4B15 Control Law Design Based on The Polynomial Method for Active Damping of Oscillatory Modes : The Application of The Delta Operator to The Polynomial Method
Tatsu Aoki · The Proceedings of the Symposium on the Motion and Vibration Control · 2010
The polynomial or algebraic method based on the transfer function can achieve simultaneously pole and zero placement. Since the method has clear physical interpretation, it is easy to introduce many different constraints such as vibration modes and the operation limit of the actuator. However, if the controlled plant is high-order, numerical problems arise in the solution of a Diophantine equation. This paper presents a new polynomial design method on the modified delta δ^^--plane instead of the s-plane and the z-plane for the microprocessor control. As an illustration, active damping of second-order system is considered. The numerical sensitivity of a Diophantine equation becomes about one thousandth of that based on the conventional design. The simulated results show that the proposed method is applicable to the high-order systems.