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

Review of fractional PID controller

“…Internal Model Control (IMC) based tuning was proposed by M. Tavakoli-Kakhki and M. Haeri in 2010 [52] . An IMC based fractional PID controller is represented as: (13) where, T i is the integral time and T d is the derivative time.…”

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

“…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]. It has been shown that the fractional order controllers are more effective in some industrial applications [12,15,20].…”

Untitled

“…They are preferred because of the advantages like better disposal of solids, easy mixing and complete drainage of solvents such as viscous liquids in industries. In spherical tank non-linearity exists due to its variation in cross-sectional area [3]. Because of the non-linearity, level control is a challenging task in spherical tank and it demands for implementation in real time.…”