Donald J. Chmielewski

On constrained infinite-time linear quadratic optimal control

This work presents a solution to the infinite-time linear quadratic optimal control (ITLQOC) problem with state and control constraints. It is shown that a single, finite dimensional, convex program of known size can yield this solution. Properties of the resulting value function, with respect to initial conditions, are also established and are shown to be useful in determining the aforementioned problem size. An example illustrating the method is finally presented.

On constrained infinite-time nonlinear optimal control

Abstract In this work, we consider the infinite-time optimal control of input affine nonlinear systems subject to point-wise in time inequality constraints on both the process inputs and outputs. Fundamental to solving this constrained infinite-time nonlinear optimal control (CITNOC) problem is the ability to calculate the value function of its unconstrained counterpart, the infinite-time nonlinear optimal control (ITNOC) problem. Unfortunately, the traditional ITNOC solution procedure of specifying an objective function and then solving for the optimal control policy and corresponding value function is computationally intractable in all but the simplest of examples. However, in many cases one can easily identify a stabilizing feedback for near operating point regulation. Building from this local policy, the proposed method is to construct a meaningful optimal control objective function as well as its corresponding value function. These functions are then used to analyze the closed-loop stability of the proposed policy. Upon return to the constrained case the constructed objective and value functions are again used to develop a self-consistent constrained finite-time scheme that will, for the first time, provide an exact solution to the CITNOC problem. The mechanics of the proposed method are then illustrated by an example from chemical reactor control.

Process systems opportunities in power generation, storage and distribution

Abstract This paper presents an overview of the current process systems opportunities in power generation, storage and distribution. It puts in perspective how process systems engineering (PSE) has contributed to the area and explores the current technical problems that PSE can contribute to. Fuel cells, solar cells, wind turbines, flow batteries and rechargeable batteries as well as their interactions with the smart grid are considered. PSE has contributed and will contribute to the design as well as optimal integration and operation of power generators, storage systems and power grids, through mathematical modeling, control and optimization.

HVAC control using infinite-horizon economic MPC

Energy consumption by Heating Ventilation and Air Conditioning (HVAC) systems is usually heaviest when electricity prices are at their highest. The method of Economic Model Predictive Control (EMPC) can be used in conjunction with Thermal Energy Storage (TES) to time-shift power consumption away from periods of high demand to periods of low energy cost. In addition to enormous computational costs, implementation of such algorithms can result in unexpected and sometimes pathological closed-loop behavior, including inventory creep and bang-bang actuation. This paper will present an infinite-horizon formulation of the EMPC problem. While the design of this controller is achieved by a fairly simple convex optimization problem, it will be shown to alleviate many of the pathological behaviors observed in the finite-horizon case as well as significantly reduce the computational effort required for implementation. The method is illustrated on a simple building example using active TES.

Demand response for chemical manufacturing using Economic MPC

The notion of demand response in electric power systems is to use time varying electricity price structures to encourage consumers to track generation availability. Specifically, when available generation is low, either due to high demand or a lack of renewable sources, an increase in electricity rates is intended to encourage smart grid participants to reduce consumption. Similarly, when on-line generation is higher than demand, smart grid participants may benefit from low electricity rates. While many think of smart grid participants as residential consumers, the commercial building and industrial sectors will likely result in a higher grid impact to implementation cost ratio. In this work we investigate potential demand response mechanisms from the chemical manufacturing industry. It will be shown that depending on the type of upgrade hardware selected the smart grid operating policy will either be an application of Real-Time Optimization (RTO) or Economic Model Predictive Control (EMPC). In the case of EMPC the impact of prediction horizon size will be highlighted.

Control of electric power transmission networks with massive energy storage using economic MPC

The classic approach to generator dispatch in large scale power generation and distribution systems (under regulated markets) is the Unit Commitment (UC) problem. As renewable power sources (that cannot be dispatched) are added to the network many have advocated the additional introduction of massive energy storage facilities. However, the inherent dynamic nature of energy storage suggests an expanded view of the classic UC operating policy. In this work, the notion of Economic Model Predictive Control (EMPC) is investigated as a generalization of the classic UC policy. Of particular interest is the selection of EMPC prediction horizon size and its impact on storage utilization.

Controller and system design for HVAC with thermal energy storage

Energy consumption by Heating Ventilation and Air Conditioning (HVAC) systems is usually heaviest when electricity prices are at their highest, presenting significant opportunities for the improvement of the underlying control algorithms. The idea being that thermal energy storage can be used to time-shift power consumption away from periods of high power demand to periods of low power cost. In this work, we present a supervisory control scheme, known as Market Responsive Control (MRC), which has the objective of minimizing the expenditure required for the cooling of a given building. The design of this controller is achieved by a fairly simple convex optimization problem. The MRC method is then embedded within an equipment design algorithm. This extended algorithm, known as MRC Embedded Equipment Design (MRC-EED), has the objective of maximizing Net Present Value (NPV) in an effort to size the storage unit and cooling device. Under the economic assumptions of this study, it is concluded that the NPV of installing Thermal Energy Storage (TES) can be significant if electric price variability is sufficiently large.

Covariance-based hardware selection-Part II: equivalence results for the sensor, actuator, and simultaneous selection problems

Recently, a number of covariance-constrained hardware selection problems have been proposed. However, underlying each is the choice of a compensating element (i.e., the state estimator for the sensor case, the feedback controller for the actuator case, and both for the simultaneous case). The subtlety is whether these compensators should be optimal or suboptimal. In this paper, we present formulations using both types of compensators and then prove that the global solution for each type of formulation is independent of the compensator assumption. However, in spite of this equivalence of solutions, the computational perspective indicates that one choice will always have an advantage. While the computational difference is minor in the sensor selection case, significant advantages can be found in the suboptimal controller version of the actuator selection problem. In particular, the suboptimal version can be used to find global solutions to the previously intractable optimal controller formulation. In the simultaneous case, similar results are presented and lead to the first global solution scheme for the covariance-based simultaneous sensor and actuator selection problem.

Load characteristics and control of a hybrid fuel cell / battery vehicle

The Polymer Electrolyte Membrane Fuel Cell (PEMFC) has been projected to be the fuel cell of choice for future automotive applications. Among the most challenging aspect of this application is the occurrence of severe and frequent changes in power demand. This paper will present a model aimed at mimicking the load expected in a fuel cell vehicle, including a DC motor, DC-DC converters and a rechargeable battery for peak-shaving and regenerative braking. The model also includes the kinematics of the vehicle (rotational and translational inertia as well as a simple wind resistance model), and thus can be connected to standardized drive cycle scenarios. In contrast to simple lab focused loads (resistive, constant current, constant voltage or constant power) where load impendence is directly manipulated, the manipulated variable within this load is the gain signal to the DC-DC converter. Based on this model we develop a control system architecture consisting of a number of low level regulatory loops, a power distributor for peak-shaving and finally a high level loop for tracking vehicle speed.

Optimal sensor network design using the minimally backed-off operating point notion of profit

We have recently proposed a new formulation of the optimal sensor selection problem for closed-loop partial state information dynamic systems. Although this formulation (a mixed integer convex program) yields to a globally optimal search scheme, the only economic information used is with regard to the capital cost of the sensors. Additionally, we have recently proposed a new stochastic based formulation of the minimally backed-off operating point (MBOP) selection problem. Although this formulation has strong profit based notions (due to its close relations to model predictive control and real-time optimization) and yields to a globally optimal search scheme (due to its convex/reverse-convex form), it assumes a fixed sensor array. Thus, the goal of this work is to combine the two formulations and arrive at a value based sensor network design scheme. In addition to utilizing the capital cost of the sensors, this formulation will incorporate the impact of the sensor network on the feasible set of backed-off operating points and thus the operational profit of the process. We will further show that this new formulation can be cast into a convex/reverse-convex form, and is thus readily solved globally via a branch and bound procedure. The proposed method is then illustrated through a CSTR example.