A cyber-physical system for building automation and control based on a distributed MPC with an efficient method for communication

Abstract

This paper introduces a cyber-physical system for building automation and control that is developed based on a distributed model predictive control. The implemented distributed method significantly reduces computation overhead with respect to the centralized methods. However, continuous data transfer between subsystems, which are often far from each other, is required when using this method. Information transmission between subsystems is very often subject to the limitations of transmission bandwidth and/or short communication range resulting in significant communication overhead. This causes significant time latency between making measurements and applying control commands, which adversely affects the control performance. Therefore, the distributed method used in this paper implements a two-level communication architecture to reduce the communication overhead. In order to avoid collision in communication inside neighborhood using this method, the TDMA-OFDMA scheme is used for wireless communication between distributed devices. Under these assumptions, the communication overhead is calculated. Then, a novel algorithm for finding the size of neighborhoods resulting in the lowest time latency between making measurements and applying control commands is presented for a typical office building. Finally, the satisfactory performance of the proposed cyber-physical system for the temperature control of a typical office building in the presence of disturbance and model inaccuracy is illustrated using computer simulations.

Introduction

Large-scale Building Automation and Control Systems (BACSs) are used for controlling the environment of buildings, such as temperature by means of Fan Coil Units (FCUs), air conditioning, and ventilation. About half of the energy consumed in commercial buildings is directly related to space heating, cooling, and ventilation [9]. There are some commercial products available that are based on wired communication technologies for setting up BACSs. However, large-scale wireless BACSs, which are easy to deploy and cost-effective, have not been well studied yet. The advent of easily controllable smart thermostats and smart meters (with wireless communication and computation capabilities) and new wireless communication infrastructures has made it possible to reduce building energy consumption by designing a wireless cyber-physical system to operate the heating, cooling,and ventilation systems in a more efficient way to address the global energy and environmental concerns.

In recent years, advances in communication as well as sensor and actuator technologies enable us to develop cyber-physical systems. These systems are the new generation of Industrial Internet of Things (IIoT) systems. IIoT systems comprise of three different layers: Field, communication,and computation. The field layer consists of distributed sensors, actuators,and other networked devices. The communication layer consists of low cost and low power consumption Machine to Machine (M2M) IoT wireless communication modules, such as Digi XBee, LoRa, Sigfox. Each distributed field device is equipped with at least one M2M IoT module in an IIoT system. This module transmits data from the attached field device to a gateway that connects the M2M module to the Internet. The computation layer includes a computer server connected to the Internet. Data gathered from the field is received by this remote computer in real time; and subsequently, it generates proper commands to be sent to field devices via the communication layer by running the optimization, estimation, data mining,or the machine learning algorithms in real time. The ease of interconnection of distributed sensors and actuators and generally speaking the field devices to IIoT systems results in larger and larger IIoT systems. As the size of IIoT systems increases, the available centralized algorithms, such as the active set method, the interior point method, the Kalman filter, etc., which the centralized computer server runs, are not able to complete their computation on time due to the huge computational complexity associated with large-scale IIoT systems. One way to overcome this computational scalability problem is to use the cloud computing concepts and exploit the available computational resources of the field. In IIoT systems, each distributed sensor, actuator,or networked device is equipped with at least one M2M IoT module, which is an embedded system equipped with a microprocessor/microcontroller. These distributed embedded systems provide us with one of the computational resources of the field. Having this computational resource, one way to overcome the aforementioned drawback is to break down the computational load of the centralized computer server to the distributed computational resources of the field and use parallel computation and consensus to complete the required centralized computation on time. In this type of IIoT systems, the computation layer is integrated to the field layer forming a new type of IIoT systems, which is known as cyber-physical systems. The main advantages of cyber-physical systems over IIoT systems are the scalability, higher reliability (due to its distributed nature), the ease of implementation, the lower cost of implementation and maintenance, etc. Therefore, the applications domain of cyber-physical systems is now very vast. It ranges from agricultural irrigation networks [19] to smart buildings [4], [27], [30], [35] and power systems.

To illustrate the application of the cyber-physical system described above, let us consider controlling the temperature of an office with several rooms and hallways. One easy way for controlling the environment of this office as used in many places is as follows: In each room and hallway (referred to as subsystem), at least a thermostat which includes a sensor, a tuning volume, and an electrical relay is deployed to measure temperature, and a fan coil unit (actuator) is also installed to maintain the temperature close to the desired value. Moreover, the temperature control policy in each room and hallway is designed in a fully decentralized fashion without considering the temperature interaction between rooms and hallways, which from now on are referred to as subsystems. However, as internal doors are opened, the distribution of subsystems temperature changes, and hence, the implemented control policy becomes inefficient as it has been designed in a fully decentralized way. Now, suppose actuators and sensors in the setup proposed in this paper are equipped with wireless communication modules. Therefore; they can collaborate with each other for the temperature regulation of the entire building. To achieve this goal, a performance criterion for the entire building that penalizes both the energy consumption and the deviation of each subsystem temperature from the desired temperature is defined. For this setup, each decision-maker is defined as the collection of the thermostat and fan coil of each subsystem equipped with at least one M2M wireless communication module. In this setup, the decision-makers can be designed to minimize this performance criterion subject to the thermal dynamics of the building and operational constraints forming a wireless cyber-physical system for building automation and control. Two main methodologies have been developed to address this optimal control problem: One is based on the centralized optimization methodology, and the other one is based on the distributed optimization methodology. The conventional and widely used methodology is the centralized methodology, e.g., [31]. However, for large-scale buildings with many subsystems, the implementation of centralized methods requires high-performance computing devices with very fast processors and very large memory, which are beyond the available computational power and memory of each distributed decision-maker. Therefore, the distributed optimization methods have been introduced in the literature for developing cyber-physical systems by distributing the computational load to distributed decision-makers [19], [32], [36], [45]. It has been shown that distributed methods are successful and superior with respect to centralized methods in many aspects, especially in terms of computational complexity [16], [18] and reliability. Because of the above reasons, we implement the distributed optimization methods for distributing the computational load to the distributed decision-makers of the proposed cyber-physical system to tune actuators settings properly.

Wireless cyber-physical systems are very often subject to communication delays. Therefore, many research papers in this area are concerned with the analysis and compensation of communication delay effects in distributed networks, e.g., [12], [17], [50]. A hierarchical (two-level) communication architecture and a three-step algorithm including an extra outer iterate step are proposed in [19], [44] to provide scope for managing the communication overhead, which is associated with the distributed optimization methods. In this distributed optimization method, distributed decision-makers are grouped into disjoint neighborhoods of nearby decision-makers; and the number of decision-makers within a neighborhood denotes the size of the neighborhood. The exchange of information between decision-makers within a neighborhood, which is subject to low communication overhead, frequently occurs after each decision variable update. In contrast, the exchange of information between neighborhoods, which is subject to high communication overhead, is limited to be less frequent. Hence, as most of the communication between distributed decision-makers is within neighborhoods (referred to as inside neighborhood communication), the communication overhead of the method of [19], [44] is much less than that of the other distributed methods, e.g., [46], that uses a single – level communication architecture. This is shown in Section 3 by calculating the communication cost for inside neighborhood communication denoted by $C_{com}^{in}$ and between neighborhood communication (referred to as all to all communication) denoted by $C_{com}^{out}$. In large-scale systems with many geographically distributed decision-makers, $C_{com}^{out}$ is much larger than $C_{com}^{in}$. Therefore, in the distributed methods that use single-level communication architecture for communication, the communication overhead is extremely high as all the time, all to all communication takes place. Hence, in this paper, we use the distributed method of [19] that uses the two-level communication architecture; because from the communication point of view, it is efficient. In this method, each decision-maker within a neighborhood frequently updates its local component of the overall decision variable by solving an optimization problem of reduced size. The updated value is then communicated to all other neighboring decision-makers. This inside neighborhood update or communication is referred to as an inner iterate. In addition to inner iterates, updates of decision variables from other neighborhoods are received periodically. They are referred to as outer iterates. Between outer iterates, distributed decision-makers continue to compute and refine the local approximation of the optimal solution with fixed values for decision variables from outside the neighborhood. These inner-outer iterates continue until an $ϵ$-convergence stopping criterion is satisfied.

Due to the superiority of distributed optimization methods with respect to the conventional centralized methods, In the proposed cyber-physical system we use the distributed optimization method introduced in [19], [44] for the temperature control of buildings by considering the effects of computational latency, which is the summation of the computation overhead and communication overhead. Note that the proofs for the feasibility, convergence, and the optimality of the distributed method used in this paper for the temperature control were previously presented in [19]. In the aforementioned reference, a novel distributed optimization method has been presented; and then a novel cyber-physical system, which is based on this optimization method, has been introduced for improving the performance of Australia’s automated irrigation network. In sum, in the wireless cyber-physical system proposed in this paper for the temperature regulation of large-scale buildings, the field layer consists of distributed decision-makers. Each subsystem (room or hallway) is equipped with a decision-maker and a decision-maker is the collection of at least one thermostat and one fan coil unit equipped with one M2M IoT module. In this cyber-physical system, distributed M2M wireless IoT modules form the communication layer and the computation layer is integrated with the field layer using the distributed optimization method of [19].

This paper introduces a cyber-physical system for building automation and control, as described above, which is developed based on the distributed optimization method of [19]. An application of this method for the temperature control of a building is presented. This method requires simultaneous communication within neighborhoods. Therefore, to avoid a collision in inside neighborhood communication using this method, the TDMA (time division multiple access)-OFDMA (orthogonal frequency division multiple access) scheme must be used for wireless communication between the distributed decision-makers. This type of communication can be easily implemented using M2M IoT modules. For example, the XBee module of Digi International provides us with this feature. Each XBee module is equipped with an embedded processor, which can also be used for distributed computation. Each subsystem of the building is equipped with a decision-maker, which includes at least a thermostat as well as a fan coil equipped with an M2M IoT module. Under this setup, the communication overhead is calculated. Then, a novel algorithm for finding the size of neighborhoods resulting in the lowest time latency between making measurements and applying control commands is presented for a typical office building. Finally, the satisfactory performance of the distributed model predictive control method, which is developed based on the distributed optimization method of [19], with minimum time latency for the temperature control of this building in the presence of disturbance and model inaccuracy, is illustrated by computer simulations. Distributed control methods for building automation and control have been investigated previously in [4], [27], [30], [35], [40]; however, unlike this paper, none of the available studies are concerned with the effects of communication and computation overheads on building automation performance, and they do not find the best trade-off between control performance, communication overhead and computation overhead for building automation.

This paper is organized as follows: the introduction was presented in Section 1. Section 2 describes building temperature control system by presenting the optimal control problem to be solved, the distributed optimization method introduced in [19], and the thermal model of a typical office building. Section 3 is devoted to the communication part. In Section 4, the optimal trade-off between control performance, communication overhead and computation overhead are determined for a typical office building of interest by finding the optimal size of neighborhoods, denoted by $m^{*}$ for this building. Using computer simulations, the satisfactory performance of the proposed wireless cyber-physical system with the optimal size of neighborhoods for the temperature control of this building in the presence of disturbance is illustrated in Section 5. Finally, the paper is concluded in Section 6.