x ss is the steady-state value of the parameter, x max is the maximum value of the parameter, and x min is the minimum value of the parameter. The maximum and minimum values are determined from this work parametric analysis.…”