Optimalpi‐coefficients of second‐order systems
Jinn‐Fwu Wu, Jia‐Sheng Heh, I‐Kong Fong, Te‐Son Kuo · Journal of the Chinese Institute of Engineers · 1992
Pi‐coefficients [4] provide a quantitative measure of system stability. With the goal of finding the largest stability range of the feedback gain in a system, the max‐p problem [9] can be formulated so that its solution gives an optimal set of pi‐coefficients. This paper simplifies the max‐p problem by analyzing the special structure of a negative semi‐definite matrix, called the M‐matrix. To find the optimal pi‐coefficients of the general second‐order systems, seven solutions corresponding to different conditions are derived. In the examples we apply the results to a model reference adaptive system, calculate the pi‐coefficients of its error dynamics model, and use the optimal pi‐coefficient curves to determine a good sampling period.