Transient Response Control of Two Mass System via Polynomial Approach

Abstract

This paper discusses the application of polynomial method in the transient response control of a benchmark twomass system. It is shown that transient responses can be directly addressed by specifying the socalled characteristic ratios and the generalized time constant. The nominal characteristic ratio assignment (CRA) is a good starting point for controller design. And the characteristic ratios with lower indices have a more dominant influence. Two practical loworder control configurations, the integralproportional (IP) and modifiedintegralproportionalderivative (mIPD) controllers are designed. The primary design strategy of the controllers is to guarantee the lowerindex characteristic ratios to be equal to their nominal values, while the higherindex characteristic ratios are determined by the interaction with the generalized time constant and the limits imposed by zeros, a specific control configuration, etc. The demonstrated relationship between the transient responses and the assignments of characteristic ratios and generalized time constant in simulation and experiments explains the effectiveness of the polynomialmethodbased controller design.