This work focuses on the robustness issues related to distributed model predictive control (DMPC) strategies in the presence of model uncertainty. The robustness of DMPC with respect to model uncertainty has been identified by researchers as a key factor in the successful application of DMPC. A first task towards the formulation of robust DMPC strategy was to propose a new systematic methodology for the selection of a control structure in the context of DMPC. The methodology is based on the trade-off between performance and simplicity of structure (e.g., a centralized versus decentralized structure) and is formulated as a multi-objective mixed-integer nonlinear program (MINLP). The multi-objective function is composed of the contribution of two indices: 1) closed-loop performance index computed as an upper bound on the variability of the closed-loop system due to the effect on the output error of either set-point or disturbance input, and 2) a connectivity index used as a measure of the simplicity of the control structure. The parametric uncertainty in the models of the process is also considered in the methodology and it is described by a polytopic representation whereby the actual process’s states are assumed to evolve within a polytope whose vertices are defined by linear models that can be obtained from either linearizing a nonlinear model or from their identification in the neighborhood of different operating conditions. The system’s closed-loop performance and stability are formulated as Linear Matrix Inequalities (LMI) problems so that efficient interior-point methods can be exploited. To solve the MINLP a multi-start approach is adopted in which many starting points are generated in an attempt to obtain global optima. The efficiency of the proposed methodology is shown through its application to benchmark simulation examples. The simulation results are consistent with the conclusions obtained from the analysis. The proposed methodology can be applied at the design stage to select the best control configuration in the presence of model errors. A second goal accomplished in this research was the development of a novel online algorithm for robust DMPC that explicitly accounts for parametric uncertainty in the model. This algorithm requires the decomposition of the entire system’s model into N subsystems and the solution of N convex corresponding optimization problems in parallel. The objective of this parallel optimizations is to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Model uncertainty is explicitly considered through the use of polytopic description of the model. The algorithm employs an LMI approach, in which the solutions are convex and obtained in polynomial time. An observer is designed and embedded within each controller to perform state estimations and the stability of the observer integrated with the controller is tested online via LMI conditions. An iterative design method is also proposed for computing the observer gain. This algorithm has many practical advantages, the first of which is the fact that it can be implemented in real-time control applications and thus has the benefit of enabling the use of a decentralized structure while maintaining overall stability and improving the performance of the system. It has been shown that the proposed algorithm can achieve the theoretical performance of centralized control. Furthermore, the proposed algorithm can be formulated using a variety of objectives, such as Nash equilibrium, involving interacting processing units with local objective functions or fully decentralized control in the case of communication failure. Such cases are commonly encountered in the process industry. Simulations examples are considered to illustrate the application of the proposed method. Finally, a third goal was the formulation of a new algorithm to improve the online computational efficiency of DMPC algorithms. The closed-loop dual-mode paradigm was employed in order to perform most of the heavy computations offline using convex optimization to enlarge invariant sets thus rendering the iterative online solution more efficient. The solution requires the satisfaction of only relatively simple constraints and the solution of problems each involving a small number of decision variables. The algorithm requires solving N convex LMI problems in parallel when cooperative scheme is implemented. The option of using Nash scheme formulation is also available for this algorithm. A relaxation method was incorporated with the algorithm to satisfy initial feasibility by introducing slack variables that converge to zero quickly after a small number of early iterations. Simulation case studies have illustrated the applicability of this approach and have demonstrated that significant improvement can be achieved with respect to computation times. Extensions of the current work in the future should address issues of communication loss, delays and actuator failure and their impact on the robustness of DMPC algorithms. In addition, integration of the proposed DMPC algorithms with other layers in automation hierarchy can be an interesting topic for future work.

Because of several advantages, e.g. compact structure, high air-gap flux density, and high torque capability, the PM synchronous motor plays an important role in recent years. The basic principle of controlling a PMSM is based on vector control. The control performance is influenced by factors as the plant parameter variations, the external load disturbances, and the unmodeled or nonlinear dynamics. In the thesis, we apply a recently proposed robust 2DOF configuration to designing controllers for PMSM to achieve the robust asymptotical tracking under perturbations in both the motor and the controllers. Two design methods are adopted to implement the desired controllers, i.e. the linear algebraic method and the design method. The effect of the well-known internal model principle is addressed in the former design method. The merit of the latter design method is that both time and frequency domain design specifications can be easily included in the design procedure. Computer simulation results are displayed to illustrate the advantages of our designs.

This thesis mainly proposes a new method to design Hinf Loop Shaping Robust Controller by choosing Weighting Function. In the paper, the author first introduces the concept of SISO Loop Shaping design. It utilizes Small Gain Theorem to achieve robust stability of the system and develops the relationship of Open Loop Transfer Function(L) to Robust Performance and to Robust Stability of the system.. These concepts can be extended to Hinf Loop Shaping method. As to Hinf loop shaping method, the author first introduces the problem of Robust Stability under the framework of Coprime Factor and the theory of Hinf Loop Shaping, and then discusses the relationship between stability margin and the different pole-zero system. Generally speaking, the control theories of the Loop Shaping are mainly used for making appropriate adjustments between the stability and performance of the system. Because the system can conform to the performance requirement through the choice of Weighting Function, the author proposes a new method toward MIMO system to design Hinf Loop Shaping Controller by choosing Weighting Function under the framework of Hinf Loop Shaping. Moreover, at the end of the paper,the author compares the result of the new method with that of the literature.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 196-200). Also available on the Internet.

Thesis (M.S. in Astronautical Engineering)--Naval Postgraduate School, December 2009. / Thesis Advisor(s): Agrawal, Brij; Kim, Jae Jun. "December 2009." Description based on title screen as viewed on January 27, 2010. Author(s) subject terms: MIMO control, Robust control, adaptive optics, segmented mirrors, flexible structures, space telescopes, Shack-Hartmann sensors, hybrid controller. Includes bibliographical references (p. 77). Also available in print.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 196-200). Also available on the Internet.

Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Jeff Shamma; Committee Member: Eric Feron; Committee Member: Magnus Egerstedt. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Maneuvering through 3D structures nimbly is pivotal to the advancement of legged locomotion. However, few methods have been developed that can generate 3D gaits in those terrains and fewer if none can be generalized to control dynamic maneuvers. In this thesis, foot placement planning for dynamic locomotion traversing irregular terrains is explored in three dimensional space. Given boundary values of the center of mass' apexes during the gait, sagittal and lateral Phase Plane trajectories are predicted based on multi-contact and inverted pendulum dynamics. To deal with the nonlinear dynamics of the contact motions and their dimensionality, we plan a geometric surface of motion beforehand and rely on numerical integration to solve the models. In particular, we combine multi-contact and prismatic inverted pendulum models to resolve feet transitions between steps, allowing to produce trajectory patterns similar to those observed in human locomotion. Our contributions lay in the following points: (1) the introduction of non planar surfaces to characterize the center of mass' geometric behavior; (2) an automatic gait planner that simultaneously resolves sagittal and lateral feet placements; (3) the introduction of multi-contact dynamics to smoothly transition between steps in the rough terrains. Data driven methods are powerful approaches in absence of accurate models. These methods rely on experimental data for trajectory regression and prediction. Here, we use regression tools to plan dynamic locomotion in the Phase Space of the robot's center of mass and we develop nonlinear controllers to accomplish the desired plans with accuracy and robustness. In real robotic systems, sensor noise, simplified models and external disturbances contribute to dramatic deviations of the actual closed loop dynamics with respect to the desired ones. Moreover, coming up with dynamic locomotion plans for bipedal robots and in all terrains is an unsolved problem. To tackle these challenges we propose here two robust mechanisms: support vector regression for data driven model fitting and contact planning, and trajectory based sliding mode control for accuracy and robustness. First, support vector regression is utilized to learn the data set obtained through numerical simulations, providing an analytical solution to the nonlinear locomotion dynamics. To approximate typical Phase Plane behaviors that contain infinite slopes and loops, we propose to use implicit fitting functions for the regression. Compared to mainstream explicit fitting methods, our regression method has several key advantages: 1) it models high dimensional Phase Space states by a single unified implicit function; 2) it avoids trajectory over-fitting; 3) it guarantees robustness to noisy data. Finally, based on our regression models, we develop contact switching plans and robust controllers that guarantee convergence to the desired trajectories. Overall, our methods are more robust and capable of learning complex trajectories than traditional regression methods and can be easily utilized to develop trajectory based robust controllers for locomotion. Various case studies are analyzed to validate the effectiveness of our methods including single and multi step planning in a numerical simulation and swing foot trajectory control on our Hume bipedal robot. / text

This work focuses on the robustness issues related to distributed model predictive control (DMPC) strategies in the presence of model uncertainty. The robustness of DMPC with respect to model uncertainty has been identified by researchers as a key factor in the successful application of DMPC. A first task towards the formulation of robust DMPC strategy was to propose a new systematic methodology for the selection of a control structure in the context of DMPC. The methodology is based on the trade-off between performance and simplicity of structure (e.g., a centralized versus decentralized structure) and is formulated as a multi-objective mixed-integer nonlinear program (MINLP). The multi-objective function is composed of the contribution of two indices: 1) closed-loop performance index computed as an upper bound on the variability of the closed-loop system due to the effect on the output error of either set-point or disturbance input, and 2) a connectivity index used as a measure of the simplicity of the control structure. The parametric uncertainty in the models of the process is also considered in the methodology and it is described by a polytopic representation whereby the actual process’s states are assumed to evolve within a polytope whose vertices are defined by linear models that can be obtained from either linearizing a nonlinear model or from their identification in the neighborhood of different operating conditions. The system’s closed-loop performance and stability are formulated as Linear Matrix Inequalities (LMI) problems so that efficient interior-point methods can be exploited. To solve the MINLP a multi-start approach is adopted in which many starting points are generated in an attempt to obtain global optima. The efficiency of the proposed methodology is shown through its application to benchmark simulation examples. The simulation results are consistent with the conclusions obtained from the analysis. The proposed methodology can be applied at the design stage to select the best control configuration in the presence of model errors. A second goal accomplished in this research was the development of a novel online algorithm for robust DMPC that explicitly accounts for parametric uncertainty in the model. This algorithm requires the decomposition of the entire system’s model into N subsystems and the solution of N convex corresponding optimization problems in parallel. The objective of this parallel optimizations is to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Model uncertainty is explicitly considered through the use of polytopic description of the model. The algorithm employs an LMI approach, in which the solutions are convex and obtained in polynomial time. An observer is designed and embedded within each controller to perform state estimations and the stability of the observer integrated with the controller is tested online via LMI conditions. An iterative design method is also proposed for computing the observer gain. This algorithm has many practical advantages, the first of which is the fact that it can be implemented in real-time control applications and thus has the benefit of enabling the use of a decentralized structure while maintaining overall stability and improving the performance of the system. It has been shown that the proposed algorithm can achieve the theoretical performance of centralized control. Furthermore, the proposed algorithm can be formulated using a variety of objectives, such as Nash equilibrium, involving interacting processing units with local objective functions or fully decentralized control in the case of communication failure. Such cases are commonly encountered in the process industry. Simulations examples are considered to illustrate the application of the proposed method. Finally, a third goal was the formulation of a new algorithm to improve the online computational efficiency of DMPC algorithms. The closed-loop dual-mode paradigm was employed in order to perform most of the heavy computations offline using convex optimization to enlarge invariant sets thus rendering the iterative online solution more efficient. The solution requires the satisfaction of only relatively simple constraints and the solution of problems each involving a small number of decision variables. The algorithm requires solving N convex LMI problems in parallel when cooperative scheme is implemented. The option of using Nash scheme formulation is also available for this algorithm. A relaxation method was incorporated with the algorithm to satisfy initial feasibility by introducing slack variables that converge to zero quickly after a small number of early iterations. Simulation case studies have illustrated the applicability of this approach and have demonstrated that significant improvement can be achieved with respect to computation times. Extensions of the current work in the future should address issues of communication loss, delays and actuator failure and their impact on the robustness of DMPC algorithms. In addition, integration of the proposed DMPC algorithms with other layers in automation hierarchy can be an interesting topic for future work.

This dissertation proposes a power management and control strategy for islanded microgrids, which consist of multiple electronically-interfaced distributed energy resource (DER) units, to achieve a prescribed load sharing scheme. This strategy provides i) a power management system to specify voltage set points based on a classical power flow analysis; 2) DER local controllers, designed based on a robust, decentralized, servomechanism approach, to track the set points; and 3) a frequency control and synchronization scheme. This strategy is then generalized to incorporate both power-controlled and voltage-controlled DER units. Since the voltage-controlled DER units do not use inner current control loops, they are vulnerable to overcurrent/overload transients subsequent to system severe disturbances, e.g., faults and overloading conditions. To prevent DER unit trip-out or damage under these conditions, an overcurrent/overload protection scheme is proposed that detects microgrid abnormal conditions, modifies the terminal voltage of the corresponding VSC to limit DER unit output current/power within the permissible range, and restores voltage controllers subsequently. Under certain circumstances, e.g., microgrid islanding and communication failure, there is a need to switch from an active to a latent microgrid controller. To minimize the resultant transients, control transition should be performed smoothly. For the aforementioned two circumstances, two smooth control transition techniques, based on 1) an observer and 2) an auxiliary tracking controller, are proposed to achieve a smooth control transition. A typical microgrid system that adopts the proposed strategy is investigated. The microgrid dynamics are investigated based on eigenvalue sensitivity and robust analysis studies to evaluate the performance of the closed-loop linearized microgrid. Extensive case studies, based on time-domain simulations in the PSCAD/EMTDC platform, are performed to evaluate performance of the proposed controllers when the microgrid is subject to various disturbances, e.g., load change, DER abrupt outage, configuration change, faults, and overloading conditions. Real-time hardware-in-the-loop case studies, using an RTDS system and NI-cRIO industrial controllers, are also conducted to demonstrate ease of hardware implementation, validate controller performance, and demonstrate its insensitivity to hardware implementation issues, e.g., noise, PWM nonidealities, A/D and D/A conversion errors and delays.