This study models a two-link rigid-flexible manipulator using two methods:
mathematical modelling with Lagrange?s equations and the finite elements method (FE model)
and constructing the model with MATLAB?s Simscape multibody tool (Simscape Model). The
FE model is validated by comparing it to a linearised version of the physical Simscape model,
taking into account structural damping, hub inertias, and payload at the flexible link?s endpoint.
The resonance frequencies of the first three modes are analysed in the frequency domain using
both models. The open-loop responses of both models are also compared in the time domain. A
linear quadratic Gaussian (LQG) controller with a Kalman filter and integral action is developed
and implemented using the Simscape Model. The simulation results using MATLAB show that
the proposed method is efficient and practical for joint angle trajectory tracking and flexible link
vibration control of the rigid-flexible manipulator. The LQG controller is shown to be more
effective in reducing vibrations and enhancing performance of flexible link manipulators when
compared to a proportional-derivative (PD) controller.