B. Erik Ydstie

A model predictive control strategy for supply chain optimization

Abstract This paper describes a model predictive control strategy to find the optimal decision variables to maximize profit in supply chains with multiproduct, multiechelon distribution networks with multiproduct batch plants. The key features of this paper are: (1) a discrete time MILP dynamic model that considers the flow of material and information within the system; (2) a general dynamic optimization framework that simultaneously considers all the elements of the supply chain and their interactions; and (3), a rolling horizon approach to update the decision variables whenever changes affecting the supply chain arise. The paper compares the behavior of a supply chain under centralized and decentralized management approaches, and shows that the former yields better results, with profit increases of up to 15% as shown in an example problem.

Process systems and passivity via the Clausius-Planck inequality

In this paper we define a process system to be a system which has actions with the Clausius-Planck and conservation properties. We use standard and well established results derived from macroscopic thermodynamics to show that a process system has actions which satisfy the dissipation inequality. Furthermore, these actions have an inner product structure and a link between the thermodynamic theory of process systems and the input-output passivity theory of nonlinear control is established. The paper therefore represents a step towards developing a passivity based approach for distributed control system design for chemical processes. A review of relevant concepts from thermodynamics is given in an appendix.

Stabilization of distributed systems using irreversible thermodynamics

We connect thermodynamics and the passivity theory of nonlinear control. The storage function is derived from the convexity of the entropy and is closely related to the thermodynamic availability. We relate dissipation to positivity of the entropy production. In this form the supply function is a product of force and flow variables in deviation form. Feedback signals originate from intensive variables like temperature, pressure and composition. We show that the physical dimension of the system matters: The larger the distributed system is, the more difficult the stationary state may be to stabilize. Any chemical process can be stabilized by distributed PID control provided that the sensor and actuator locations are suitable. We apply the results to heat conduction and reaction diffusion equations.

Passivity based control via the second law

Abstract In the paper we develop methods for stability analysis and control design for single phase, distributed chemical processes in one spatial dimension. The physical phenomena we model include reaction, diffusion, heat transfer and convection. The approach is motivated by the formalism of non-equilibrium thermodynamics, the energy methods of fluid mechanics and the passivity theory of non-linear control. We provide two distinct contributions. First, we give a tutorial overview of background material and examples to illustrate. Second, we introduce a new approach for stabilization of non-equilibrium, fluid flow systems. Some applications to systems of conservation laws are presented and connected with boundary and inventory control. We also develop an approach to study the classical problem of minimum entropy production in stationary flow.

Process systems, passivity and the second law of thermodynamics

Abstract In this paper we use the first and second laws of thermodynamics to motivate a theory for nonlinear process control. Our main tenets are: positive entropy production, boundedness of entropy in terms of energy, concavity of the entropy density and Helmholtz free energy as a storage function. These give the process system a causal input-output description, zero state detectability and stabilizability. To make the theory apply to practical systems we follow ideas from classical irreversible thermodynamics and extend the concept of entropy of the non-equilibrium by assuming local equilibrium.

Silicon solar cell production

Abstract A significant role can be played by the systems engineering community in the optimization of the production process for silicon solar cells. Many of the techniques utilized for cell manufacturing are of recent origin and the amount of experience in the industry as a whole is limited. Some of the individual processes and steps are poorly adapted for continuous production since they were designed for micro-electronics applications rather than photovoltaics. Only very recently has the industry grown to the point where intermediate products, such as solar grade silicon, solar silicon wafers, solar cells and solar panels are commodities having global market potential. Finally, industry consolidation has generated large commercial entities which can better take advantage of tools from process systems engineering. The chemical and process systems and engineering communities can contribute to this booming industry by providing methods for improved control, process optimization and retro-fitting of existing processes, as well as encouraging process innovation and scale-up. This paper describes the complete production process for solar cells, highlights challenges relevant to systems engineering, and overviews work in three distinct areas: the application of real time optimization in silicon production, the development of scale-up models for a fluidized bed poly-silicon process and a new process concept for silicon wafer production.

Analytical expression of explicit MPC solution via lattice piecewise-affine function

An analytical expression of the explicit solution to linear model predictive control (MPC) is proposed by the introduction of a lattice piecewise-affine (PWA) function. A systematic procedure is developed for building a lattice PWA representation from a continuous explicit MPC solution obtained by a multi-parametric program. A simple method is presented to remove the redundant parameters in the lattice expression of MPC control laws. The effectiveness of this approach is supported by the study of three benchmark MPC problems. The proposed analytical expression provides a very efficient and practically viable method for implementing the explicit MPC solutions regarding its online calculation and memory space requirements.

The steady-state process with periodic perturbations☆

Abstract To analyze the feasibility of periodic operation, a generalized Π-criterion is developed in this paper. Using averaging, it is shown that the criterion can be used to describe not only the effect of perturbations around the optimum steady state, but it can also be used to analyze the effect of periodic perturbations around any given stable steady state. Expressions reflecting the relative change in averaged steady state performance are developed for a few sample systems and the results are applied to periodically forced CSTRs and polymerization reactions. The approximate expressions are used to determine the optimal shape of the periodic inputs. This paper also includes an analysis of a periodic feedback control law using relay controllers with hysteresis and integral action. With single-input periodic control, the controller can be paired with a suitable output so that the effects due to measurement errors and disturbances can be minimized

Interior point SQP strategies for large-scale, structured process optimization problems

Successive quadratic programming (SQP) has been the method of choice for the solution of many nonlinear programming problems in process engineering. However, for the solution of large problems with SQP based codes, the combinatorial complexity associated with active set quadratic programming (QP) methods can be a bottleneck in exploiting the problem structure. In this paper, we examine the merits of incorporating an interior point QP method within an SQP framework. This provides a novel interpretation of popularly used predictor-corrector interior point (IP) methods. The resulting large-scale SQP algorithm, with an interior point QP, also allows us to demonstrate significant computational savings on problems drawn from optimal control and nonlinear model predictive control.

Dynamics and control of chemical process networks: Integrating physics, communication and computation

Abstract This paper provides the theoretical foundation for the modeling, analysis and control of integrated chemical process networks, or, in short, “process networks.” The dynamics of process networks is represented using state-space descriptions derived from classical irreversible thermodynamics and constrained by the second law so that dissipation is always non-negative. The state descriptions (models) derived from this point of view provide exact process representations. A unique, quadratic Lyapunov function for stability analysis and control design is derived directly from the entropy. The resulting process models are complex and simplifications may be needed in practical applications. Time-scale decomposition and singular perturbation theory provide the basis for exploring the network-level dynamic behavior that emerges as a result of tight inventory integration, and developing appropriate reduced-order models and a hierarchy of control systems for managing inventories and inventory flows. Model-based networked control and Lyapunov theory are leveraged to develop an integrated control and communication strategy that manages the information flows between the network components and explicitly accounts for communication constraints.