Stability analysis for the intermediate servo/regulation PID tuning

This paper introduces the stability analysis for the so-called intermediate-tuning PID controller. Thus, each of the three PID parameters is proposed to lie within the convex hull of two extreme values, being defined as the optimal tuning settings for servo and regulation modes respectively. The result ensures that all the PID controllers generated for each frozen value of the interpolating parameters guarantee the stability of the closed-loop.