Synthesised fractional‐order PD controller design for fractional‐order time‐delay systems based on improved robust stability surface analysis

Abstract

An improved robust stability surface analysis method is proposed in this study for fractional‐order time‐delay systems. Through the stabilisation process, a synthesised fractional‐order PD controller can be designed with guaranteed robustness specifications. Firstly, the specification for improved robustness requirements is proposed. In order to find selectable robust controller design parameter combinations for the controlled system, stability region is discussed based on the stability boundary locus, and the robust stability surface is derived straight after. Secondly, the selectable parameter combinations are checked to find the one that best fulfils all the proposed robustness specifications. Finally, numerical simulations are given to demonstrate the effectiveness and flexibility of the presented control algorithm.

Robust stabilization of interval fractional‐order plants with an interval time delay by fractional‐order proportional integral derivative controllers

“…Furthermore, as mentioned previously, the method proposed in [20] cannot be considered reliable in general. Moreover, the previous works [19, 21–26] and [35] do not sufficiently tackle the issue of designing robust FOPID controllers. Furthermore, the method proposed in [37] is limited to the range of $$0<\alpha <1$$, and only a sufficient condition has been derived for robust stability analysis.…”

“…Step responses corresponding to the FOPI controller $$C(s) = -0.3 + {0.2}/{s^{0.4}}$$ for randomly generated samples of the interval plant $$P(s)$$ in Equation (39) have been shown in Figure 9. Although, the methods proposed in [17–19, 21–26] and [35] are inefficient in designing a robust FOPID stabilization of the closed‐loop system in the presence of uncertainty in the time delay term. The method proposed in this paper can investigate such characteristic functions having interval plant with an interval time delay.…”

“…Despite the extensive study concerning the problem of robustly calculating the stabilizing region of FOPID controllers for fractional-order systems having time delay [21][22][23][24][25][26], a valid mathematical proof of calculating the value set for these systems seems to be elusive. It should be noted that, for the interval fractional-order plants with an interval time delay, the study of the stabilizing region of FOPID controllers has not been well elaborated and it is a renewed research area.…”