Abstract
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.
Highlights
In recent years, the fractional-order proportional-integral-derivative (FOPID) controller, which is first proposed by Podlubny [1], has attracted more attention of many researchers in the field of control systems
Three examples of the well-known TITO processes are considered to demonstrate the performances of the proposed method in comparison with those of other existing methods
A new formula of fractional PID controller is proposed to apply for a two-input two-output process
Summary
The fractional-order proportional-integral-derivative (FOPID) controller, which is first proposed by Podlubny [1], has attracted more attention of many researchers in the field of control systems. Sci. 2019, 9, 5262 approaches such as prediction error method (PEM), linear least square in frequency domain [16], and coefficient matching (CM) [17,18] These mentioned methods are only suitable for reducing to integer-order transfer functions. To improve the performances of a system, a generalized PI/PID controller, known as fractional-order PI/PID (FOPI/FOPID) controller, is suggested for decoupled systems. The IMC-based FOPI/FOPID design is adopted to find out analytical tuning rules of both FOPI and FOPID controllers for TITO processes. A new fractional order PID controller is proposed and analytical tuning rules are derived based on the internal model control structure.
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