Modeling, identification and control of a wheeled balancing system

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Murdock, Daniel
Taylor, David G.
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The purpose of this research is to develop a comprehensive modeling, identification, and control methodology for several inverted balancing systems. Symbolic software tools are created based on the general dynamic equation to derive the equations of motion for each system. Embedded programming techniques are designed and implemented to acquire data, perform sensor calibration, and impose actuator voltages. Actuator nonlinearities are characterized using only the hardware intended for implementation by processing the measured responses to specific embedded experiments; this low-cost approach does not require additional measurement devices or other expensive high-precision equipment. State-space integral controllers are designed to perform robust output feedback compensation and accomplish reference tracking. Several practical implementation issues are investigated such as disturbance rejection, digital controller design, switched mode reference tracking, and integrator anti-windup. Before implementation, a software environment is created to predict system performance with high-fidelity by testing how the full-order nonlinear plant dynamics respond to the two-time scale controller design while accounting for higher order friction effects, cogging torque, gearbox backlash, sensor bias, and parameter mismatch. The three applications this methodology is applied to are the reaction wheel pendulum (RWP), wheeled inverted pendulum (WIP), and wheeled balancing system (WBS); where the WBS is by definition a mechanical superposition of RWP and WIP technologies. Simulated predictions of the RWP and WIP are strongly validated by experimental measurements, and the developed methodology is theoretically applied in simulation to prove the success of the WBS concept.
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