Observer Based Nonlinear Quadratic Dynamic Matrix Control for State Space and I/O Models

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Gattu, Gangadhar
Zafiriou, Evanghelos
Observer based nonlinear QDMC algorithm is presented for use with nonlinear state space and input-output models. The proposed algorithm is an extension of Nonlinear Quadratic Dynamic Matrix Control (NLQDMC) by Garcia (1984) and its extension by Gattu and Zafiriou (1992a). Garcia proposed an extension of linear Quadratic Dynamic Matrix Control (QDMC) to nonlinear processes. Although a nonlinear model is used, only a single Quadratic Program (QP) is solved on-line. Gattu and Zafiriou extended this formulation to open-loop unstable systems, by incorporating a Kalman filter. The requirement of solving only one QP on-line at each sampling time makes this algorithm an attractive option for industrial implementation. This extension of NLQDMC to open-loop unstable systems was ad hoc and did not address the problem of offset free tracking and disturbance rejection in a general state space setting. Independent white noise was added to the model states to handle unstable processes. The approach can stabilize the system but leads to an offset in the presence of persistent disturbances. To obtain offset free tracking Gattu and Zafiriou added a constant disturbance to the predicted output as done in DMC-type algorithms. This addition is ad hoc and does not result from the filtering/prediction theory. The proposed algorithm eliminates the major drawbacks of the algorithm presented by Gattu and Zafiriou and extends that algorithm for nonlinear models identified based on input-output information. An algorithm schematic is presented for measurement delay cases. The algorithm preserves the computational advantages when compared to the other algorithms based on nonlinear programming techniques. The illustrating examples demonstrate the usage of tuning parameters for unstable and stable systems and points out the benefits and short comings of the algorithm.