Design of a class of fractional controllers from frequency specifications with guaranteed time domain behavior

Fractional order model reduction approach based on retention of the dominant dynamics: Application in IMC based tuning of FOPI and FOPID controllers

“…Among different kinds of fractional order controllers, fractional order PI (FOPI) and fractional order PID (FOPID) controllers as the generalizations of classical PI and PID controllers have attracted more attention of the researchers in this field. So far different strategies have been suggested for tuning the parameters of these classes of fractional order controllers [26][27][28][29][30][31]. In some of the existing methods a simple model of the process is utilized for tuning the parameters of FOPID controllers [26][27][28].…”

Analytical design of fractional order PID controllers based on the fractional set-point weighted structure: Case study in twin rotor helicopter

“…Based on relations (16), (17), (20), and (21), by applying the SWFOPID controller in the control structure shown in Fig. 4, the sensitivity function SðsÞ ¼ 1= 1 þ G c ðsÞPðsÞ ð Þand the complementary sensitivity function TðsÞ ¼ G c ðsÞPðsÞ= 1 þ G c ðsÞPðsÞ ð Þ are respectively obtained as…”

“…The existence of the tunable order a in the structure of the fractional order pre-filters makes these filters more flexible in comparison with the classical pre-filters [7]. This is due to the fact that the fractional calculus has a great potential to improve the traditional methods in different fields of control systems; such as controller design [11][12][13][14][15][16][17][18][19][20] and system identification [21][22][23][24][25]. Fractional order concepts are employed in simple and advanced control methodologies; such as set-point weighted fractional order PID (SWFOPID) controller [11,19], phase lead and lag compensator [14,26], internal model based fractional order controller [27], Smith predictor based fractional order controller [18,21], optimal fractional order controller [28,29], robust fractional order control systems [30][31][32], fuzzy fractional order controller [33], fractional order sliding mode controller [34], fractional order switching systems [35], and adaptive fractional order controller [17,36].…”

Improving integral square error performance with implementable fractional‐order PI controllers

“…The extra degrees of freedom in setting the orders of differentiations, λ and μ , lead to a more flexible tuning strategy for achieving control requirements as compared with the classical controllers. The freedom to design λ and μ will also provide for a better adjustment of controller's dynamic properties and increases the closed‐loop system's robustness against parameter uncertainties .…”

“…Accordingly, the extra degrees of freedom provided by the fractional orders of differentiation and integration allow for the simultaneous satisfaction of a larger set of design specifications. The authors in handle examples that involve both frequency‐domain and time‐domain specifications, and they derive parametrized sets of controllers that satisfy the desired conditions. The parametrized sets are derived using polynomial fits, and they are expressed in terms of relations between time‐domain and frequency‐domain specifications.…”