Sparse and Decoupling Control Strategies Based on Takagi–Sugeno Fuzzy Models

In order to better handle the coupling effects when controlling multiple-input multiple-output (MIMO) systems, taking the decentralized control structure as the basis, this paper proposes a sparse control strategy and a decoupling control strategy. Type-1 and type-2 Takagi-Sugeno (T-S) fuzzy models are used to describe the MIMO system, and the relative normalized gain array-based criterion is employed to measure the coupling effects. The main contributions include: 1) compared to the previous studies, a manner with less computational cost to build fuzzy models for the MIMO systems is provided, and a more accurate method to construct the so-called effective T-S fuzzy model (ETSM) to express the coupling effects is developed; 2) for the sparse control strategy, four indexes are defined in order to extend a decentralized control structure to a sparse one. Afterward, an ETSM-based method is presented that a sparse control system can be realized by designing multiple independent single-input single-output (SISO) control loops; and 3) for the decoupling control strategy, a novel and simple ETSM-based decoupling compensator is developed that can effectively compensate for both steady and dynamic coupling effects. As a result, the MIMO controller design can be transformed to multiple noninteracting SISO controller designs. Both of the sparse and decoupling strategies allow to use linear SISO control algorithms to regulate a closely coupled nonlinear MIMO system without knowing its exact mathematical functions. Two examples are used to show the effectiveness of the proposed strategies.