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The continuous and discrete time Linear Quadratic Regulator (LQR) theory hasbeen used in this paper for the design of optimal analog and discrete PIDcontrollers respectively. The PID controller gains are formulated as theoptimal state-feedback gains, corresponding to the standard quadratic costfunction involving the state variables and the controller effort. A real codedGenetic Algorithm (GA) has been used next to optimally find out the weightingmatrices, associated with the respective optimal state-feedback regulatordesign while minimizing another time domain integral performance index,comprising of a weighted sum of Integral of Time multiplied Squared Error(ITSE) and the controller effort. The proposed methodology is extended for anew kind of fractional order (FO) integral performance indices. The impact offractional order (as any arbitrary real order) cost function on the LQR tunedPID control loops is highlighted in the present work, along with the achievablecost of control. Guidelines for the choice of integral order of the performanceindex are given depending on the characteristics of the process, to becontrolled.

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index