Polynomial-Method-Based Design of Low-Order Controllers for Two-Mass Systems

In this paper, low-order integral-proportional (IP), modified IP (m-IP), and modified integral-proportional-derivative (m-IPD) controllers are designed for the speed control of a two-mass system based on a normalized model and polynomial method. In order to have sufficient damping, the parameters of the controllers are determined through characteristic-ratio assignment under the principle that all the characteristic ratios should be larger than two. It is found that for an inertia ratio smaller than one-third, an IP controller can effectively suppress the vibrations with proper damping, while for a relatively larger inertia ratio, an m-IP controller (i.e., IP controller with an additional low-pass filter) is effective. m-IPD control is theoretically effective for a large inertia ratio. However, the necessity of a negative derivative gain leads to a very poor robustness. Both simulation and experimental results verified the effectiveness of the designed IP and m-IP controllers when the inertia ratio is relatively small. For the m-IPD controller, its poor robustness is demonstrated by introducing a large gear backlash in experiments, while the IP and m-IP controllers show promising results of a much better robustness against the gear backlash nonlinearity.