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Working with a physical system, the search for a model (plant) could be computed mainly via physical equations or system identification when input/output data is available. Models which closely describe physical systems are difficult or impossible to precisely characterize. A model could be thoroughly detailed but it is never an exact representation of the real physical system; and in many applications, noise is clearly present. Modeling errors shall be considered as they might affect the performance of the system. It is at this point where the term uncertainty appears, referring to the differences between the models and the real system. Parametric uncertain models consist of a set of models derived from arange of the uncertain parameters. In linear time-invariant (LTI) control systems, input shaping (IS) is a technique originally used for defining a shaped command input to eliminate or reduce unwanted system vibration. With the input shaping schemes being inherently open-loop, uncertainties in the model can lead to system performance degradation. By its nature, the nominal model-based input shaping cannot compensate for errors in the model, since it rejects any possible variations in the parameters. For parametric uncertain models, a process to compute a robust input signal that works for the set of models derived from the uncertain parameters is required. Robustness in a system is defined as its qualification to generate the desired output over disturbances and uncertainties. In general, robust control consists of the control methods utilized to operate in the uncertain parameters of a model. The process defined in this dissertation considers the problem of robust input shaping, where a single input signal is designed for a range of variability in the parameters of a dynamic model. This work proposes an approach to robust input shaping based on the extreme models, initially derived from the extreme values of the uncertain parameters. Robustness is then achieved by considering the extreme cases in the range of the parameters variations. The result is a single input signal that guarantees tracking of a planned trajectory within a specified accuracy and operating constraints.

We investigate the implementation of nontraditional open-loop and closed-loop control techniques to systems at the micro and macro scales. At the macro level, we consider a quay-side container crane. It is known that the United States relies on ocean transportation for 95% of cargo tonnage that moves in and out of the country. Each year over six million loaded marine containers enter U.S. ports. Current growth predictions indicate that container cargo will quadruple in the next twenty years. To cope with this rapid growth, we develop a novel open-loop input-shaping control technique to mitigate payload oscillations on quay-side container cranes. The proposed approach is suitable for automated crane operations, does not require any alterations to the existing crane structure, uses the maximum crane capabilities, and is based on an accurate two-dimensional four-bar-mechanism model of a container crane. The shaped commands are based on a nonlinear approximation of the two-dimensional model frequency and, unlike traditional input-shaping techniques, our approach can account for large hoisting operations. For operator-in-the-loop crane operations, we develop a closed-loop nonlinear delayed-position feedback controller. Key features of this controller are that it: does not require major modifications to the existing crane structure, accounts for motion inversion delays, rejects external disturbances, and is superimposed on the crane operator commands. To validate the controllers, we construct a 1:10 scale model of a 65-ton quay-side container crane. The facility consists of a 7-meter track, 3.5-meter hoisting cables, a trolley, a traverse motor, two hoisting motors, and a 50-pound payload. Using this setup, we demonstrated the effectiveness of the controllers in mitigating payload oscillations in both of the open-loop and closed-loop modes of operation. At the micro level, we consider a micro optical device known as the torsional micromirror. This device has a tremendous number of industrial and consumer market applications including optical switching, light scanning, digital displays, etc. To analyze this device, we develop a comprehensive model of an electrically actuated torsional mirror. Using a Galerkin expansion, we develop a reduced-order model of the mirror and verify it against experimental data. We investigate the accuracy of representing the mirror using a two-degrees-of-freedom lumped-mass model. We conclude that, under normal operating conditions, the statics and dynamics of the mirror can be accurately represented by the simplified lumped-mass system. We utilize the lumped-mass model to study and analyze the nonlinear dynamics of torsional micromirrors subjected to combined DC and resonant AC excitations. The analysis is aimed at enhancing the performance of micromirrors used for scanning applications by providing better insight into the effects of system parameters on the microscanner's optimal design and performance. Examining the characteristics of the mirror response, we found that, for a certain DC voltage range, a two-to-one internal resonance might be activated between the first two modes. Due to this internal resonance, the mirror exhibits complex dynamic behavior. This behavior results in undesirable vibrations that can be detrimental to the scanner performance. Torsional micromirrors are currently being implemented to provide all-optical switching in fiber optic networks. Traditional switching techniques are based on converting the optical signal into electrical signal and back into optical signal before it can be switched into another fiber. This reduces the rate of data transfer substantially. To realize fast all-optical switching, we enhance the transient dynamic characteristics and performance of torsional micromirrors by developing a novel technique for preshaping the voltage commands applied to activate the mirror. This new approach is the first to effectively account for inherent nonlinearities, damping effects, and the energy of the significant higher modes. Using this technique, we are able to realize very fast switching operations with minimal settling time and almost zero overshoot.