Control Law Design Based on the Polynomial Method for Active Damping of Oscillatory Modes -The Application of the Delta Operator to the Polynomial Method-

Abstract

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, when the controlled plant is high-order, numerical problems arise in the solution of a Diophantine equation or a Sylvester matrix. In order to make the conventional polynomial method practicable, this paper presents an improved polynomial method based on the modified delta operator δ for the microprocessor control. The modified delta form can significantly improve numerical conditioning of a Sylvester matrix on pole and zero assignment in controller design. As an example of a controlled plant, a 10th-order plant is considered. Then, the numerical sensitivity of a Sylvester matrix reduces at one millionth of the conventional one obtained on the z-plane. The simulated results show that the proposed method can be applied to a high-order plant and a robust controller can be developed. Therefore, the proposed method would be useful for the computer controlled plants in industry.