A study of rootlocus with applicationto the design of PD controllerfor linear control systems

In this paper, the break-away and break-in (BABI) condition used in root-locus approach for two-parameter linear control systemsis derived. The condition for one-parameter control system can also be obtained from those results, which agrees with the well-known results by using sensitivity function (e.g., Kuo, 2009). Based on those conditions, an algorithm is proposed to construct the PD control gains of linear control systems for meeting designed specifications of timing response. Compared with the conventional design by using root-contours, the proposed approach can give a guideline for choosing control gains instead of those obtained by trial-and-error from the root-contours scheme. An example of the 3rd-order linear systemwith PD control is also given to demonstrate the feasibility of the proposed design.