Reconfigurable Fractional-Order Operator and Bandwidth Expansion Suitable for PI^α Controller

Abstract

This article presents a reconfigurable fractional-order operator circuit with a bandwidth expansion technique for applications such as automation and robotics. The advantages of continued fraction expansion (CFE) and Newton–Raphson's methods are amalgamated to achieve three high-accuracy first-order bilinear functions. By adding two bilinear functions (fifth-order approximation), the bandwidth expansion technique is provided. In contrast to conventional approximation techniques, this novel technique can provide a wide bandwidth of up to four decades and errors better than 20%. This technique also enables extended bandwidth by adding more bilinear functions. The circuit realization can be easily constructed by cascading the factorized first-order bilinear functions. The proposed fractional-order operator can be reconfigured between the differentiator and the integrator using a selector switch without changing any circuit topology. The fractional-order operator's frequency response ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω</i> ) and order ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</i> ) can be independently tuned using the bias current. The fractional-order proportional–integral (PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> ) controller in the throttle and brake of autonomous vehicles is investigated to confirm the performance compared with the theoretical results. The experimental results based on commercially available operational transconductance amplifiers are validated and found to be in agreement with the theoretical analysis. Therefore, it can pave the way for further programmable system-on-chip for industries.