This article describes a pressure generation technique that has been applied to the task of calibrating hydraulic pressure transducers. The technique combines principles given by the Lorentz Force and Faraday's Law of Induction to generate a hydrostatic pressure within a cavity. The time history of this pressure is given by the device without reliance on a reference transducer or knowledge of: the local gravity; thermodynamic properties of the working fluid; or acceleration of the cavity. In this way, the Pascal can be defined by reference only to the standards of the Amp, the Volt, the Meter, and -- in the case of time varying pressure -- the Second. Using this technique, a prototype device has been developed using commonly available tooling and can generate pressures in the range of 0.1 to 600 Pa with relative errors of 1.5%. / Master of Science

This dissertation addresses the design of controllers for multi variable finite-dimensional, linear, autonomous dynamical systems with distinct sets of slow and fast dynamics, which thus display multiple time scale behavior. It seeks, specifically, to compose overall controllers from lower-order dynamic output compensators, which are designed separately for slow and fast approximating models of the given plant. Reduction of the dynamic order of the design problem and the avoidance of numerically ill-conditioned interaction between modes of disparate orders of magnitude are among the patent advantages which pertain to such a design. As is well known, the explicit singularly perturbed systems, as a class, possess the multiple time scale property, while the broader class of implicit singularly perturbed systems and the multiple time scale systems are partially overlapping system classes. A composite state feedback controller scheme for the explicit singularly perturbed system has long been known. In connection with dynamic output controllers, however, only the case of the explicit singularly perturbed system with, restrictively, open-loop-stable fast dynamics has so far received attention in the literature. The dissertation, in providing a composite dynamic controller design suitable as well to the implicit singularly perturbed multiple time scale system, which furthermore is permitted to exhibit fast (or "parasitic") as well as slow (or "normal") open-loop instabilities, thus presents a more comprehensive dynamic controller strategy for this system than so far reported in the literature. Working with multivariable transfer functions, the dissertation applies certain fractional representation techniques of modem Algebraic System Theory to the frequency domain study of the multiple time scale system. Following the work of D. W. Luse and H. K. Khalil, we replace the transfer matrix of the multiple time scale system with two or more lower-order transfer functions, each of which has validity, in its own respective frequency range, as an approximation to the first. Following the work. of M. Vidyasagar, we write the rational transfer function of each of these approximating lower-order subsystems as a "fraction" over the Ring of proper and stable rational matrices. Parametrizations, in terms of "free" matrices belonging to this Ring, of the sets of stabilizing controllers for the lower-order subsystems :md the corresponding achievable stable closed-loop behaviors then enable the relevant design syntheses to be achieved. In this development we exploit, specifically, a Theorem proved by Luse and Khalil concerning the relation of the closed-loop poles in a feedback configuration of multiple time scale systems to the poles in corresponding lower-order closed-loop systems. The dissertation's novel contribution thus resides in (i) interpreting the Theorem of Luse and Khalil as the outline for a possible separate and-composite dynamic output controller strategy, and in (ii) adapting algebraic techniques derivative from Vidyasagar for actually realizing the putative strategy as a set of concretely implementable design procedures. Three specific design procedures are developed and formalized in the dissertation: the first for achieving mere stabilization of the multiple time scale system, the second for the placement of slow and fast poles within specified subregions of the Complex Plane, and the third for achieving entirely arbitrary pole placement. Since these procedures derive, methodologically, from Vidyasagar's fractional representations, they are intrinsically multivariable in character. Since the procedures are validated by the Theorem of Luse and Khalil, they are applicable, in principle, to the very broadest class of linear autonomous multiple time scale systems. The dissertation presents its three design procedures in high-Ievel-algorized form. For application to the explicit singularly perturbed system, the three procedures entail no further matrix operations than addition, multiplication, inversion and the determination of linear constant controller and observer gains, the most basic of operations in any available Control software. In connection with the implicitly singularly perturbed multiple time scale system, their concrete application requires some further computational development pertaining to the attainment of coprime factorizations of general rational matrices, a topic of independent active interest in the current literature on Control. Elsewhere in the literature, singularly perturbed discrete time, distributed, multidimensional, time-varying and nonlinear systems have been studied. Such systems have been studied, furthermore, in several contexts involving optimal and stochastic control, but nearly always from the time domain point of view. The dissertation tackles only the problems of robust stabilization and pole placement in the finite-dimensional, linear, autonomous case. Future work will attempt to extend its results on stabilization and pole-placement, appropriately, to some of the other general multiple time scale system classes. Further frequency domain investigations, related to the dissertation, may as well explore other problems pertaining to the multiple time scale systems which so far have received treatment only in the available time domain literature.

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System identification techniques were applied to obtain mathematical expressions relating column flotation operating parameters. The empirical data were derived by making individual step changes in tailings rate, wash water rate, feed rate, frother addition and air rates, while measuring the pulp level and air holdup responses. The dynamic behavior of the flotation column is also analyzed for the conditions at which the tests were performed. After converting these mathematical equations into continuous and discrete transfer function matrices, several control algorithms were simulated on this column flotation empirical representation. Suggestions are provided to deal with the complexities of the process when designing a control scheme. / Master of Science

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Coordination of multi-robot systems to improve communication and achieve flocking is the topic of this thesis. Methods are proposed for mobile autonomous robots to follow trajectories in a way that improves communications with a base station. Further, a decentralized algorithm is presented that yields flocking with obstacle avoidance. The communication-aware trajectory tracking is adapted to radio communication in indoor environments. Our experimental data show that the effect of multipath fading, well-known in the radio communication literature, causes significant variations in the signal strength between a mobile robot and a base station. A contribution of this thesis is to formulate a tradeoff between tracking a reference trajectory and maintaining communication, first for a stationary reference position and then for a general trajectory. For the general case, the robot and an onboard communication buffer are modelled as a hybrid system, switching between standing still to communicate at positions with good signal strength and driving to catch up with the reference. This problem is solved using relaxed dynamic programming. For the case of a stationary reference position, experimental validation shows that loss of communication is avoided and that the method yields a gain in signal strength. The algorithm for flocking is based on Voronoi partitions. They can be approximated using only local information and allow the agents to avoid collisions. Our contribution is to add obstacle avoidance and movement towards a goal by using a navigation function - a scalar potential field with exactly one local minimum at the goal. To bound the inter-agent distances and thus avoid flock dispersion, any agent on the boundary of the flock uses a mirroring mechanism to create virtual neighbors that drive it inwards. We can prove collision safety and bounded group dispersion, and simulations show reliable goal convergence even in the presence of non-convex obstacles. A version of the algorithm with lower computational complexity is also presented. It can be used for formation control and it is proven to be locally asymptotically stable for a particular case. A hierarchical control structure is proposed for implementing the flocking on non-holonomic vehicles. It has been tested on a realistic car-like robot model in a flight dynamics simulator and the results confirm that the results on safety, group dispersion and goal convergence apply also in this case. / QC 20101111