Nonlinear predictive controller based on S-PARAFAC Volterra models applied to a communicating two tank system

International audienceThis paper proposes a new predictive controller approach for nonlinear process based on a reduced complexity homogeneous, quadratic discretetime Volterra model called quadratic S-PARAFAC Volterra model. The proposed model is yielded by using the symmetry property of the Volterra kernels and their tensor decomposition using the PARAFAC technique which provide a parametric reduction compared to the conventional Volterra model. This property allows synthesizing a new nonlinear model based predictive control (NMBPC). We develop the general form of a new predictor and so, we propose an optimization algorithm formulated as a Quadratic Programming (QP) under linear and nonlinear constraints. The performances of the proposed quadratic S-PARAFAC Volterra model and the developed NMBPC algorithm are illustrated on a numerical simulation and validated on a benchmark as a continuous Stirred Tank Reactor (CSTR) system. Moreover the efficiency of the proposed quadratic SPARAFAC Volterra model and the NMBPC approach are validated on an experimental Communicating Two Tank system (CTTS)

Transition and control of nonlinear systems by combining the loop shaping design procedure and the gap metric theory

International audienceIn this paper, in order to synthesize a control law we propose a new approach that enables identification of the intermediate equilibrium points of a nonlinear system, knowing the first and the last ones. These points are those around which the nonlinear system is linearized and therefore yields local models (sub-models) that contribute to forming the multimodel describing the nonlinear system. This approach is based on the transition from a given point (source) to the next by varying a scheduling parameter (SP) defining the source point sub-model. The variation of this parameter is limited by the maximum value of the stability margin determined by the loop shaping design procedure approach (LSDP) applied to such a sub-model. Hence, the new equilibrium point is defined by the new obtained value of the SP for which the gap metric between this sub-model and the one corresponding to the new value of SP is larger than the given stability margin. The different robust controllers synthesized for the different equilibrium points will be used to synthesize the robust control of the nonlinear system, by applying the gain-scheduling technique. The proposed transition approach as well as the robust control algorithm were validated on the continuous stirred tank reactor (CSTR) system