(40d) Distributed Model Predictive Control Based on NLP Sensitivity

Tianyu Yu ^a, Jun Zhao ^a, Zuhua Xu ^a, Xi Chen ^a, Lorenz T. Biegler ^b

^a State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou, 310027, Zhejiang, P. R. China

^b Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA

Abstract

Model predictive control (MPC) has been widely used in the control of industrial processes over the past thirty years. It can handle constraints effectively and account for system interactions explicitly. Centralized and decentralized MPC are two common strategies in large-scale systems. In centralized scheme, a single controller is designed to calculate all the manipulated variables, which may encounter heavy computational burden and reliability issues for a large scale system. In decentralized scheme, the plant is divided into several subsystems and each one is controlled by a MPC controller without communication with the other controllers. The decentralized scheme may lead to poor performance due to the ignorance of subsystem interactions. Distributed MPC (DMPC) is developed as a compromise in which several controllers are used to control the whole process and the communication among controllers is applied to improve control performance. DMPC can be classified into two types, the cooperative DMPC and the non-cooperative DMPC. Their main difference is the objective function used in the optimization problem. The cooperative DMPC uses a global cost function while the other uses several local cost functions[1,2]. For implementation of DMPC, one key difficulty lies in the online solution of the optimization, especially for strongly nonlinear systems.

To speed up the real-time computation, a novel cooperative DMPC algorithm is proposed with NLP sensitivity in this paper. A distributed optimization structure is built with all the subsystems’ optimal inputs being evaluated in parallel. For a single MPC controller, at each sampling time, the future state at the next step can be calculated using its nominal model with its current state and control action. Therefore, the predicted optimization problem can be solved in advance. If this problem can be solved within one step, the predicted control action is available at the next step. This strategy can remove the computational delay and preserve the stability properties of the controller. After that, a fast approximate solution at the next step can be computed by taking a perturbed Newton step when a new state is obtained[3]. This concept can be extended to distributed scheme. In this paper, a cooperative DMPC strategy is used based on [4], in which many problems are solved in parallel. In background, optimal solutions of different subsystems can be obtained in each iteration. After that, these solutions are transmitted to each other, and the iteration continues until stopping criteria is met. When new states are available, the approximate optimal solutions of subsystems can be calculated using the same updating method. In this way, fast feedback is obtained by analyzing the parametric property of the problems. A case study is presented to demonstrate how the algorithm works efficiently.

Keywords: Distributed Control, Predictive Control, NLP Sensitivity

References:

[1] P. D. Christofides, R. Scattolini, D. M. de la Peña, J. Liu, Distributed model predictive control: A tutorial review and future research directions, Computer and Chemical Engineering 51 (2013) 21-41.

[2] M. J. Tippett, J. Bao, Distributed Control of Chemical Process Networks, International Journal of Automation and Computing 12(4) (2015) 368-381.

[3] V. M. Zavala, L. T. Biegler, The advanced-step NMPC controller: Optimality, stability and robustness, Automatica 45 (2009) 86-93.

[4] B. T. Stewart, A. N. Venkat, J. B. Rawlings, S. J. Wright, G. Pannocchia, Cooperative distributed model predictive control, Systems & Control Letters 59(2010) 460-469.