Trajectory Pattern Method Applied to a Nonlinear Flexible Pointing System

In this study, the Trajectory Pattern Method [1-5] is used to synthesize motion trajectories and generate inverse dynamics model based feedforward actuating signals for the test fixture described in [2]. The test fixture is constructed as a system with structural flexibility due to the presence of a flexible beam and a flexible joint. The main contribution of this study is the derivation of the inverse dynamics model of the system in parametric form and synthesis of trajectories for point to point motions such that the resulting actuating torques do not contain the harmonic with frequency of the dominant first natural mode of vibration of the flexible beam. With this trajectory pattern, point to point motions with minimal residual vibration can be accomplished with zero end point jerk. A feedforward (computed torque) controller together with a PD feedbeck loop is constructed and implemented on the testbed. The computer simulation of the open-loop response of the system is presented. The effectiveness of the approach is verified experimentally.