Reducing variation in key product features is a very important goal in process improvement. Finding and trying to control the cause(s) of variation is one way to reduce variability, but is not cost effective or even possible in some situations. In such cases, Robust Parameter Design (RPD) is an alternative. The goal in RPD is to reduce variation by reducing the sensitivity of the process to the sources of variation, rather than controlling these sources directly. That is, the goal is to find levels of the control inputs that minimize the output variation imposed on the process via the noise variables (causes). In the literature, a variety of experimental plans have been proposed for RPD, including Robustness, Desensitization and Taguchi’s method. In this thesis, the efficiency of the alternative plans is compared in the situation where the most important source of variation, called the “Dominant Cause”, is known. It is shown that desensitization is the most appropriate approach for applying the RPD method to an existing process.

Metric spaces, which generalise the properties of commonly-encountered physical and abstract spaces into a mathematical framework, frequently occur in computer science applications. Three major kinds of questions about metric spaces are considered here: the intrinsic dimensionality of a distribution, the maximum number of distance permutations, and the difficulty of reverse similarity search. Intrinsic dimensionality measures the tendency for points to be equidistant, which is diagnostic of high-dimensional spaces. Distance permutations describe the order in which a set of fixed sites appears while moving away from a chosen point; the number of distinct permutations determines the amount of storage space required by some kinds of indexing data structure. Reverse similarity search problems are constraint satisfaction problems derived from distance-based index structures. Their difficulty reveals details of the structure of the space. Theoretical and experimental results are given for these three questions in a wide range of metric spaces, with commentary on the consequences for computer science applications and additional related results where appropriate.

The problem of detecting monotonic increasing/decreasing trends in variances from k samples is widely met in many applications, e.g. financial data analysis, medical and environmental studies. However, most of the tests for equality of variances against ordered alternatives rely on the assumption of normality. Such tests are often non-robust to departures from normality, which eventually leads to unreliable conclusions. In this thesis, we propose a combination of a robust Levene-type test and a finite-intersection method, which relaxes the assumption of normality. The new combined procedure yields a more accurate estimate of sizes of the test and provides competitive powers. In addition, we discuss various modifications of the proposed test for unbalanced design cases. We present theoretical justifications of the new test and illustrate its applications by simulations and case studies.

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.

Existing microactuator limitations prevent control of small-scale, spin-stabilized vehicles. These applications require actuators insensitive to shock that have forces on the order of Newtons and millisecond control periods. This research presents batch-fabrication lamination approaches for the realization of large arrays of high-impulse, short-duration gas generator actuators (GGAs), and system implementation approaches to integrate these GGAs into a small-scale, spin-stabilized projectile for the purpose of generating steering forces on the projectile. Electronic packaging and MEMS processing are combined to batch-fabricate millimeter-scale GGAs insensitive to large shocks. Robust, prefabricated thermoplastic and metal films are patterned by laser machining or photolithography, and multilayer devices are assembled by adhesive lamination. The GGAs remained operational after 10,000 g shocks. Optimized design and propellant selection enables control of the force profile and actuation timing. Rapid force rise times are achieved using appropriately selected solid propellants and specially designed hot-wire igniters that create a larger combustion fronts. By reshaping the combustion profile of the solid propellant, tens of Newtons are generated within milliseconds. In addition to force control, the timing of the force application was controllable to within 1 ms for optimized GGAs. Performance results demonstrate that GGA actuator arrays actuate within appropriate timescales and with enough authority to control a 40 mm projectile with a spin rate of 60 Hz. After actuator characterization, GGAs, control electronics, and power supply are mounted into a 40 mm diameter projectile, and a full flight system was flown to demonstrate divert authority of the GGAs.

This research focuses on developing comprehensive frameworks for developing robust parameter design methodology for dynamic systems with automatic control and for synthesis of nanostructures. In many automatically controlled dynamic processes, the optimal feedback control law depends on the parameter design solution and vice versa and therefore an integrated approach is necessary. A parameter design methodology in the presence of feedback control is developed for processes of long duration under the assumption that experimental noise factors are uncorrelated over time. Systems that follow a pure-gain dynamic model are considered and the best proportional-integral and minimum mean squared error control strategies are developed by using robust parameter design. The proposed method is illustrated using a simulated example and a case study in a urea packing plant. This idea is also extended to cases with on-line noise factors. The possibility of integrating feedforward control with a minimum mean squared error feedback control scheme is explored. To meet the needs of large scale synthesis of nanostructures, it is critical to systematically find experimental conditions under which the desired nanostructures are synthesized reproducibly, at large quantity and with controlled morphology. The first part of the research in this area focuses on modeling and optimization of existing experimental data. Through a rigorous statistical analysis of experimental data, models linking the probabilities of obtaining specific morphologies to the process variables are developed. A new iterative algorithm for fitting a Multinomial GLM is proposed and used. The optimum process conditions, which maximize the above probabilities and make the synthesis process less sensitive to variations of process variables around set values, are derived from the fitted models using Monte-Carlo simulations. The second part of the research deals with development of an experimental design methodology, tailor-made to address the unique phenomena associated with nanostructure synthesis. A sequential space filling design called Sequential Minimum Energy Design (SMED) for exploring best process conditions for synthesis of nanowires. The SMED is a novel approach to generate sequential designs that are model independent, can quickly "carve out" regions with no observable nanostructure morphology, and allow for the exploration of complex response surfaces.

In this thesis we propose a robust PID controller to regulate the hydrogen flow of proton exchange membrane fuel cells. The controller allows the so-called hydrogen excess ratio to track a desired value rapidly in order to achieve saving hydrogen and to avoid damage of the fuel cell when the power output of the fuel cell varies from one level to another. The fuel cell system is governed by a set of complicated nonlinear dynamical equations. To ease the control design task, we model the system, at each operating point, as a feedback interconnection of a linear time-invariant nominal part with a norm-bounded perturbation. We use the technique of system identification to acquire the transfer function representation of the nominal part and the size of the perturbation. To do this, the chirp signal is adopted to excite the system and the observed response is analyzed using spectral analysis to obtain the model. Based on the model, a $H_{infty}$ PID controller is designed for the fuel cell system. The design is tested on an experimental platform. The experimental results verify that the proposed controller can regulate the hydrogen excess ratio rapidly under load variation, and effectively reject the influence of external disturbances.

In this paper, we explore a cooperative code-division-multiple-access(CDMA) network. Users cooperate by forwarding each other¡¦s messages toward the destination. For simplicity, we assume that signal reception at the destination is well-synchronized. Due to practical design issues of CDMA systems, spreading waveforms allocated to users are not perfectly orthogonal in general. This results in multiple-access interference(MAI) at relays and destination. In CDMA uplink networks one common approach is to adopt decorrelating multi-user detection, but it will lead to noise amplification[16,17]. Therefore, we employ relay-assisted decorrelating multiuser detector(RAD-MUD) to mitigate MAI[1] by performing half of decorrelation at the relay and destination respectively. Based on the availability of CSI at relays, we can further adopt cooperative strategies to improve performance, e.g., transmit beamforming and selective relaying. The destination side will use minimum mean-square error(MMSE) detector to demodulate source symbols. In the existing literatures, channel state information(CSI) is assumed to be perfectly known at relay and destination. Actually, CSI is obtained from channel estimation, which usually contains estimation errors. In order to alleviate effects of channel estimation, one goal of this thesis is to design a robust system. Using estimated CSI and statistical property channel estimation errors, we design robust precoder and detector for the relay and destination. It shows that, even with distortion on channel estimations, the system still achieve excellent transmission efficiency. From the simulation results, it shows that the robust design is better than the system without consider channel estimation errors. Finally, we can see that the stable robust design can effectively mitigate effects of imperfect CSI.

Smart devices with multiple on-board sensors, networked through wired or wireless links, are distributed in physical systems and environments. Broad applications of such sensor networks include manufacturing quality control and wireless sensor systems. In the operation of sensor systems, robust methods for retrieving reliable information from sensor systems are crucial in the presence of potential sensor failures. Existence of sensor redundancy is one of the main drivers for the robustness or fault tolerance capability of a sensor system. The redundancy degree of sensors plays two important roles pertaining to the robustness of a sensor network. First, the redundancy degree provides proper parameter values for robust estimator; second, we can calculate the fault tolerance capability of a sensor network from the redundancy degree. Given this importance of the redundancy degree, this dissertation presents efficient algorithms based on matroid theory to compute the redundancy degree of a clustered sensor network. In the efficient algorithms, a cluster pattern of a sensor network allows us to decompose a large sensor network into smaller sub-systems, from which the redundancy degree can be found more efficiently. Finally, the robustness analysis as well as its algorithm procedure is illustrated using examples of a multi-station assembly process and calibration of wireless sensor networks.