Stability Analysis of a Class of Nonlinear Controllers

The stability analysis of a class of nonlinear PD-plus-feedforward controllers is presented for the tracking control of rigid robot manipulators. The controller structure is composed of a nonlinear gain PD feedback controller and a manipulator dynamics feedforward term. The class of representations used for the nonlinear gain PD feedback controller is extended and global exponential stability is proved. Simulation results are included to illustrate the performance of this class of nonlinear controllers.

Concurrent Design of Input Shaping and Proportional Plus Derivative Feedback Control

Systems that exhibit flexible dynamics are widespread and present a very challenging control problem when their performance is pushed to the limit. If there is some knowledge of the flexible modes, then command signals can be generated to negate the detrimental dynamics. These vibration-reducing commands are dependent on the feedback controller gains because the gains influence the flexible modes. This paper presents a method for concurrently designing a PD feedback controller and a command generator so that performance is optimized. The design method takes into account limits on allowable overshoot, residual vibration, and actuator effort. Furthermore, the structure of the method allows a wide range of performance requirements, such as disturbance rejection, to be integrated into the design. Results demonstrate that a PD controller cannot achieve the same performance as a PD controller augmented with a command generator.