Artificial neural network control of a nonminimum phase, single-flexible-link

A single-link flexible manipulator with a rotary actuator at one end and a mass at the other is modeled using the Lagrangian method coupled with an assumed modes vibration model. A SIMO state space model is developed by linearizing the equations of motion and simplified by neglecting natural damping. Laplace domain pole-zero plots between torque input and tip position show nonminimum phase behavior. Nonminimum phase behavior causes difficulty for both conventional and artificial neural network (ANN) inverse-model control. The most promising ANN method for the control of flexible manipulators does not appear to converge to a solution when the system is lightly damped. To overcome this limitation, a modified cost function is proposed. Simulations show that the ANN is able to converge to a solution even in the case of no damping. The modified approach fails, however, for beams exceeding some critical length measure. Identification of the critical length and proposals for extending the result are discussed