UC San Diego

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.