A Novel Design of Fractional PI/PID Controllers for Two-Input-Two-Output Processes

In this paper, a new formulation of fractional order proportional integral (PI)/ proportional integral derivative (PID) controller is proposed. The proposed controller will be justified for some well-known two-input-two-output (TITO) processes. In order to deal with interactions between process variables in a multivariable system, as well as multiple delay times in process transfer functions, the simplified decoupling Smith predictor (SDSP) structure is also used. The issue of decoupling realizability is solved by the PSO algorithm and fractional order processes are also suggested for model reduction. The tuning rules of the controller are derived in analytical terms based on the internal model control (IMC) structure. The effectiveness and robust stability of the proposed approach are illustrated by comparing it with other methods. To have a fair comparison, the robustness criterion using the M-Δ structure with μ-synthesis is adopted and the μ value of the proposed method is always kept smaller than the value of the others.