Analog Realizations of Fractional-Order Integrators/Differentiators: A Comparison

Non-integer differential or integral operators can be used to realize fractional-order controllers, which provide better performance than conventional PID controllers, especially if controlled plants are of non-integer-order. In many cases, fractional-order controllers are more flexible than PID and ensure robustness for high gain variations. This paper compares three different approaches to approximate fractional-order differentiators or integrators. Each approximation realizes a rational transfer function characterized by a sequence of interlaced minimum-phase zeros and stable poles. The frequency-domain comparison shows that best approximations have nearly the same zero-pole locations, even if they are obtained starting from different points of view.