The Assignment of Generalized Time Constant for A Non-All-Pole System

This paper discusses the assignment of generalized time constant for a non-all-pole system. The generalized time constant is found to be important because it simultaneously influences the speed of response, damping (i.e., overshoot), and robustness. For the ease of explanation, a general two-mass system is introduced as a case study, which has one pair of jω-axis zeroes. Under an ideal two-parameter control configuration, the exact lower bound of the generalized time constant is determined that results in monotonic step responses, while a moderate generalized time constant is shown to be desirable for robustness purposes. A modified-Integral-Proportional-Derivative control configuration is then adopted for the implementation of the ideal two-parameter controller. It is found that, in real applications, a specific control configuration and signal delay may also impose limits on the assignment of the generalized time constant and characteristic ratios. Due to the clear physical meaning of the polynomial method, the tradeoff relationship among the speed of response, damping, and robustness can be explicitly represented. This unique advantage leads to a straightforward controller design procedure. Finally, the theoretical analysis is validated by experimental results.