Least-restrictive robust MPC of periodic affine systems with application to building climate control

Robust state-feedback model predictive control (MPC) of discrete-time periodic affine systems is considered. States and inputs are subject to periodically time-dependent, hard, convex, polyhedral constraints. Disturbances are additive, bounded and subject to periodically time-dependent bounds. The control objective is given in terms of periodically time-dependent costs. First, maximum robust periodic controlled invariant sets are formally characterized and subsequently employed in the design of least-restrictive robustly strongly feasible periodic MPC problems. Finally, the proposed methods are applied to controlling room temperatures in buildings

Least-restrictive robust periodic model predictive control applied to room temperature regulation

State-feedback model predictive control (MPC) of constrained discrete-time periodic affine systems is considered. The periodic systems’ states and inputs are subject to periodically time-dependent, hard, polyhedral constraints. Disturbances are additive, bounded and subject to periodically time-dependent bounds. The objective is to design MPC laws that robustly enforce constraint satisfaction in a manner that is least-restrictive, i.e., have the largest possible domain. The proposed design method is demonstrated on a building climate control example. The proposed method is directly applicable to time-invariant MPC

Optimal Control of Energy Efficient Buildings

The building sector consumes a large part of the energy used in the United States and is responsible for nearly 40% of greenhouse gas emissions. Therefore, it is economically and environmentally important to reduce the building energy consumption to realize massive energy savings. Commercial buildings are complex, multi-physics, and highly stochastic dynamic systems. Recent work has focused on integrating modern modeling, simulation, and control techniques to solving this challenging problem. The overall focus of this thesis is directed toward designing an energy efficient building by controlling room temperature. One approach is based on a distributed parameter model represented by a three dimensional (3D) heat equation in a room with heater/cooler located at ceiling. The finite element method is implemented as part of a novel solution to this problem. A reduced order model of only few states is derived using Proper Orthogonal Decomposition (POD). A Linear Quadratic Regulator (LQR) is computed based on the reduced model, and applied to the full order model to control room temperature. Also, a receding horizon constrained linear quadratic Gaussian (LQG) controller is developed by minimizing energy cost of heating and cooling while satisfying hard and probabilistic temperature constraints. A stochastic receding horizon controller (RHC) is employed to solve the optimization problem with the so-called chance constraints governed by probability temperature levels. Furthermore, a constrained stochastic linear quadratic control (SLQC) approach was developed for such purposes. The cost function to be minimized is quadratic, and two different cases are considered. The first case assumes the disturbance is Gaussian and the problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. The second case assumes the disturbance is norm-bounded with distribution unknown and the problem is formulated as a min-max problem. By using SLQC, both problems are reduced to semidefinite optimization problems, where the optimal control may be computed efficiently. Later, some discussions on solving more requirements by SLQC are provided. Simulation and numerical results are given to demonstrate the validity of the proposed techniques shown in this thesis

Strongly feasible stochastic model predictive control

In this article we develop a systematic approach to enforce strong feasibility of probabilistically constrained stochastic model predictive control problems for linear discrete-time systems under affine disturbance feedback policies. Two approaches are presented, both of which capitalize and extend the machinery of invariant sets to a stochastic environment. The first approach employs an invariant set as a terminal constraint, whereas the second one constrains the first predicted state. Consequently, the second approach turns out to be completely independent of the policy in question and moreover it produces the largest feasible set amongst all admissible policies. As a result, a trade-off between computational complexity and performance can be found without compromising feasibility properties. Our results are demonstrated by means of two numerical examples

Green Scheduling of Control Systems

Electricity usage under peak load conditions can cause issues such as reduced power quality and power outages. For this reason, commercial electricity customers are often subject to demand-based pricing, which charges very high prices for peak electricity demand. Consequently, reducing peaks in electricity demand is desirable for both economic and reliability reasons. In this thesis, we investigate the peak demand reduction problem from the perspective of safe scheduling of control systems under resource constraint. To this end, we propose Green Scheduling as an approach to schedule multiple interacting control systems within a constrained peak demand envelope while ensuring that safety and operational conditions are facilitated. The peak demand envelope is formulated as a constraint on the number of binary control inputs that can be activated simultaneously. Using two different approaches, we establish a range of sufficient and necessary schedulability conditions for various classes of affine dynamical systems. The schedulability analysis methods are shown to be scalable for large-scale systems consisting of up to 1000 subsystems. We then develop several scheduling algorithms for the Green Scheduling problem. First, we develop a periodic scheduling synthesis method, which is simple and scalable in computation but does not take into account the influence of disturbances. We then improve the method to be robust to small disturbances while preserving the simplicity and scalability of periodic scheduling. However the improved algorithm usually result in fast switching of the control inputs. Therefore, event-triggered and self-triggered techniques are used to alleviate this issue. Next, using a feedback control approach based on attracting sets and robust control Lyapunov functions, we develop event-triggered and self-triggered scheduling algorithms that can handle large disturbances affecting the system. These algorithms can also exploit prediction of the disturbances to improve their performance. Finally, a scheduling method for discrete-time systems is developed based on backward reachability analysis. The effectiveness of the proposed approach is demonstrated by an application to scheduling of radiant heating and cooling systems in buildings. Green Scheduling is able to significantly reduce the peak electricity demand and the total electricity consumption of the radiant systems, while maintaining thermal comfort for occupants

Model-based predictive control methods for distributed energy resources in smart grids.

This thesis develops optimization-based techniques for the control of distributed energy resources to provide multiple services to the power network. It is divided into three parts. The first part of this thesis focuses on the development of a framework for the efficient control of a single resource that is subject to the effect of periodic stochastic uncertainties. More specifically, resources that can be described by the general class of periodic constrained linear systems are considered and a method, based on Stochastic MPC, to control the over-time-average constraint violations is developed. Finally, the effectiveness of the control framework is tested, by means of a simulation analysis, for the case of the climate control of a building. The second part of the thesis introduces the required background for the electric power grid, energy markets, and distributed energy resources providing grid support services. First, the control problem of scheduling the operation of a set of energy resources offering multiple services to the grid is formally stated as a multi-stage uncertain optimization problem. In particular, the problem is designed so as to maximize the provision of a shared tracking service while enforcing the satisfaction of the operational constraints on both the individual resources, as well as on the hosting distribution network. Two computationally tractable approximated solution methods are then presented, which are based on robust-optimization techniques and on a linearization of the power flow equations around a general linearization point. A simulation-based analysis demonstrates the capability of the proposed framework to adapt to different levels of uncertainty acting on the overall system. Finally, a quantitative and qualitative comparison between the two approximation schemes is presented and general guidelines are given. The last part of the thesis demonstrates the practical relevance of the control framework developed in Part II. In particular, the aggregation of an electrical battery system and of an office building is considered, and two case studies are investigated. The first deals with the provision of secondary frequency control in the Swiss market, whereas the second deals with the problem of dispatching the operation of an active distribution feeder characterized by the presence of stochastic prosumers. In both cases, we show how to adapt the general framework of Part II so as to accommodate the given application. Then, we design a hierarchical multi-timescale controller in order to reliably deliver the service by coordinating the controllable resources during real-time operation. The results of both experimental campaigns demonstrate the effectiveness and robustness of the control methodology against the wide range of uncertainty involved. In fact, in both cases, high-quality tracking performance could be achieved without jeopardizing the occupants' comfort in the building nor violating the operational constraints of the battery. Finally, the results also show the benefit of combining resources with complementary technical capabilities as the building and the battery

Model Predictive Control (MPC) for Enhancing Building and HVAC System Energy Efficiency: Problem Formulation, Applications and Opportunities

In the last few years, the application of Model Predictive Control (MPC) for energy management in buildings has received significant attention from the research community. MPC is becoming more and more viable because of the increase in computational power of building automation systems and the availability of a significant amount of monitored building data. MPC has found successful implementation in building thermal regulation, fully exploiting the potential of building thermal mass. Moreover, MPC has been positively applied to active energy storage systems, as well as to the optimal management of on-site renewable energy sources. MPC also opens up several opportunities for enhancing energy efficiency in the operation of Heating Ventilation and Air Conditioning (HVAC) systems because of its ability to consider constraints, prediction of disturbances and multiple conflicting objectives, such as indoor thermal comfort and building energy demand. Despite the application of MPC algorithms in building control has been thoroughly investigated in various works, a unified framework that fully describes and formulates the implementation is still lacking. Firstly, this work introduces a common dictionary and taxonomy that gives a common ground to all the engineering disciplines involved in building design and control. Secondly the main scope of this paper is to define the MPC formulation framework and critically discuss the outcomes of different existing MPC algorithms for building and HVAC system management. The potential benefits of the application of MPC in improving energy efficiency in buildings were highlighted

Integration of Photovoltaics into Building Energy Usage through Advanced Control of Rooftop Unit

As the United States sees the continued expansion of photovoltaic (PV) and other distributed solar generation technologies into the distribution grid, there is an increased need to find approaches to mitigate integration challenges associated with renewable resources. Depending on the renewable resource, the integration challenges will vary. Much of the challenge with integration is associated with the uncontrolled oscillations of output power, for example, from a PV array. Both solar and wind resources rely on environmental conditions to produce power. However compared to wind, solar generation resources such as PV typically produce more second to minute oscillations due to cloud patterns. With low levels of penetration, the impact is minimal. This paper focuses on developing advanced control strategies for building equipment like the rooftop units along with energy storage technologies to support seamless PV integration into buildings. A forecasting approach for PV is presented along with model-based control strategies for using load to support the integration of PV. The forecasting model takes as input solar irradiance and module temperature to estimate the output power of PV based on an interconnected voltage. The first step is to poll the cloud patterns for the day and utilize this information to project the cloud density each hour. The trained neural network defines relationship of this cloud cover to the amount of expected solar irradiance that is measured. Temperature data is collected from weather application and is inserted as an initial temperature to the PV model and thermal model. The model develops the corresponding PV curves based on the current module temperature reading and the solar irradiance data provided. The model predicts the average power output of the PV array over the next one-hour time window. A control algorithm for the rooftop unit is presented that utilizes this PV forecast to optimize the energy consumption to match the PV peak generation. The model is validated using irradiance, temperature, and PV output power measurements from Oak Ridge National Laboratory’s 50kW PV array