The significance of poles and zeros: Emulate Wilbur Wright and learn the significance of poles and zeros

摘要

Wilbur Wright's understanding of complex, dynamic problems contributed to his and his brother Orville's successful first airplane flight. Wilbur understood, for example, that, to turn a bicycle to the left, you must first turn the handlebars a little to the right and then, as the bicycle inclines to the left, you must turn them a little to the left. He understood countersteering. In mathematical language, the transfer function between the steer torque applied to the handlebars and the straight-line-path deviation has a right-half-plane zero, which imposes a limit on maneuverability. The path deviation has an inverse-response behavior; that is, in response to a positive step-torque input you apply to the handlebars, the path deviation is initially positive and then becomes negative. This effect has contributed to numerous motorcycle accidents, but countersteering could prevent these accidents.