Control-relevant nonlinearity measure and integrated multi-model control

Abstract

A control-relevant nonlinearity measure (CRNM) method is proposed based on the gap metric and the gap metric stability margin to measure the nonlinear degree of a system once a linear control strategy is selected. Supported by the CRNM method, an integrated multi-model control framework is developed, in which the multi-model decomposition and local controller design are closely integrated, model redundancy is avoided, computational load is reduced, and dependency on a prior knowledge is reduced. Besides, a 1/δ gap-based weighting method is put forward to combine the local controllers. On one hand, the 1/δ gap-based weighting method has merely one tuning parameter and can be computed off-line; on the other hand, it is sensitive to the tuning parameter, flexible and easy to tune. Two continuous stirred tank reactor (CSTR) systems are investigated. Closed-loop simulations validate the effectiveness and benefits of the proposed integrated multi-model control approach based on CRNM.

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

“…The system is ready to be evaluated by the proposed NLI for its extent of nonlinearity by using the data from Section 4.1. A comparison with a recently proposed Nonlinearity Measure (NM) by Du et al (2017) 59 is also made to further demonstrate the efficacy of NLI. The values of the NLI proposed in this study are shown in Table 5.…”

“…NM Calculation. The Nonlinearity Measure proposed by Du et al 59 is compared with the proposed NLI. The comparison will be made based on the ability to show a consistent increase in system nonlinearity as the system moves toward the azeotropic region or widens the existing operating range.…”

“…The comparison will be made based on the ability to show a consistent increase in system nonlinearity as the system moves toward the azeotropic region or widens the existing operating range. According to Du et al, 59 the Nonlinearity Measure can be calculated by the following equation:…”

A Control-Performance-Based Partitioning Operating Space Approach in a Heterogeneous Multiple Model

“…Following our previous work [33,34], which proposed an integrated framework of operating space partition and optimal control of the homogeneous multiple model, this paper proposes a new systematic operating space partition method of the heterogeneous multiple model where the closed loop performance is considered. The heterogeneous multiple model of nonlinear systems is obtained by an identification technique and formulated by an input-output model.…”

“…The decomposition is first accomplished, and then the combination of sub-models is carried out [33]. Du et al used the gap metric to decompose the nonlinear system into model bank determination [34]. Song et al developed a closed loop decomposition method based on an optimal control problem for nonlinear systems [35,36].However, the above-mentioned decomposition/combination method is mostly applied to homogeneous multiple model structures.…”