Distributed and cooperative control with applications to building HVAC systems

• Main Author: Long, Yushen
• Other Authors: Xie Lihua
• Format: Theses and Dissertations
• Language: English
• Published: 2017
• Subjects: DRNTU::Engineering::Electrical and electronic engineering
• Online Access: http://hdl.handle.net/10356/69494
• Institution: Nanyang Technological University

According to the environment programme report\cite{Sylvie09} published by the United Nations, buildings account for 40\% of energy consumption and resources and one third of greenhouse gas emissions. Thus to improve the energy efficiency of buildings becomes more and more attractive. Heating, ventilation and air-conditioning (HVAC) system composes one third to half of building energy use\cite{AswaniM} so to optimize the energy efficiency of it is one of the most promising directions. To this end, developing energy-efficient control strategies for building HVAC systems is necessary for both economy and environment protection. Model Predictive Control (MPC) has attracted more and more attention to improve the energy efficiency of HVAC systems. Because of its optimality nature and ability to handle input and output constraints, MPC usually can achieve better performance compared with traditional control strategies. In recent years, a lot of research works have been published on using MPC approaches to reduce the energy cost of HVAC systems while keeping the temperature in a comfortable region, see, e.g.\cite{Ma09}, \cite{Ma12} and so on. There are two difficulties when MPC is applied to building HVAC systems. The first one comes from the large scale of an HVAC system in a building. The number of states of the system depends on the number of zones whose temperatures need to be maintained in a comfortable region. The number of decision variables in the corresponding optimization problems for MPC grows fast when a long prediction horizon is considered. Therefore, the optimization problem which should be solved in every sample interval becomes large and even computationally intractable. A traditional centralized controller is no longer suitable for building HVAC systems. The other difficulty is uncertainties such as weather condition and occupancy. To use model predictive control, one needs to predict evolution of the system to find the optimal control input. However, because of the uncertainties, it is impossible to get a precise prediction. It has been pointed out in \cite{Grimm03} and \cite{Grimm04} that the robustness of model predictive control is a non-trivial topic. Even arbitrarily small disturbance may destabilize a nominally stable system. Therefore, it is necessary to propose some novel strategies which are robust with respect to external disturbance and/or model uncertainty. In this thesis, we present research results on the design of distributed and robust MPC with their applications on building HVAC systems. First, we introduce a scenario-based distributed stochastic MPC algorithm. We consider the weather condition and occupancy as stochastic disturbance and use probabilistic constraints to confine the temperature of each zone within a comfortable region with a predefined probability. Since the evaluation of the probabilistic constraints requires the computation of multi-integral, the resulted stochastic optimization problem becomes intractable. Furthermore, the distributions of the weather condition and the occupancy are hard to model. To overcome these issues, a scenario-based approach is used to approximate the probabilistic constraints by a group of deterministic ones such that the stochastic optimization problem is approximated by a deterministic one. After that, the distribution of the uncertainties is not required any more. A Lagrange dual problem is formulated and it is decomposed by taking advantage of its separable structure. A sub-gradient algorithm is used to solve the dual problem in a distributed way. Though the scenario-based approach can handle stochastic uncertainty efficiently, it is hard to have guarantee on recursive feasibility and convergence. To overcome this issue, we propose a distributed robust MPC based on reduced order models. Considering the complex nature of the heat transfer process, first order model usually is over simplified for a zone with furniture and walls which have different heat capacity. A model based on computational fluid dynamics, though it is accurate enough and widely used in civil and environmental engineering \cite{Kim01},\cite{Moukalled11}, is too complex for controller design and analysis. In the proposed algorithm, the off-line design is based on higher order model such that the controller can capture the system property as much as possible. In the on-line implementation phase, the optimal control problem is based on a reduced order model so that the computational burden is alleviated and the implementation becomes practical. The modelling error introduced by the model reduction is considered as a bounded disturbance and a tube-based approach is used to shape the system behaviour. The on-line optimization generates an open-loop control action which steers the nominal system to the equilibrium while a linear feedback controller which is designed off-line is used to compensate the uncertainties. After introducing two MPC based on linear discrete time models, we present research results based on nonlinear continuous-time models. Though convex optimization problems can be formulated by using linear discrete time models and efficient numerical solvers are available, system behaviour between sampling intervals cannot be handled and the nonlinearity of the building system is not considered. On the other hand, due to the development of nonlinear programming \cite{ipopt}, nonlinear optimal control problem is no longer intractable. Thus, to use nonlinear continuous-time model provides more potentials on the improvement of the system performance without too much additional computational burden. By using nonlinear continuous-time model, we first present a distributed MPC algorithm based on contraction property. Most of the existing nonlinear continuous-time MPC is based on the Lipschitz constant of the system. Due to the inherent conservativeness, the resulted algorithms are usually impractically conservative. To overcome this issue, we consider a special class of nonlinear systems with contraction property \cite{Lohmiller00}. Instead of using the Lipschitz constants of the local systems, contraction coefficients are used to estimate the prediction error, which greatly improve the conservativeness. Sufficient conditions on feasibility and stability are also derived. Next, we apply the proposed contraction theory based distributed MPC to building HVAC systems. We design a hierarchical structure to handle the system in two levels: the building level and the zone level. The upper layer collects the global information which includes the temperature measurements of each room, the occupancy and the weather prediction, and it generates temperature and control references for each zone. The lower layer, on the contrary, only makes use of local information and the reference signal to optimize the local performance. Two layers work with different frequencies. The upper layer updates slowly with a long prediction horizon while the lower layers update more frequently with a short prediction horizon. In the previous control schemes we assume perfect communication between controllers and sensors/actuators. However, in smart buildings, digital wireless communication is widely used and channel capacity is limited so that perfect communication is impossible. Therefore, we also study a networked MPC design problem. To equip the valves and the dampers of HVAC systems with advanced controllers is not practical because of the limited space of duct. A more practical strategy is that control signals are computed by remote controllers and transmitted to the actuators which can adjust the valves and dampers. Due to the limited bandwidth of digital communication channel, we study the quantization effect on the control signals and the state measurements. Sufficient conditions are provided to guarantee feasibility and stability.