Performance enhancement of non-minimum phase feedback systems by fractional-order cancellation of non-minimum phase zero on the Riemann surface: New theoretical and experimental results

In the field of linear time-invariant systems, a process is identified as a nonminimum phase (NMP) system if its transfer function has at least one right half-plane (RHP) zero, or a RHP pole, or a time delay. Among others, systems with RHP zero(s) constitute a very important category of NMP systems, both from theoretical and practical point of view. Such zeros appear in many realworld systems such as flexible link robots [1, 2], step-up DC-DC converters [3, 4], floating-wind turbines [5], aircrafts [6], bicycles [7], driving a car backwards [8], continuous stirred tank reactors [9], nano positioning devices [10], and many others. One classical fact in relation to NMP zeros is that they cannot be cancelled by the same poles of controller according to the internal instability problem [11]. The other well-known fact is that NMP zeros of the process put some limitations on the performance of the corresponding feedback system [12]. One main reason for this limitation is that in order to achieve a good command following and disturbance rejection behavior, any feedback system needs large open-loop gains at lower frequencies, which is often provided by the controller [11]. On the other hand, according to the classical root-locus method, any closed-loop system has