Design of set-point weighting PIλ + Dμ controller for vertical magnetic flux controller in Damavand tokamak

Abstract

In this paper, a simple method is presented for tuning weighted PI(λ) + D(μ) controller parameters based on the pole placement controller of pseudo-second-order fractional systems. One of the advantages of this controller is capability of reducing the disturbance effects and improving response to input, simultaneously. In the following sections, the performance of this controller is evaluated experimentally to control the vertical magnetic flux in Damavand tokamak. For this work, at first a fractional order model is identified using output-error technique in time domain. For various practical experiments, having desired time responses for magnetic flux in Damavand tokamak, is vital. To approach this, at first the desired closed loop reference models are obtained based on generalized characteristic ratio assignment method in fractional order systems. After that, for the identified model, a set-point weighting PI(λ) + D(μ) controller is designed and simulated. Finally, this controller is implemented on digital signal processor control system of the plant to fast/slow control of magnetic flux. The practical results show appropriate performance of this controller.

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

“…By equating HðsÞ in (18) with H desired ðsÞ in (19), the proportional gain of the FOPID controller ðk p Þ and the filter denominator coefficient ðhÞ are respectively obtained as (6) for different values of commensurate order a depicted in w-plane where w ¼ s a [51]. Therefore, according to relations (15)- (17), (20), and (21), the parameters of the FOPID controller, the set-point weight, and the constant coefficient of fractional order filter can be determined uniquely.…”

“…It has been shown that the fractional order controllers are more effective in some industrial applications [12,15,20]. Also, this type of controllers have been applied in a wide range of practical applications; such as control of magnetic flux in tokamak machine [19], heat flow platform [20], hexapod robot [37], permanent magnetic synchronous motors [38], and power electronic buck converters [39].…”

“…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].…”

“…In [11], an effective way is proposed to tune the setpoint weights when the FOPID controller is designed to optimize the disturbance rejection performance based on the standard fractional set-point weighted control structure. In [19], a simple analytical method is proposed for tuning the parameters of the SWFOPID controller based on the standard fractional set-point weighted control structure.…”

“…Different strategies are available for tuning the parameters of the set-point weighted PI and PID controllers [46][47][48]. Also in recent years, different methods have been proposed for designing the parameters of the SWFOPID controllers [11,19]. In [11], an effective way is proposed to tune the setpoint weights when the FOPID controller is designed to optimize the disturbance rejection performance based on the standard fractional set-point weighted control structure.…”