Design of Complex-Order PI/PID Speed Controllers and its FPAA Realization

Complex-order controllers are a generalized version of conventional integer-order controllers and are known to offer greater flexibility, better robustness, and improved system performance. This paper discusses the design of complex-order PI/PID controllers to control the speed of an induction motor drive and an electric vehicle. The speed-tracking performance of the complex-order controllers is compared with fractional-order controllers and conventional integer-order controllers. Implementing complex-order controllers is challenging due to commercial complex-order fractance element unavailability. Hence, it is carried out by approximating the complex-order controller transfer function using an integer-order rational function with a curve-fitting approach, namely the Sanathanan Koener (SK) iterative method. This method is quite simple and can fit the required frequency range compared to the conventional Matsuda and Oustaloup approaches. The approximated controller transfer function can easily be realized by employing the AN231E04 Field Programmable Analog Array (FPAA). Simulation and experimental results highlight that the controller behaviour is in good agreement with the theoretical expectations.