A typical chemical plant consists of transporting material through numerous connected processing units (and buffer tanks) in order to produce the final product with a desired quality. The primary control objective in the plant is to maintain the production rate and quality at their given set-points in the presence of disturbances; however, this control objective is jeopardized when an intermediate process unit is shutdown (i.e., no flows into or out of the unit) for a finite duration of time due to equipment failure or to perform necessary maintenance operations. This scenario is classified as a partial shutdown of the plant and typically does not allow continuation of operation at the nominal operating point. As a result, the plant is either completely shutdown, which has significant economic ramifications, or ad-hoc modifications to the pre-shutdown control policy are made. Adopting these ad-hoc approaches, however, can also potentially result in temporarily shutting down the entire plant due to the onset of hazardous conditions. In this work, we propose a systematic approach to reconfigure the plant control strategy during shutdown in order to achieve optimal operation during the shutdown and a smooth transition to the nominal operation once the shutdown unit is recovered.The key to successful plant operation during a partial shutdown is to effectively utilize the capacities of the processing units and carefully placed buffer tanks. In general, buffer tanks in a chemical plant play an important role by attenuating or dampening the effects of disturbances along the production line. During a partial shutdown, buffer tanks become particularly important since their available capacities can be exploited to maintain plant operation to some extent. To understand this, suppose there is a buffer tank preceding and following the shutdown unit. During the shutdown period, the preceding buffer tank can serve as a holdup tank, allowing for continued operation of the upstream units while the buffer tank following the shutdown unit can serve as a feed tank for the downstream units. In operating the upstream and downstream plants, however, the finite capacities of the buffer tanks and the processing units together with the knowledge of the shutdown period length must be accounted for in any control strategy implemented during the shutdown. In addition, since the primary control objective remains to operate the plant at its nominal operating point, the shutdown controller must also steer the upstream and downstream plants in such a way that they can be efficiently recovered back to their nominal operating points once the shutdown unit is reinserted into the network. In , this problem was addressed using a model predictive control (MPC) design where the control objective during the partial shutdown was to maximize the plant profit while satisfying a restoration constraint that (implicitly) required all the process states at the end of the shutdown period to be in a region from where the nominal operation can be resumed. However, the feasibility of this optimization problem was assumed but not guaranteed. In this work, by recognizing that the plant is essentially decomposed into two decoupled batch subsystems (one comprised of the upstream units and the other comprised of the downstream units) during the shutdown, we recast the partial shutdown problem as two separate batch control problems wherein the control objective in each batch subsystem is to reach a desired end-point neighborhood from where the nominal operation of the plant can be resumed at the end of shutdown. With this interpretation of the partial shutdown problem, we unite the safe-parking and safe-steering frameworks proposed in  and  to come up with a predictive controller for each subsystem (independently) with guarantees on recovering the process to its nominal operating point. The controller design for each subsystem begins with explicitly characterizing the stability region of the nominal operating point in each unit of the subsystem (using the tools as in ) and then using a subset of these regions to define the desired end-point neighborhood. Next, we use the concept of reverse-time reachability regions (RTRRs) (defined as the set of states from where a batch process can be driven to the desired end-point neighborhood by batch termination subject to input constraints) to formulate a computationally efficient predictive controller that maintains the subsystem states within its corresponding RTRRs for the duration of the shutdown period. By doing so, the desired end-point neighborhood based on which the RTRRs are generated is guaranteed to be reachable. The implication of this is that we can transition back to the nominal operating point at the end of the shutdown period since the desired end-point neighborhood was defined using the stability regions of the individual units. To demonstrate the efficacy of the proposed approach, we consider a multi-unit nonlinear process with carefully placed buffer tanks subject to input constraints and a partial shutdown in one of the intermediate units. The partial shutdown scenario considered precludes the possibility of maintaining operation at the nominal operating point during the entire shutdown period, and calls for a reconfiguration of the plant controllers. By implementing RTRR-based predictive controllers for the two resulting batch subsystems, the downstream and upstream batch plants were operated such that the nominal plant operation was resumed efficiently once the shutdown unit was recovered.
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