Dynamic Analysis and Control of a Stewart Platform Using A Novel Automatic Differentiation Method
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This paper presents a kinematic based Lagrangian approach to generate the equations of motion and design an adaptive control law for multi-body systems. This methodology is applied to dynamic analysis and controller design study for a Stewart platform. Novel means of utilizing automatic differentiation are employed to generate and solve the equations of motion, using only high level geometric and kinematic descriptions of the system. Based on deriving and coding only the kinematic descriptions of the system, the nonlinear motion of the platform is solved automatically and the analyst is freed from deriving, coding, and validating the lengthy nonlinear equations of motion. Lyapunov stability theory and concepts from adaptive control are used to formulate a nonlinear feedback control law. The control law is of the model reference adaptive structure, designed to track a prescribed smooth trajectory. By designing an adaptive update rule for the system mass and inertia parameters, the tracking errors are proven to be asymptotically stable for arbitrary parameter errors. Also, a PID adaptive control law is designed to guarantee bounded stability in the presence of bounded disturbances. Numerical results are included to illustrate the performance of the algorithm in the presence of large parameter errors and external disturbance.
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AIAA/AAS Astrodynamics Specialist Conference and Exhibit
