Continuous crystallizers are distributed dynamical systems. Physical modeling of these systems using basic principles results in partial and integro-differential equations. To exploit the physical models, in the analysis of the system behavior and the design of an appropriate controller, requires complicated measurement techniques especially in the spatial domain (crystal size distribution or crystal population density). Therefore, obtaining a lumped model structure is desirable. The lumped model of a continuous crystallizer can be obtained either from the physical model, using conventional techniques such as the discretization or function separation methods, or from input and output measurements using system identification approaches. Studies of the crystallization process have indicated that in order to improve the control performance, expressing the process dynamics using single-input, single-output models is insufficient. The aim of this thesis was to investigate the process behavior in a multivariable framework. In this regard, the dynamics of a continuous cooling KCl crystallizer were identified using three-input, three-output linear and nonlinear model structures. The autoregressive exogenous model structures were employed in linear modeling of the process. The nonlinear modeling was performed using several architectures of feedforward and recurrent neural networks. Simulation results demonstrated that the linear modeling, using a single model for the entire dynamics, is not adequate. Either multi-model or nonlinear modeling is recommended. The performance of different neural network structures in the nonlinear modeling of the process was illustrated and, based on the results, some comparisons were made between these networks. The next step in the study of the crystallization process as a multivariable system was to design and apply a multivariable control scheme. Simulation results from the modeling of the process indicated that strong interactions are present among different loops of the system. The process is nonlinear and some of the outputs exhibit inverse or non-minimum-phase responses. The model predictive control strategy is known to perform well in the control of the systems with the behaviors found in the crystallization process. To ensure a feasible solution, the feasible sequential quadratic optimization algorithm was successfully exploited in a model predictive controller. Computer simulations of the controller were performed in order to demonstrate control of the crystal size distribution, crystal purity, and production rate. The effects of different control parameters were illustrated using the simulation results. A brief discussion on how to select these parameters was also provided. Robustness of the model predictive controller was studied in the presence of mismatch between the model and the process.

Current robot manipulation and control paradigms have largely been developed for static or highly structured environments such as those common in factories. For most techniques in robot trajectory generation, such as heuristic-based geometric planning, this has led to putting a high cost on contact with the world. This approach and methodology can be prohibitive to robots operating in many unmodeled and dynamic environments. This dissertation presents work on using haptic based feedback (torque and tactile sensing) to formulate a controller for robot manipulation in clutter. We define “clutter” as any environment in which we expect the robot to make both incidental and purposeful contact while maneuvering and manipulating. The controllers developed in this dissertation take the form of single or multi-time step Model Predictive Control (a form of optimal control which incorporates feedback) which attempts to regulate contact forces at multiple locations on a robot arm while reaching to a goal. The results and conclusions in this dissertation are based on extensive testing in simulation (tens of thousands of trials) and testing in realistic scenarios with real robots incorporating tactile sensing. The approach is novel in the sense that it allows contact and explicitly incorporate the contact and predictive model of the robot arm in calculating control effort at every time step. The expected broader impact of this research is progress towards a new foundation of reactive feedback controllers that will include a higher likelihood of success in many constrained and dynamic scenarios such as reaching into containers without line of sight, maneuvering in cluttered search and rescue situations or working with unpredictable human co-workers.

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.

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This thesis presents a data-driven approach to constrained control in the form of a subspace-based state-space system identification algorithm integrated into a model predictive controller. Generally this approach has been termed model-free predictive control in the literature. Previous research into this area focused on the system identification aspects resulting in an omission of many of the features that would make such a control strategy attractive to industry. These features include constraint handling, zero-offset setpoint tracking and non-stationary disturbance rejection. The link between non-stationary disturbance rejection in subspace-based state-space system identification and integral action in state-space based model predictive control was shown. Parameterization with Laguerre orthonormal functions was proposed for the reduction in computational load of the controller. Simulation studies were performed using three real-world systems demonstrating: identification capabilities in the presence of white noise and non-stationary disturbances; unconstrained and constrained control; and the benefits and costs of parameterization with Laguerre polynomials.

Thèse (D.Eng.) -- Université du Québec à Chicoutimi, 2007. / La p. de t. porte en outre: Thèse présentée à l'Université du Québec à Chicoutimi comme exigence partielle du doctorat en ingénierie. Bibliogr.: f. 169-181. Document électronique également accessible en format PDF. CaQQUQ

Thesis (M. S.)--Aerospace Engineering, Georgia Institute of Technology, 2005. / Bottasso, Carlo, Committee Chair ; Hodges, Dewey, Committee Member ; Bauchau, Olivier, Committee Member. Includes bibliographical references.

Thesis (Ph. D.)--West Virginia University, 2004. / Title from document title page. Document formatted into pages; contains viii, 104 p. : ill., map. Includes abstract. Includes bibliographical references (p. 101-108).