Fractional order Modeling and Control of a Quadruple-tank Process

In recent years, fractional calculus attracts considerable attention from researchers in modeling and control of systems due to its flexibility in describing the behaviors of the dynamic systems. In this paper, a control design method based on fractional order will be proposed for a multi-input multi-output (MIMO) process. To deal with the interactions between system variables, the decoupling technique using simplified decoupling is adopted. However, in this paper, the PSO algorithm is proposed to approximate the complex decoupled transfer function into a simple form of fractional-order transfer function. The tuning rules of a fractional-order PID (FOPID) controller are also derived analytically based on the internal model control (IMC) structure. To validate the proposed method in real applications, the identification of a multivariable process (MIMO), the quadruple tank system, is presented by using the diagonal form of matrix fraction description (MFD) which transforms a MIMO process into multi-input single-output (MISO) sub-models. Then, the proposed controller is simulated as well as implemented based on the identified models to illustrate the effectiveness of the proposed method.