Exploiting high altitude wind energy using power kites is an emerging topic in the field of renewable energy. The claimed advantages of power kites over traditional wind power technologies are the lower construction costs, less land occupation and more importantly, the possibility of efficiently harvesting wind energy at high altitudes, where more dense and steady wind power exists. One of the most challenging issues to bring the power kite concept to real industrialization is the controller design. While traditional wind turbines can be inherently stabilized, the airborne nature of kites causes a strong instability of the systems. This thesis aims to develop a novel economic model predictive path-following control (EMPFC) framework to tackle the path-following control of power kites, as well as provide insightful stability analysis of the proposed control scheme. Chapter 3 is focused on the stability analysis of EMPFC. We proceed with a sampled-data EMPC scheme for set-point stabilization problems. An extended definition of dissipativity is introduced for continuous-time systems, followed by giving sufficient stability conditions. Then, the EMPFC scheme for output path-following problems is proposed. Sufficient conditions that guarantee the convergence of the system to the optimal operation on the reference path are derived. Finally, an example of a 2-DoF robot is given. The simulation results show that under the proposed EMPFC scheme, the robot can follow along the reference path in forward direction with enhanced economic performance, and finally converges to its optimal steady state. In Chapter 4, the proposed EMPFC scheme is applied to a challenging nonlinear kite model. By introducing additional degrees of freedom in the zero-error manifold (i.e., the space where the output error is zero), a relaxation of the optimal operation is achieved. The effectiveness of the proposed control scheme is shown in two aspects. For a static reference path, the generated power is increased while the kite is stabilized in the neighborhood of the reference path. For a dynamic reference path, the economic performance can be further enhanced since parameters for the reference path are treated as additional optimization variables. The proposed EMPFC achieves the integration of path optimization and path-following, resulting in a better economic performance for the closed-loop system. Simulation results are given to show the effectiveness of the proposed control scheme. Finally, Chapter 5 concludes the thesis and future research topics are discussed. / Graduate / 2020-05-14

Process economic improvement subject to safety, operational and environmental constraints is an ultimate goal of using on-line process optimization and control techniques. The dynamic nature of present-day market conditions motivates the consideration of process dynamics within the economic optimization calculation. Two key paradigms for implementing real-time dynamic economic optimization are a dynamic real-time optimization (DRTO) and regulatory MPC two-layer architecture, and a single-level economic model predictive control (EMPC) con figuration. In the two-layer architecture, the economically optimal set-point trajectories computed in an upper DRTO layer are provided to the MPC layer, while in the single-layer EMPC con figuration the economics are incorporated within the MPC objective function. There are limited studies on a systematic performance comparison between these two approaches. Furthermore, these studies do not simultaneously consider the economic, disturbance rejection and computational performance criteria. Thus, it may not be clear under what conditions one particular method is preferable over the other. These reasons motivate a more comprehensive comparison between the two paradigms, with both open and closed-loop predictions considered in the DRTO calculations. In order to conduct this comparison, we utilize two process case studies for the economic analysis and performance comparison of on-line optimization systems. The first case study is a process involving two stirred-tank reactors in-series with an intermediate mixing point, and the second case study is a linear multi-input single-output (MISO) system. These processes are represented using a fi rst principles model in the form of differential-algebraic equations (DAEs) system for the first case study and a simplified linear model of a polymerization reactor for the second case study problem. Both of the case study processes include constraints associated with input variables, safety considerations, and output quality. In these case study problems, the objective of optimal process operation is net profit improvement. The following performance evaluation criteria are considered in this study: (I) optimal value of the economic objective function, (II) average run time (ART) over a same operating time interval, (III) cumulative output constraint violation (COCV) for each constraint. The update time of the single-layer approach is selected to be equal to that of the control layer in the two-layer formulations, while the update time of the economic layer in the two-layer formulation is bigger than that of the single-layer approach. The nonlinear programing (NLP) problems which result in the single-layer and two-layer formulations and the quadratic programing problem which corresponds to the MPC formulation are solved using the fmincon and quadprog optimization solvers in MATLAB. Performance assessment of the single-layer and two-layer formulations is evaluated in the presence of a variety of unknown disturbance scenarios for the first case study problem. The effect of a dynamic transition in the product quality is considered in the performance comparison of the single-layer and two-layer methods in the second case-study problem. The first case study problem results show that for all unknown disturbance scenarios, the economic performance of the single-layer approach is slightly higher than that of the two layer formulations. However, the average computation times for the DRTO-MPC two-layer formulations are at least one order of magnitude lower than that of the EMPC formulation. Also, comparison results of the COCV for the EMPC formulation for different sizes of update time intervals could justify the necessity of the MPC control layer to reduce the COCV for the economic optimization problems with update times larger than that of the MPC control layer. A similar computational advantage of the OL- and CL-DRTO-MPC over the EMPC is observed for the second case study problem. In particular, it is shown that increasing the economic horizon length in the EMPC formulation to a sufficiently large value may result a higher economic improvement. However, the increase in economic optimization horizon would increase the resulting NLP problem size. The computational burden could limit the use of the EMPC formulation with larger economic optimization horizons in real-time applications. The ART of the dual-layer methods is at least two orders of magnitude lower than that of the EMPC methods with an appropriate horizon length. The CL-DRTO-MPC economic performance is slightly less than that of the EMPC formulation with the same economic optimization horizon. In conclusion, the performance comparison on the basis of multiple criteria in this study demonstrates that the economic performance criterion is not necessarily the only important metric, and the operational constraint limitations and the optimization problem solution time could have an important impact on the selection of the most suitable real-time optimization approach. / Thesis / Master of Applied Science (MASc)

In this thesis I propose methods and strategies for the design of advanced model predictive control designs. The contributions are in the areas of data-driven model based MPC, model monitoring and explicit incorporation of closed-loop response considerations in the MPC, while handling issues such as plant-model mismatch, constraints and uncertainty. In the initial phase of this research, I address the problem of handling plant-model mismatch by designing a subspace identification based MPC framework that includes model monitoring and closed-loop identification components. In contrast to performance monitoring based approaches, the validity of the underlying model is monitored by proposing two indexes that compare model predictions with measured past output. In the event that the model monitoring threshold is breached, a new model is identified using an adapted closed-loop subspace identification method. To retain the knowledge of the nominal system dynamics, the proposed approach uses the past training data and current input, output and set-point as the training data for re-identification. A model validity mechanism then checks if the new model predictions are better than the existing model, and if they are, then the new model is utilized within the MPC. Next, the proposed MPC with re-identification method is extended to batch processes. To this end, I first utilize a subspace-based model identification approach for batch processes to be used in model predictive control. A model performance index is developed for batch process, then in the case of poor prediction, re-identification is triggered to identify a new model. In order to emphasize on the recent batch data, the identification is developed in order to increase the contribution of the current data. In another direction, the stability of data driven predictive control is addressed. To this end, first, a data-driven Lyapunov-based MPC is designed, and shown to be capable of stabilizing a system at an unstable equilibrium point. The data driven Lyapunov-based MPC utilizes a linear time invariant (LTI) model cognizant of the fact that the training data, owing to the unstable nature of the equilibrium point, has to be obtained from closed-loop operation or experiments. Simulation results are first presented demonstrating closed-loop stability under the proposed data-driven Lyapunov-based MPC. The underlying data-driven model is then utilized as the basis to design an economic MPC. Finally, I address the problem of control of nonlinear systems to deliver a prescribed closed-loop behavior. In particular, the framework allows for the practitioner to first specify the nature and specifics of the desired closed-loop behavior (e.g., first order with smallest time constant, second order with no more than a certain percentage overshoot, etc.). An optimization based formulation then computes the control action to deliver the best attainable closed loop behavior. To decouple the problems of determining the best attainable behavior and tracking it as closely as possible, the optimization problem is posed and solved in two tiers. In the first tier, the focus is on determining the best closed-loop behavior attainable, subject to stability and tracking constraints. In the second tier, the inputs are tweaked to possibly improve the tracking of the optimal output trajectories given by the first tier. The effectiveness of all of the proposed methods are illustrated through simulations on nonlinear systems. / Dissertation / Doctor of Philosophy (PhD)