REVISITING BODE’S IDEAL LOOPS: INTEGRAL SQUARE ERROR OPTIMALITY OF BODE’S IDEAL LOOPS AND BODE’S IDEAL LOOP INVERSE CONTROLLER DESIGN

Bode’s ideal loop models have been utilized in control system designs to obtain performance robustness for the Direct Current (DC) gain variations. However, effects of crossover frequency and fractional order on control optimality of Bode's ideal loop reference models have not been sufficiently discussed, and it may raise a question of whether a control system design based on Bode’s ideal loop reference model is optimal. In this regard, this study revisits Bode’s ideal loops to investigate Integral Square Error (ISE) optimality of Bode’s ideal loops. For this purpose, the ISE optimality of Bode’s ideal loop is theoretically investigated by using Parseval’s theorem, and an ISE optimality condition is suggested in terms of crossover frequency and fractional order. Then, a generic controller family, which achieves an exact matching with the characteristics of the ISE optimal Bode’s ideal loop, was implemented for inverse fractional-order control of a class of minimum phase fractional order plant models. The authors present a numerical experiment on an ISE optimal Bode’s ideal loop inverse (OBILI) controller, and the ISE optimality and performance robustness of the designed control system were investigated for closed-loop control of a heat furnace system model via Monte Carlo simulations.