Centralised fractional order LQI controller design for quadruple tank process — An optimisation approach

Abstract

In this paper, a centralised Fractional Order Linear Quadratic Integral (FOLQI) controller is proposed for highly interacting Multi Input Multi Output (MIMO) system to reject the load disturbance conditions. An optimisation problem to minimise the control effort as an objective function is formulated in addition to meet the desired time domain inequality constraints. The parameters of the FOLQI controller are obtained by using sequential quadratic programming optimisation approach. For illustration, the quadruple tank process is considered as a case study which exhibits both minimum and non-minimum phase characteristics. To show the performance of the FOLQI controller, the simulation is performed under disturbance and parameter uncertainty conditions. The performance indices such as maximum peak overshoot, settling time and steady state error are computed for FOLQI controller. To show the superiority of FOLQI controller, these indices are compared with the responses obtained using the existing Integer Order Linear Quadratic Integral (IOLQI) and Linear Active Disturbance Rejection (LADR) controllers.

Keywords

• Quadruple tank process
• Minimum and non-minimum phase
• Fractional LQI controller
• Disturbance rejection controller
• Parameter uncertainty