(162e) A Formulation of Advanced-Step Carleman Linearization-Based Nonlinear Model Predictive Control

Authors: 
Fang, Y. - Presenter, The Pennsylvania State University
Armaou, A. - Presenter, Pennsylvania State University

The need of tight operating conditions in chemical, pharmaceutical, and petroleum industries has given rise to the development of advanced control methods. Model Predictive Control (MPC) started gaining attention three decades ago for optimal transitions between operating modes. The application of Dynamic Optimization (DO) enables MPC many advantages over traditional control strategies. Nonlinear MPC (NMPC) converts a constrained control problem of a nonlinear system into an optimization problem. This basic architecture makes NMPC capable of handling large state-space multi-variable systems with constraints, and dealing with model-mismatches and disturbances readily.

The computation time of control policy is required to be less than one sampling time for online operation. However, this requirement is most of the times impossible to meet when the system has high nonlinearity. That becomes one of the most significant reasons holding back the application of NMPC. As a result, there is strong motivation to develop an advanced formulation of NMPC that demands less computational effort and thus decides the control actions faster.

A Carleman linearization-based formulation of NMPC has been proposed to address this issue in [1] [2].  Nonlinear systems are approached with polynomial expressions and then represented with extended bilinear forms. This enables analytical anticipation of future states and analytically providing the sensitivity of the cost function to the control signals as the searching gradient. Consequently, the computation of optimal control policy is accelerated and the computational delay is removed.

In this paper, we propose an advanced reformulation of Carleman linearization-based NMPC with a combination of Advanced-step NMPC methodology published in [3] [4] [5]. Using NLP sensitivity analysis to find approximations and update solutions on-line enables this reformulation of NMPC increased capability of dealing with measurement noises and model mismatches. It is suitable to apply Advanced-step NMPC methodology to the method proposed in [1] [2] due to its bilinear formulation of the control problem. A case study example illustrating the proposed method uses a perturbed unstable Continuous Stirred Tank Reactor with high nonlinearity in the neighborhood of the nominal point. It shows the proposed NMPC controller removes computational delay while it achieves the same stability properties as traditional NMPC controllers do.

REFERENCE

[1] A. Armaou and A. Ataei, “Piece-wise constant predictive feedback control of nonlinear systems,” J. Process Control, vol. 24, no. 4, pp. 326–335, Apr. 2014.

[2] Y. Fang and A. Armaou, “Nonlinear Model Predictive Control Using a Bilinear Carleman linearization-based Formulation for Chemical Processes,” 2015 Am. Control Conf., Jul. 2015.

[3] V. M. Zavala and L. T. Biegler, “The advanced-step NMPC controller: Optimality, stability and robustness,” Automatica, vol. 45, no. 1, pp. 86-93, Jan. 2009.

[4] X. Yang and L. T. Biegler, “Advanced-multi-step nonlinear model predictive control,”J. Process Control, vol. 23, no. 8, pp. 1116-1128, Sep. 2013.

[5] R. Huang, V. M. Zavala and L. T. Biegler, “Advanced step nonlinear model predictive control for air seperation units,” J. Process Control, vol. 19, no. 4, pp. 678-685, Apr. 2009.

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