Gap Metric Concept and Implications for Multilinear Model-Based Controller Design

Abstract

The gap metric concept is used within the context of multilinear model-based control. The concept of distance between dynamic systems is used as a criterion for selecting a set of models that can explain the nonlinear plant behavior in a given operating range. The case studies presented include a CSTR and a pH neutralization reactor. The gap metric is used to analyze the relationships among candidate models, resulting in a reduced model set that provides enough information to design multilinear controllers. The simulation and experimental results indicate good performance and stability features.

An integrated state space partition and optimal control method of multi-model for nonlinear systems based on hybrid systems

“…First, according to Eqs. (9) and (10), the value function of the considered infinite optimal control problem is obtained as Fig. 2.…”

“…This has triggered the development of multilinear model approaches to tackle nonlinear systems problems. Multilinear model approaches turn out to be an ideal candidate for dealing with strong nonlinear chemical processes with wide operating ranges and large set-point changes, and has attracted much attention and been studied extensively in the past years (see [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and the references therein).…”

“…Though it remains largely unanswered [6,11], some efforts have been lit on this way. For instance, [9] uses gap metric to analyze the relationships among candidate models to get a reduced model bank. [13] extends the method in [9] to integrate the procedure of selecting operating points and local controller design.…”

“…For instance, [9] uses gap metric to analyze the relationships among candidate models to get a reduced model bank. [13] extends the method in [9] to integrate the procedure of selecting operating points and local controller design. Along with the concept of gap metric, [15] presents a gap metric-based method which aims to perform the operating range decomposition and the minimum linear model bank determination of a nonlinear system.…”

Multilinear Model Control of Hammerstein-like Systems Based on an Included Angle Dividing Method and the MLD-MPC Strategy

“…9 And because nonlinearity is always incorporated in the original control problem, for it usually involves both the physical output and the physical input, separating the nonlinearity from the control problem therefore may lead to a decreased performance. 10 The multilinear model control approach has attracted much attention and has been studied extensively in the past years [11][12][13][14][15][16][17][18] for its potential ability to control chemical processes with highly nonlinear characteristics as a result of wide operating ranges and large set-point changes. The key concept is to represent the nonlinear system as a combination of linear systems to which classical controller design techniques can be easily applied.…”