Performance of integrated production scheduling and advanced process control with disturbances is summarized and reviewed with four progressive stages of scheduling and control integration and responsiveness to disturbances: open-loop segregated scheduling and control, closed-loop segregated scheduling and control, open-loop scheduling with consideration of process dynamics, and closed-loop integrated scheduling and control responsive to process disturbances and market fluctuations. Progressive economic benefit from dynamic rescheduling and integrating scheduling and control is shown on a continuously stirred tank reactor (CSTR) benchmark application in closed-loop simulations over 24 h. A fixed horizon integrated scheduling and control formulation for multi-product, continuous chemical processes is utilized, in which nonlinear model predictive control (NMPC) and continuous-time scheduling are combined.
Abstract:A novel formulation for combined scheduling and control of multi-product, continuous chemical processes is introduced in which nonlinear model predictive control (NMPC) and noncyclic continuous-time scheduling are efficiently combined. A decomposition into nonlinear programming (NLP) dynamic optimization problems and mixed-integer linear programming (MILP) problems, without iterative alternation, allows for computationally light solution. An iterative method is introduced to determine the number of production slots for a noncyclic schedule during a prediction horizon. A filter method is introduced to reduce the number of MILP problems required. The formulation's closed-loop performance with both process disturbances and updated market conditions is demonstrated through multiple scenarios on a benchmark continuously stirred tank reactor (CSTR) application with fluctuations in market demand and price for multiple products. Economic performance surpasses cyclic scheduling in all scenarios presented. Computational performance is sufficiently light to enable online operation in a dual-loop feedback structure.
Integrated scheduling and control (SC) seeks to unify the objectives of the various layers of optimization in manufacturing. This work investigates combining scheduling and control using a nonlinear discrete-time formulation, utilizing the full nonlinear process model throughout the entire horizon. This discrete-time form lends itself to optimization with time-dependent constraints and costs. An approach to combined SC is presented, along with sample pseudo-binary variable functions to ease the computational burden of this approach. An initialization strategy using feedback linearization, nonlinear model predictive control, and continuous-time scheduling optimization is presented. The formulation is applied with a generic continuous stirred tank reactor (CSTR) system in open-loop simulations over a 48-hour horizon and a sample closed-loop implementation. The value of timebased parameters is demonstrated by applying cooling constraints and dynamic energy costs of a sample diurnal cycle, enabling demand response via combined scheduling and control.
This work presents a detailed case study for the optimization of the expansion of a district energy system evaluating the investment decision timing, type of capacity expansion, and fine-scale operational modes. The study develops an optimization framework to find the investment schedule over 30 years with options of investing in traditional heating sources (boilers) or a next-generation combined heat and power (CHP) plant that provides heat and electricity. In district energy systems, the selected capacity and type of system is dependent on demand-side requirements, energy prices, and environmental costs. This work formulates capacity planning over a time horizon as a dynamic optimal control problem considering both operational modes and capital investment decisions. The initial plant is modified by the dynamic optimization throughout the 30 years to maximize profitability. The combined optimal controller and capital investment planner solves a large scale mixed integer nonlinear programming problem to provide the timing and size of the capacity investment (30 year outlook) and also guidance on the mode of operation (1 hour time intervals). The optimizer meets optimal economic, environmental, and regulatory constraints with the suggested design and operational guidance with daily cyclical load following of heat and electricity demand.
Linear model predictive control is extended to both control and optimize a product grade schedule. The proposed methods are time scaling of the linear dynamics based on throughput rates and grade-based objectives for product scheduling based on a mathematical program with complementarity constraints. The linear model is adjusted with a residence time approximation to timescale the dynamics based on throughput. Although nonlinear models directly account for changing dynamics, the model form is restricted to linear differential equations to enable fast online cycle times for large-scale and real-time systems. This method of extending a linear time-invariant model for scheduling is designed for many advanced control applications that currently use linear models. Simultaneous product switching and grade target management is demonstrated on a reactor benchmark application. The objective is a continuous form of discrete ranges for product targets and economic terms that maximize overall profitability.
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