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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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