(740g) Novel Block Decentralized MPC Control for Local Autonomy

In this work, a novel block decentralized MPC approach is implemented in order to coordinate the control of interacting process units (blocks) in a chemical plant. There are generally two distinct categories of objectives for block MPC. In one category, the goal is to achieve, or approach it closely, the centralized performance with distributed computation (e.g., Venkat, Rawlings, and Wright 2004; Jia and Krogh, 2004). In the second category, the goal is to enable each block to optimize its own control performance by adjusting only its manipulated variables while accounting for dynamic interactions among blocks (e.g., Charos and Arkun, 1993; Shingeo and Hong, 2005). The goal of this research is to develop coordinated control for the second category, which occurs whenever multiple MPC's are implemented within a plant.

A simultaneous algorithm, termed D-MPC, is proposed that replaces multiple optimizations (from several, interacting MPC controllers). The solution is obtained by expressing every optimization as a KKT problem and solving all optimality conditions simultaneously, yielding a single-level optimization problem. The resulting problem consists of linear and complementarity equations, which are non-linear and non-convex, making reliable solution problematic (Clark and Westerberg, 1990). Therefore, an efficient active set heuristic is proposed for real time computation. The approach is computationally tractable, yielding a small set of convex problems to be solved sequentially and providing reliable solutions with good dynamic performance for the cases studied.

Integrity is important for control designs, and generally, block designs with negative and zero Block Relative Gains (BRG) have poor integrity (Manousiouthakis, Savage, and Arkun, 1986), and such designs cannot be controlled with published approaches. In contrast, the D-MPC approach successfully provides good integrity for processes with all BRG signs while maintaining the desired autonomy of each individual block. We note that even if the original block design has a positive BRG, common occurrences, such as manipulated variables saturation, can lead to a system with a zero or negative block relative gain.

The solution existence, uniqueness, and stability of the proposed controller will be discussed in order to delimit the processes that can be controlled using the proposed D-MPC controller. A simple D-MPC formulation is analyzed to demonstrate a previously unrecognized feature of block MPC, specific ranges of controller tuning can lead to the loss of nominal stability for negative BRG systems. Therefore, a step-wise D-MPC design procedure was developed that integrates a stability analysis to ensure that the tuning is selected for nominal stability.

Case studies with all signs of BRG and sizes from 2x2 to 4x4 will be presented to demonstrate the computational tractability, good dynamic performance and integrity of D-MPC controller designs developed with the design procedure and implemented with the heuristic algorithm.

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