Reduced inverse integer-order controller design for a class of fractional-order model: Case study on two-tank liquid-level process

Abstract

In this study, a reduced inverse integer-order controller design methodology for single fractional-order pole model is proposed. First, the higher integer-order equivalent of this model is found using the Oustaloup approximation to fractional operator. Then, the poles and zeros of the higher integer-order model are determined in terms of fractional-order system model parameters employing characteristic equation format and root-locus idea. The order of the higher integer-order model is reduced using dominant pole–zero couples. The proximity of the pole–zero couples to each other as well as their proximity to the origin is key dominance requirement for order reduction. The controller is obtained inverting the reduced order integer system model in terms of fractional-order system model parameters. The proposed controller is compared with integer and fractional proportional–integral–derivative (PID) controllers using the experiments carried out on two-tank liquid-level process. The real-time experiment outcomes demonstrate that the proposed controller has superior performance over integer and fractional proportional–integral–derivative controllers.

Bi-fractional-order reference model parameters-based control system design

“…The algorithm begins with the selection of the initial settling time as 0.63 s, which is the settling time of the open-loop system, as seen in Figure 11. Then, the natural frequency v n is found as 5.52 by using the corresponding reference model in equation (14). The initial controller is obtained according to the fifth step of the algorithm C initial (s) = 0:17368 1:9 + 1:3224s 0:95 + 30:47 0:8721s 2 + 7:4221s…”

“…[9][10][11] Moreover, numerous integer-order control strategies are also adapted to their fractional counterparts. [12][13][14][15][16][17] The transfer functions of closed-loop systems that exhibit the desired system dynamics are often called reference models. These models profit from meeting the 1 requirements without causing difficulties in their control system implementations, and therefore, there are many control techniques in which the direct synthesis method is employed.…”

“…9–11 Moreover, numerous integer-order control strategies are also adapted to their fractional counterparts. 12–17…”