Design, Scheduling and Control: A Simultaneous Approach By Multi-Parametric Programming

The long term operation of a plant requires decision making in several different levels; decisions that significantly affect the initial capital investment, optimal operation and economic, environmental and energy impact over its life span. The inherent uncertainty of a plant’s long term operation is among the critical aspects associated with its overall performance. A variety of approaches have been considered including in particular, the consideration of (i) operability and design under uncertainty [1] as well as (ii) the system controllability with regulatory control structure selection and its tuning [2] and (iii) the design and model predictive control with stability and robustness aspects taken into account in a unified framework [3]. During the last few years there has also been great interest in the field of optimal operation, with several studies in literature exploring the interactions between shorter term operational decisions (regulatory and model-based control) with their longer term counterparts (scheduling and planning techniques) thus attempting to bridge the gap between the two [4-7]. The aim of this approach targets the long-term optimal operation of a process while taking into account its control aspects and the inherent handling of uncertainty [8].

In this work we consider decisions in three different time scales spanning from the lifetime operation timescale to the 1-second operation timescale of the plant.

I. The long term decisions include the optimal size of the plant equipment. The design of the equipment is a here-and-now decision that affects the process operability and controllability as well as its economic assessment throughout its lifespan. More, specifically, the design of the plant influences heavily the operational strategies that result into optimal operation. The operating bounds and performance metrics are determined by the design.

II. In processes where multiple products are considered, the design affects the overall production structure as well. In such processes, the production strategies focus on the alternation of production focus based on uncertainty associated with the raw material acquisition cost, product demand and resources availability. We enhance the multi-parametric Rolling Horizon Optimization (mp-RHO) policies presented in [9] by considering the design of the plant as a unknown but bounded parameter. Furthermore, we take into consideration the interactions of the control policies with the schedule within the mp-RHO formulation.

III. Model based control strategies, and more specifically their multi-parametric programming counterparts, are developed to ensure efficient set-point tracking. The control formulation takes into account the design of the plant in a similar way to the scheduling formulation. Based on the production scheduling different control schemes and structures are considered.

IV. The development of the receding horizon policies follow the principles presented in [10]. Starting from a high fidelity model developed in gPROMS®, different multi-parametric optimization problems are designed and validated. In terms of the optimal scheduling policies we derive actions as a function of (i) the system operational state, (ii) the uncertain demand and pricing, (iii) the process design and (iv) the control interactions. Similarly, the optimal control policies are a function of (i) the system operational state, (ii) the process design and (iii) the operating set-points. The design of the system is determined by the formulation and solution of a (mixed integer) dynamic optimization problem based on the process at hand, the optimal operation of which is ensured by the multi-parametric optimization based policies.

V. The approach is demonstrated on a domestic cogeneration unit that provides usable heat and power upon demand [11]. More specifically, the size of the internal combustion engine of the CHP is optimized under optimal operation which is ensured by design dependent scheduling and control policies. This multi-product process requires the derivation of different decentralized control schemes to account for the different operating policies as well as design dependent scheduling policies that determine the operational focus under uncertainty. We show that the simultaneous optimization of the design and operation of the process at hand achieves maximum economic benefits to the user while ensuring optimal operation.

References:

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