An overview of FOPID controller design in v-domain: design methodologies and robust controller performance

The complex v-plane is an emerging design domain for fractional order control system design. Recently, several works demonstrated the advantages of tuning FOPID controllers in v-plane. These approaches essentially perform the minimum angle pole placement to a target angle within the stability region of the v-plane and facilitate fractional order control system design tasks because of inherently guaranteed stabilisation of fractional order transfer functions. Accordingly, the optimal FOPID controller tuning problem can be simplified to placement of minimum angle system pole to a target point within the stability region of the v-plane. After reviewing previous v-domain design works, authors investigate prominent target points that can result in improved FOPID control performance for the v-domain design task. The consideration of target points in polar coordinates can provide two design parameters (angle and magnitude), which can convey essential system knowledge associated with the stability and control performance of FOPID control systems. In this perspective, effects of minimum angle pole positions on control performance indices are investigated in detail, and some prominent target points to manage FOPID design in v-domain have been reported. The v-domain design examples are illustrated to reveal the effects of the sampled pole positions on the robust control performance.