IJCAS

This paper introduces a frequency response based extremum seeking controller (FRB-ESC) that utilizes the natural frequencies and antiresonances of the system in the design of the FRB-ESC. Starting from a natural frequency and transitioning in a continuous way onto the antiresonance of the system allows the minimization of vibrations at the free end. Designing control schemes for flexible-link manipulators is rather complex due to the system distributed nature that is modeled by infinite degrees of freedom, where for control purposes there is only a finite number of sensors and actuators, with a finite bandwidth. The control objective consists on simultaneous trajectory tracking and vibration minimization at the free end of the flexible manipulator employing a single actuator, an optical encoder at the hub of the flexible manipulator and an accelerometer at the free end. Unlike conventional control strategies that add damping to the system, the FRB-ESC minimizes the vibration at the free end. To illustrate the capabilities of the control to minimize vibrations in the most extreme case the reference trajectory is a sinusoidal signal whose frequency is equal to the first mode of vibration of the system. The FRB-ESC achieves attenuation of the free end vibrations and decreases the angular error in the transient state with the use of a single actuator at the hub of the system. The FRB-ESC results are then compared to a PID and a positive position feedback (PPF) controllers achieving up to 42% reduction of the second derivative of the elastic deflection.

Keywords: Bernoulli’s beam, extremum seeking control, flexible-link, trajectory tracking.