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 research work proposes two robust empirical model-based predictive control algorithms for nonlinear processes. Chemical process are generally highly nonlinear thus predictive control algorithms that explicitly account for the nonlinearity of the process are expected to provide better closed-loop performance as compared to algorithms based on linear models. Two types of models can be considered for control: first-principles and empirical. Empirical models were chosen for the proposed algorithms for the following reasons: (i) they are less complex for on-line optimization, (ii) they are easy to identify from input-output data and (iii) their structure is suitable for the formulation of robustness tests. One of the key problems of every model that is used for prediction within a control strategy is that some model parameters cannot be known accurately due to measurement noise and/or error in the structure of the assumed model. In the robust control approach it is assumed that processes can be represented by models with parameters' values that are assumed to lie between a lower and upper bound or equivalently, that these parameters can be represented by a nominal value plus uncertainty. When this uncertainty in control parameters is not considered by the controller the control actions might be insufficient to effectively control the process and in some extreme cases the closed-loop may become unstable. Accordingly, the two robust control algorithms proposed in the current work explicitly account for the effect of uncertainty on stability and closed-loop performance. The first proposed controller is a robust gain-scheduling model predictive controller (MPC). In this case the process is represented within each operating region by a state-affine model obtained from input-output data. The state-affine model matrices are used to obtain a state-space based MPC for every operating region. By combining the state-affine, disturbance and controller equations a closed-loop representation was obtained. Then, the resulting mathematical representation was tested for robustness with linear matrix inequalities (LMI's) based on a test where the vertices of the parameter box were obtained by an iterative procedure. The result of the LMI's test gives a measure of performance referred to as γ that relates the effect of the disturbances on the process outputs. Finally, for the gain-scheduling part of the algorithm a set of rules was proposed to switch between the available controllers according to the current process conditions. Since every combination of the controller tuning parameters results in a different value of γ, an optimization problem was proposed to minimize γ with respect to the tuning parameters. Accordingly, for the proposed controller it was ensured that the effect of the disturbances on the output variables was kept to its minimum. A bioreactor case study was presented to show the benefits of the proposed algorithm. For comparison purposes a non-robust linear MPC was also designed. The results show that the proposed algorithm has a clear advantage in terms of performance as compared to non-robust linear MPC techniques. The second controller proposed in this work is a robust nonlinear model predictive controller (NMPC) based on an empirical Volterra series model. The benefit of using a Volterra series model for this case is that its structure can be split in two sections that account for the nominal and uncertain parameter values. Similar to the previously proposed gain-scheduled controller the model parameters were obtained from input-output data. After identifying the Volterra model, an interconnection matrix and its corresponding uncertainty description were found. The interconnection matrix relates the process inputs and outputs and is built according to the type of cost function that the controller uses. Based on the interconnection representing the system a robustness test was proposed based on a structured singular value norm calculation (SSV). The test is based on a min-max formulation where the worst possible closed-loop error is minimized with respect to the manipulated variables. Additional factors that were considered in the cost function were: manipulated variables weighting, manipulated variables restrictions and a terminal condition. To show the benefits of this controller two case studies were considered, a single-input-single-output (SISO) and a multiple-input-multiple-output (MIMO) process. Both case studies show that the proposed controller is able to control the process. The results showed that the controller could efficiently track set-points in the presence of disturbances while complying with the saturation limits imposed on the manipulated variables. This controller was also compared against a non-robust linear MPC, non-robust NMPC and non-robust first-principles NMPC. These comparisons were performed for different levels of uncertainty and for different values of the suppression or control actions weights. It was shown through these comparisons that a tradeoff exists between nominal performance and robustness to model error. Thus, for larger weights the controller is less aggressive resulting in more sluggish performance but less sensitivity to model error thus resulting in smaller differences between the robust and non-robust schemes. On the other hand when these weights are smaller the controller is more aggressive resulting in better performance at the nominal operating conditions but also leading to larger sensitivity to model error when the system is operated away from nominal conditions. In this case, as a result of this increased sensitivity to model error, the robust controller is found to be significantly better than the non-robust one.

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.

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.

Thesis (M.S.)--University of Missouri--Rolla, 2007. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed March 27, 2008) Includes bibliographical references (p. 86-89).

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (M.App.Sc.) - Carleton University, 2006. / Includes bibliographical references (p. 83-89). Also available in electronic format on the Internet.

Thesis (M.S.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.