The Mechatronics group in the Mechanical Engineering department of Cal Poly is interested in creating a demonstration of a ball-and-plate trajectory tracking controller on hardware. The display piece will serve to inspire engineering students to pursue Mechatronics and control theory as an area of study. The ball-and-plate system is open-loop unstable, underactuated, and has complicated, nonlinear equations of motion. These features present substantial challenges for control - especially if the objective is trajectory tracking. Because the system is underactuated, common nonlinear trajectory tracking control techniques are ineffective. This thesis lays out a theoretical foundation for controlling the hardware. Several important concepts related to ball-and-plate trajectory tracking control are presented. Models of the system, with various assumptions, are given and used in deriving control law candidates. To limit project scope, reasonable control criteria are introduced and used to evaluate designs from the thesis. Several control architectures are explored, these being Full-State Feedback with Integral Action, Single-Input-Single-Output Sliding Mode, and Full-State Feedback with Feed Forward. The mathematical reasoning behind each is detailed, simulation results are shown to validate their practicality and demonstrate features of the architectures, and trajectory similarity measure studies are produced to evaluate controller performance for a wide range of setpoint functions. The Full-State Feedback with Feed Forward controller is recommended based on its theoretical advantages and compliance with the control criteria over the competing designs. The control architecture has a proof of asymptotic tracking in the linear model, has excellent performance in simulations that use a nonlinear plant model, and produces the most pleasing visual experience when viewed in animation.

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Tethered satellite systems (TSS) can be utilized for a wide range of space-based applications, such as satellite formation control and propellantless orbital maneuvering by means of momentum transfer and electrodynamic thrusting. A TSS is a complicated physical system operating in a continuously varying physical environment, so most research on TSS dynamics and control makes use of simplified system models to make predictions about the behavior of the system. In spite of this fact, little effort is ever made to validate the predictions made by these simplified models. In an ideal situation, experimental data would be used to validate the predictions made by simplified TSS models. Unfortunately, adequate experimental data on TSS dynamics and control is not readily available at this time, so some other means of validation must be employed. In this work, we present a validation procedure based on the creation of a top-level computational model, the predictions of which are used in place of experimental data. The validity of all predictions made by lower-level computational models is assessed by comparing them to predictions made by the top-level computational model. In addition to the proposed validation procedure, a top-level TSS computational model is developed and rigorously verified. A lower-level TSS model is used to study the dynamics of the tether in a spinning TSS. Floquet theory is used to show that the lower-level model predicts that the pendular motion and transverse elastic vibrations of the tether are unstable for certain in-plane spin rates and system mass properties. Approximate solutions for the out-of-plane pendular motion are also derived for the case of high in-plane spin rates. The lower-level system model is also used to derive control laws for the pendular motion of the tether. Several different nonlinear control design techniques are used to derive the control laws, including methods that can account for the effects of dynamics not accounted for by the lower-level model. All of the results obtained using the lower-level system model are compared to predictions made by the top-level computational model to assess their validity and applicability to an actual TSS. / Ph. D.