Hill-Climbing for Plantwide Control to Economic Optimum - American

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Hill-climbing for Plantwide Control to Economic Optimum Vivek Kumar, and Nitin Kaistha Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie502798t • Publication Date (Web): 29 Sep 2014 Downloaded from http://pubs.acs.org on October 5, 2014

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Industrial & Engineering Chemistry Research

Hill-climbing for Plantwide Control to Economic Optimum Vivek Kumar and Nitin Kaistha* Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016 (India)

Abstract The application of hill-climbing control to ‘seek’ and drive the unconstrained setpoint of controlled variables (CVs) to their economic optimum is proposed for economic plantwide control. Its application is demonstrated on a reactor-column recycle process for energy efficiency maximization at given throughput (Mode I) and also for maximizing process throughput (Mode II). In Mode I, a one degree-of-freedom (dof) hill-climbing feedback controller on top of the regulatory layer is shown to reduce reboiler duty by 3.7% for a 25% throughput increase compared to constant setpoint operation. Similarly, in Mode II, a one-dof hill-climber achieves 3.0% throughput increase compared to constant setpoint operation. These results highlight the effectiveness of hill-climbing for economic plantwide control. Keywords:

*

Economic plantwide control, economic process operation, hill-climbing control

Corresponding author. Tel: +91-512-2597513; Email: [email protected]

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Introduction The imperatives of fierce market competition and sustainability concerns are pushing the process industry towards practical plantwide process control system solutions that ‘seek’ and drive the process operation to the economic optimum steady state. As shown in Figure 1, the state-of-the-art consists of a hierarchical three-layered control structure with the layer below receiving setpoint adjustments from the layer above. At the bottom is the regulatory layer with decentralized PI controllers which close the individual unit material, energy and component balances as well as the overall plantwide balances, for safe and stable process operation. Conventionally, the regulatory layer throughput manipulator (TPM), which is the setpoint used to effect a production rate change, is located at a process fresh feed. Other setpoints that affect the plant steady state and hence its economics are adjusted periodically by a real-time optimizer (RTO)1 that optimizes these setpoints for an economic criterion using an adaptively fitted plant model. The optimum steady state solution usually has multiple hard active constraints. These must be controlled tightly to push the plant operation as close as possible to the optimum, without violating the hard limit. The back-off from the hard limit necessary for avoiding constraint violation during worst-case transients directly translates to an unrecoverable economic loss. To reduce the back-off and hence improve the process economics, an intermediate MPC supervisory layer is usually employed. It adjusts appropriate setpoints in the regulatory layer to mitigate the transients in these hard active constraint variables for reducing the back-off. For a given active constraint set, literature reports have demonstrated that the regulatory layer control structure can and should be systematically altered via TPM relocation2 and input-output pairing choice3 to propagate transients away from the economically dominant hard active constraints or out of the material/energy recycle loop.4 The inventory control scheme of such a structure is then naturally aligned for tight control of the economically dominant active constraints and achieves significantly


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tighter constraint control compared to supervisory MPC constraint control with a conventional regulatory structure with the TPM at a process feed.5 Assuming tight control of the active constraints, either using supervisory MPC of regulatory layer setpoints or by regulatory layer structure design (including TPM location choice), optimal steady process operation requires that the remaining unconstrained regulatory layer setpoints be at their optimum values. The optimum value however is not known apriori and changes with operating conditions and disturbances. The RTO approach attempts to obtain this optimum by fitting a steady state model to the available plant data, optimizing the fitted model and cascading the optimum setpoints to the layers below. In the late 60s and early 70s, the statistical process control community developed evolutionary operation (EVOP)6 as a systematic way of improving process operation by making small adjustments to process operating conditions using a factorial design experiment. Typically, a "local" surface response curve model is fitted to the experimental results and depending on the result, the operating conditions are revised towards the surface response curve optimum. Even as EVOP has existed for more than 40 years now, there are very few literature reports on its application in the chemical process industry. Another possibility is to convert the optimization problem into a control problem, where one seeks to control an appropriate process variable, which when held constant provides near optimum operation despite large process disturbances. In other words the economic penalty for constant setpoint operation with no re-optimization upon change in the process operating condition/disturbance remains negligibly small. Luyben7 referred to such control structures as eigenstructures. Skogestad8 has further refined the concept to suggest that the plantwide control design problem is the search for the best selfoptimizing control structure and demonstrated its application to example processes.9 Even for a self optimizing control structure, the optimum value of the controlled process variable is not known apriori and must be obtained.



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The ideal process variable for self-optimizing control is the gradient of the economic objective function with respect to the unconstrained regulatory layer setpoints. Driving this gradient to zero drives the process operation to optimality. A more direct approach for optimal operation then is to apply feedback control to drive the gradient to zero. The basic idea is to keep adjusting the unconstrained setpoint till the steady state slope of the economic objective function with respect to the unconstrained setpoint is driven to zero. For maximization problems, we thus attempt hill-climbing via feedback. Even as hill-climbing control has been applied for optimal operation of stand-alone isolated units, e.g. maximizing solar flux utilization in solar panels power10 or minimizing expensive buffer usage in pH control11, its application to the economic plantwide control of a complete chemical process with material recycle has not been evaluated before, at least to our knowledge. A systematic evaluation of the same for an example process is the major novel contribution of this work. We note that in RTO and EVOP, the estimated gradient of the process model (first principles or statistical) is driven to zero whereas in hill-climbing, the estimated gradient of the actual process is driven to zero via feedback. Also, the feedback in the RTO/EVOP approaches occurs indirectly through the plant model fitting cum setpoint update exercise. Lastly in RTO, the plant is not perturbed and the available plant data is used to update the plant model. In contrast, EVOP and hill-climbing require that small perturbations be made to the plant. In this work, we consider Shinskey’s hill-climbing feedback controller

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for seeking and driving

an economically significant unconstrained regulatory layer setpoint to its economic optimum for a reactor-separator-recycle process and quantify its economic benefit over constant setpoint operation. Economic optimality is sought for two operating modes. In Mode I, the reboiler steam (expensive utility) consumption is minimized for a fixed throughput. In Mode II, the plant throughput is maximized. In the following, we briefly describe the process along with optimal steady state operation results for the two operating modes. The regulatory control structures for the two modes are then


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synthesized systematically in light of the optimally active constraints. We also present the override controls necessary for switching between the two structures. This is followed by a brief description of Shinskey’s one-dof dynamic hill-climber and its application to the example process. Closed loop dynamic control results for both modes are then presented and the economic benefit is compared to constant set-point operation. The article ends with the conclusions that can be drawn from the work.

Process Description The reactor-separator-recycle process flowsheet studied here is shown in Figure 2 along with the salient design and operating conditions. This process module has been widely used in the plantwide control literature to highlight and address key issues in plantwide control (see e.g. 5,13). Fresh A (FA) and fresh B (FB) are mixed with the recycle stream and fed to a heated CSTR. The irreversible exothermic reaction A + B → C occurs in the boiling reactor. The reactor effluent is sent to a simple distillation column to recover 99 mol% pure C as the bottoms product and recycle the distillate containing unreacted A and B with some C impurity, back to the CSTR. The hypothetical component properties, reaction kinetics and thermodynamic package used in the Hysys process simulation are noted in Table 1. The process has 9 independent control valves (control dofs). Of these 2 valves would be used for controlling the column reflux drum and bottom sump levels, which are non-reactive liquid inventories with no steady state effect. Another valve would be used for column operation at given design pressure. This leaves 6 remaining valves that may be adjusted to move the process to a particular steady state. The process steady state operating dof is then 6. These correspond to two dofs for the fresh feeds (FA and FB), two for reactor and two for the column. We use the following six specification variables to exhaust the steady state process dofs and converge the flowsheet: fresh B feed rate (FB), reactor level and temperature (URxr and TRxr), column reflux to feed ratio and bottoms purity (L/FCol and xCBot) and reactor B mol fraction (xBRxr).



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Optimum Steady Process Operation The available steady state dofs should be exploited for economically optimal process operation. We consider two modes of process operation. In Mode I, the throughput (FB) is given, fixed e.g. by market demand-supply considerations, and the remaining five steady state dofs are optimized to maximize the process energy efficiency. Since steam is the expensive utility here, optimal Mode I operation corresponds to minimizing column boil-up, VCol. The steam consumption in the reactor is ignored here as it is a small fraction (

Hill-Climbing for Plantwide Control to Economic Optimum - American

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