Integrated scheduling and control in discrete-time with dynamic parameters and constraints

Abstract

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.

GEKKO Optimization Suite

“…Additional example problems are shown in the back matter, with an example of an artificial neural network in Appendix A and several dynamic optimization benchmark problems shown in Appendix B. Since the GEKKO Fortran backend is the successor to APMonitor [37], the many applications of APMonitor are also possible within this framework, including recent applications in combined scheduling and control [46], industrial dynamic estimation [43], drilling automation [47,48], combined design and control [49], hybrid energy storage [50], batch distillation [51], systems biology [44], carbon capture [52], flexible printed circuit boards [53], and steam distillation of essential oils [54].…”

“…The final example demonstrates an approach to combining the scheduling and control optimization of a continuous, multi-product chemical reactor. Details regarding the model and objectives of this problem are available in [46]. This problem demonstrates GEKKO's ability to efficiently solve large-scale problems, the ease of using the built-in discretization for differential equations, the applicability of special variables and their built-in tuning to various problems, and the flexibility provided by connections and custom objective functions.…”

Proactive Energy Optimization in Residential Buildings with Weather and Market Forecasts

“…MHE is often used in conjunction with MPC, which uses the current system parameters regressed by MHE to predict future values given a set of control moves [33]. Dynamic Optimization, MPC, and MHE have wide application across a broad range of industries including continuous chemical process optimization [62][63][64], cryogenic carbon capture [65,66,[66][67][68], energy system capacity planning [69], and drilling automation [70][71][72]. The optimal control over the future prediction horizon is determined by dynamic optimization.…”

Economic Benefit from Progressive Integration of Scheduling and Control for Continuous Chemical Processes

“…This formulation inherently considered only steady-state production with no external or dynamic factors (such as time-of-day pricing or dynamic constraints) during production periods. Discrete-time ISC formulations [18][19][20]66,67] have been shown to effectively incorporate external and dynamic factors, such as cooling constraints and time-of-day energy pricing. This incorporation enables demand response to time-of-day pricing by reducing or increasing production during periods of steady-state product manufacturing and moving the time of transitions to take advantage of times with relaxed constraints (such as relaxed cooling constraints on exothermic processes).…”