Two-scale command shaping for arresting motion in nonlinear systems

This paper presents a feedforward technique for arresting motion in nonlinear systems based on two-scale command shaping (TSCS). The advantages of the proposed technique arise from its feedforward nature and ease of implementation in linear and nonlinear systems. Using the TSCS strategy, the control input required to arrest motion is decomposed into two scales-the first arrests dynamics associated with the linear subproblem, while the second eliminates response from the nonlinearities. Using direct numerical integration, the method is assessed using a traditional Duffing system and multi-degree-of-freedom nonlinear systems. Experiments are conducted on a compound pendulum attached to a servomotor, documenting effective arrest of the system in close agreement with theoretical predictions.