Formulation and Application of an Economic Model Predictive Control Scheme for Thermostats

Within the last ten years, growing pressure to reduce energy consumption of buildings has led to an increased focus on the development and deployment of advanced control strategies. Heating, Ventilation, and Air-Conditioning (HVAC) constitutes the majority of the energy consumption of buildings. Model predictive control (MPC) has gained significant attention in HVAC control as it computes the control inputs for a given system by iteratively solving an optimal control problem on-line. The problem formulation accounts for the system operating objective and constraints. Several application studies of MPC applied to buildings have been reported in the literature. These studies have demonstrated the benefits of the application of MPC schemes to buildings. However, one theme that appears in some of the literature is the lamentation on the difficulty to apply MPC broadly to buildings. This is a challenging problem because the MPC system design needs to include a robust and broadly applicable system identification methodology to effectively address this problem. Moreover, in many building applications, the desired sensors measuring key variables are not available (e.g., a heat disturbance load and power consumption measurements are usually not available for residential zones controlled by a thermostat). In this work, an economic MPC scheme is developed to manipulate the temperature setpoint of a zone controlled by a thermostat. The MPC scheme is equipped with an economically-oriented objective that includes a system identification procedure, a state estimator, and a control problem formulation. The economically-oriented MPC seeks to minimize the utility bill by manipulating the setpoint to leverage the building mass as thermal energy storage while maintaining the zone temperature setpoint within a comfortable range. Given the lack of a power or HVAC load measurement in a typical thermostat, the HVAC load is approximated by a filtered version of the thermostat stage commands, which provides a normalized time-average version of the HVAC load. All the components of the resulting MPC scheme are designed in a manner to address general applicability of the resulting MPC. Simulation results are presented to demonstrate the effectiveness of the strategy

Practice-Oriented System Identification Strategies for MPC of Building Thermal and HVAC Dynamics

The increasingly competitive HVAC market has made it necessary to develop technologies that exploit the economic potential in such systems to reduce energy consumption. Smart HVAC operation through optimization-based control strategies, such as model predicative control (MPC), serves as one method for achieving this goal. MPC and Economic MPC have gained significant attention due to their ability to optimally operate HVAC system in order to minimize their energy consumption and/or energy cost while maintaining desired comfort temperatures. Several research work have attempted to use system identification in order to model building thermal and HVAC dynamics. Nonetheless, empirically modeling HVAC systems in a robust and scalable manner is very challenging due to the non-convexity of the system identification optimization problem and the existence of complex actuator saturation limits. Therefore, this work develops grey-box system identification strategies that attack these challenges to enable the development of accurate empirical models of HVAC systems in practice settings. Saturation refers to the usage of the maximum or minimum HVAC capacity to track a desired temperature set-point for buildings under heating and cooling modes. The existence of significant saturation in the data collected is a common problem that poses many challenges for identifying the dynamics of HVAC systems since they can affect the quality of the collected data and result in an inaccurate identified model. Classical approaches for dealing with saturation in system identification, such as using nonlinear functions to capture the saturation behavior, are not implementable due to the complex saturation behavior associated with HVAC systems. In addition, another challenge faced in identifying HVAC and building thermal dynamics is the existence of many roots in such non-convex system identification problems. Therefore, it is desirable in industry to avoid using initial guesses that lead to local optima which result in inaccurate models. In the first part of this work, we develop an algorithm that is capable of detecting and removing saturation data from system identification experiment input-output data. This is done to extract the useful data sections that represent the cited HVAC system dynamics which are necessary to identify reliable models of the HVAC dynamics. The second part of this work develops a strategy that avoids solving system identification problems all the way to local optimality using initial guesses that lead to local optima which result in poor models. The algorithm attempts to eliminate poor initial guesses and yield initial guesses that ultimately lead to great fits of the model to the data. The parameters of the grey-box models were identified via a two-step parameter estimation approach. In the first step, the model parameters were identified using simulation prediction error method. In the second step, the model was augmented with a disturbance model and the estimation gain (i.e., Kalman gain) was identified using the standard 1-step prediction error method. The proposed strategies were applied to data collected from real building HVAC systems and have shown to successfully work in practice. The results demonstrate accurate 1-step and multi-step predictions which are necessary for the implementation of MPC

Economic Model Predictive Control of Nonlinear Process Systems Using Empirical Models

Economic model predictive control (EMPC) is a feedback control technique that attemptsto tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. As its name implies, EMPC requires the availability of a dynamic model to compute its control actions and such a model may be obtained either through application of first-principles or though system identification techniques. However, in industrial practice, it may be difficult in general to obtain an accurate first-principles model of the process. Motivated by this, in the present work, Lyapunov-based economic model predictive control (LEMPC) is designed with an empirical model that allows for closed-loop stability guarantees in the context of nonlinear chemical processes. Specifically, when the linear model provides a sufficient degree of accuracy in the region where time-varying economically optimal operation is considered, conditions for closed-loop stability under the LEMPC scheme based on the empirical model are derived. The LEMPC scheme is applied to a chemical process example to demonstrate its closed-loop stability and performance properties as well as significant computational advantage

Economic Model Predictive Control Using Data-Based Empirical Models

The increasingly competitive and continuously changing world economy has made it necessary to exploit the economic potential of chemical processes which has led engineers to economically optimize process operation to provide long-term economic growth. Approaches for increasing the profitability of industrial processes include directly incorporating process economic considerations into the system’s operation and control policy. A fairly recent control strategy, termed economic model predictive control (EMPC), is capable of coordinating dynamic economic plant optimization with a feedback control policy to allow real-time energy management. The key underlying assumption to design and apply an EMPC is that a rocess/system dynamic model is available to predict the future process state evolution. Constructing models of dynamical systems is done either through first-principles and/or from process input/output data. First-principle models attempt to account for the essential mechanisms behind the observed physico-chemical phenomena. However, arriving at a first-principles model may be a challenging task for complex and/or poorly understood processes in which system identification serves as a suitable alternative. Motivated by this, the first part of my doctoral research has focused on introducing novel economic model predictive controlschemes that are designed utilizing models obtained from advanced system identification methods. Various system identification schemes were investigated in the EMPC designs including linear modeling, multiple models, and on-line model identification. On-line model identification is used to obtain more accurate models when the linear empirical models are not capable of capturing the nonlinear dynamics as a result of significant plant disturbances and variations, actuator faults, or when it is desired to change the region of operation. An error-triggered on-line model identification approach is introduced where a moving horizon error detector is used to quantify prediction error and trigger model re-identification when necessary. The proposed EMPC schemes presented great economic benefit, precise predictions, and significant computational time reduction. These benefits indicate the effectiveness of the proposed EMPC schemes in practical industrial applications. The second part of the dissertation focuses on EMPC that utilizes well-conditioned polynomial nonlinear state-space (PNLSS) models for processes with nonlinear dynamics. A nonlinear system identification technique is introduced for a broad class of nonlinear processes which leads to the construction of polynomial nonlinear state-space dynamic models which are well-conditioned with respect to explicit numerical integration methods. This development allows using time steps that are significantly larger than the ones required by nonlinear state-space models identified via existing techniques. Finally, the dissertation concludes by investigating the use of EMPC in tracking a production schedule. Specifically, given that only a small subset of the total process state vector is typically required to track certain production schedules, a novel EMPC is introduced scheme that forces specific process states to meet the production schedule and varies the rest of the process states in a way that optimizes process economic performanc

Economic Model Predictive Control Using Data-Based Empirical Models

The increasingly competitive and continuously changing world economy has made it necessary to exploit the economic potential of chemical processes which has led engineers to economically optimize process operation to provide long-term economic growth. Approaches for increasing the profitability of industrial processes include directly incorporating process economic considerations into the system’s operation and control policy. A fairly recent control strategy, termed economic model predictive control (EMPC), is capable of coordinating dynamic economic plant optimization with a feedback control policy to allow real-time energy management. The key underlying assumption to design and apply an EMPC is that a rocess/system dynamic model is available to predict the future process state evolution. Constructing models of dynamical systems is done either through first-principles and/or from process input/output data. First-principle models attempt to account for the essential mechanisms behind the observed physico-chemical phenomena. However, arriving at a first-principles model may be a challenging task for complex and/or poorly understood processes in which system identification serves as a suitable alternative. Motivated by this, the first part of my doctoral research has focused on introducing novel economic model predictive controlschemes that are designed utilizing models obtained from advanced system identification methods. Various system identification schemes were investigated in the EMPC designs including linear modeling, multiple models, and on-line model identification. On-line model identification is used to obtain more accurate models when the linear empirical models are not capable of capturing the nonlinear dynamics as a result of significant plant disturbances and variations, actuator faults, or when it is desired to change the region of operation. An error-triggered on-line model identification approach is introduced where a moving horizon error detector is used to quantify prediction error and trigger model re-identification when necessary. The proposed EMPC schemes presented great economic benefit, precise predictions, and significant computational time reduction. These benefits indicate the effectiveness of the proposed EMPC schemes in practical industrial applications. The second part of the dissertation focuses on EMPC that utilizes well-conditioned polynomial nonlinear state-space (PNLSS) models for processes with nonlinear dynamics. A nonlinear system identification technique is introduced for a broad class of nonlinear processes which leads to the construction of polynomial nonlinear state-space dynamic models which are well-conditioned with respect to explicit numerical integration methods. This development allows using time steps that are significantly larger than the ones required by nonlinear state-space models identified via existing techniques. Finally, the dissertation concludes by investigating the use of EMPC in tracking a production schedule. Specifically, given that only a small subset of the total process state vector is typically required to track certain production schedules, a novel EMPC is introduced scheme that forces specific process states to meet the production schedule and varies the rest of the process states in a way that optimizes process economic performanc