Numerical Methods for Nonlinear Optimal Control Problems and Their Applications in Indoor Climate Control

OF THE DISSERTATION Numerical Methods for Nonlinear Optimal Control Problems and Their Applications in Indoor Climate Control by Runxin He Doctor of Philosophy in Electrical Engineering Washington University in St. Louis, August 2017 Research Advisor: Humberto Gonzalez Efficiency, comfort, and convenience are three major aspects in the design of control systems for residential Heating, Ventilation, and Air Conditioning (HVAC) units. In this dissertation, we study optimization-based algorithms for HVAC control that minimizes energy consumption while maintaining a desired temperature, or even human comfort in a room. Our algorithm uses a Computer Fluid Dynamics (CFD) model, mathematically formulated using Partial Differential Equations (PDEs), to describe the interactions between temperature, pressure, and air flow. Our model allows us to naturally formulate problems such as controlling the temperature of a small region of interest within a room, or to control the speed of the air flow at the vents, which are hard to describe using finite-dimensional Ordinary Partial Differential (ODE) models. Our results show that our HVAC control algorithms produce significant energy savings without a decrease in comfort. Also, we formulate a gradient-based estimation algorithm capable of reconstructing the states of doors in a building, as well as its temperature distribution, based on a floor plan and a set of x thermostats. The estimation algorithm solves in real time a convection-diffusion CFD model for the air flow in the building as a function of its geometric configuration. We formulate the estimation algorithm as an optimization problem, and we solve it by computing the adjoint equations of our CFD model, which we then use to obtain the gradients of the cost function with respect to the flow’s temperature and door states. We evaluate the performance of our method using simulations of a real apartment in the St. Louis area. Our results show that the estimation method is both efficient and accurate, establishing its potential for the design of smarter control schemes in the operation of high-performance buildings. The optimization problems we generate for HVAC system’s control and estimation are largescale optimal control problem. While some optimal control problems can be efficiently solved using algebraic or convex methods, most general forms of optimal control must be solved using memory-expensive numerical methods. In this dissertation we present theoretical formulations and corresponding numerical algorithms that can find optimal inputs for general dynamical systems by using direct methods. The results show these algorithms’ performance and potentials to be applied to solve large-scale nonlinear optimal control problem in real time.

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