Programmable analogue fractional controller realization

A fractional-order controller is an infinite-memory system. It is described by a continuous time irrational transfer function. Its realization is a delicate problem especially when its parameters are real time tunable. This paper presents a real-time programmable analogue fractional controller implementation. The controller is based on a sum of a novel real-time programmable analogue first-order low-pass filter. The signal within the circuit remains analogue and is not converted into discrete values. Real-time adjustments are made using digital potentiometers and operational amplifiers. The proposed first-order low-pass filter offers several advantages. In particular, the time constant and DC gain are independently adjusted without relying on the ohmic value of digital potentiometers. The time constant and DC gain depend on the resolution of the digital potentiometers. The high resolution of the digital potentiometer enables the circuit to achieve a wide bandwidth and allows for the use of small capacitors at lower frequencies. The proposed real-time programmable analogue fractional controller is experimented to achieve a fractional integrator. The circuit yields good similarity between theoretical simulations and experimental measurements.