Optimal PI controller design for second order plus time delay processes based on gain margin and improved error integration indices

In this paper, we present an optimal PI controller design method for second order plus time delay models using gain margin (GM) index and any one of the improved error integration indices: improved integral of absolute error (ISE) index, improved integral of square error (IAE) index and improved integral of time absolute error (ITAE) index. GM index has been used to guarantee system stability and determine the search region. Different error integration indices are compared, results show that the improved error integration indices are essentially the same and they give the same design results. System's unit step response curve show that the PI controllers designed by improved error integration indices have an optimal control performance.