Numerically Efficient Fuzzy MPC Algorithm with Advanced Generation of Prediction—Application to a Chemical Reactor

Abstract

In Model Predictive Control (MPC) algorithms, control signals are generated after solving optimization problems. If the model used for prediction is linear then the optimization problem is a standard, easy to solve, quadratic programming problem with linear constraints. However, such an algorithm may offer insufficient performance if applied to a nonlinear control plant. On the other hand, if a model used for prediction is nonlinear, then non–convex optimization problem must be solved at each algorithm iteration. Then the numerical problems may occur during solving it and the time needed to calculate the control signals cannot be determined. Therefore approaches based on linearized models are preferred in practical applications. A fuzzy algorithm with an advanced generation of the prediction is proposed in the article. The prediction is obtained in such a way that the algorithm is formulated as a quadratic optimization problem but offers performance very close to that of the MPC algorithm with nonlinear optimization. The efficiency of the proposed approach is demonstrated in the control system of a nonlinear chemical control plant—a CSTR (Continuous Stirred–Tank Reactor) with van de Vusse reaction.

The Model Order Reduction Method as an Effective Way to Implement GPC Controller for Multidimensional Objects

“…The complexity of industrial processes typically requires that the model be constrained to be a maximum of 3rd order to accurately capture the relationship between input and output. The generic form of model is shown in (10):…”

“…e −st (10) where Q1 and Q2 can be equal −1, 0 or 1. The parameters R1, R2, T1, T2, and T3 and process delay in the real project are identified experimentally, where the experiment depends on the specific industrial installation and used equipment.…”

“…The transfer functions used in the examples structurally correspond to the third order models used in the DCS software to identify industrial process models given by (10). The values of time constants used in the examples were invented to show the problem of creating high-order models.…”

“…Furthermore, in MPC, unlike PID control, all necessary constraints may be incorporated systematically in the control law. Additionally, MPC can be applied to nonlinear systems [8][9][10] using the structure of fuzzy models [11][12][13][14][15][16][17] or online linearization of the process model at each MPC algorithm iteration [18,19]. In large-scale industrial applications, MPC algorithms are implemented in Distributed Control Systems (DCS) using Programmable Logic Controllers (PLC) [20] or specialized industrial controllers [21].…”

Tuning of Multivariable Model Predictive Control for Industrial Tasks

“…In particular, MPC algorithms make it possible to obtain excellent control quality in the case of Multiple-Input Multiple-Output (MIMO) processes with constraints. As a result, MPC methods have been used to numerous industrial processes [7], e.g., chemical reactors [8], distillation columns [9], waste water treatment plants [10], solar power stations [11], cement kilns [12], pasteurization plants [13] and pulp digesters [14]. In addition to that, MPC algorithms are more and more popular in other areas; example applications are: fuel cells [15], active vibration attenuation [16], combustion engines [17], robots [18], synchronous motors [19], mechanical systems [20], freeway traffic congestion control [21] and autonomous driving [22].…”