Abstract
Fractional-order control system design can be used for systems with non-local dynamics involving long-term memory effects. However, implementation of a fractional-order controller in industrial systems is complicated, because of the excessive demand for computational power. The following paper presents the step-by-step design procedure, parameter tuning, and experimental evaluation of the fractional order proportional-integral-derivative (FOPID) controller. The control algorithm is based on the Continued Fraction Expansion approximation of the fractional-order operators. It is implemented on a standard industrial Programmable Logic Controller. The FOPID control system is verified and evaluated in terms of efficiency and robustness using a new laboratory benchmark of a temperature control in the pipeline. The proposed solution shows increased efficiency in terms of robustness compared to the standard PID closed-loop control.
Highlights
The Proportional-Integral-Derivative (PID) algorithm is one of the most used algorithms in the industry to control processes
Most of the processes associated with complex systems have non-local dynamics involving long-term memory effects
The major problem with control engineering applications of fractional calculus was the complicated method of solving the differential equations
Summary
The Proportional-Integral-Derivative (PID) algorithm is one of the most used algorithms in the industry to control processes. The major problem with control engineering applications of fractional calculus was the complicated method of solving the differential equations It was overcome with finding the proper geometric and physical interpretation of the fractional operators [56] and their efficient numerical approximations, like Power Series Expansion (PSE) [54] or Continued Fraction Expansion (CFE) [7], among others. Implementations of fractional operators based on CFE approximation using SIEMENS S7-1200 PLC are presented in [42], and Hardware-in-the-Loop (HIL) experiments are described in [43]. This article synthesizes the mentioned works and describes the step-by-step design procedure, parameter tuning, and implementation of the PIkDl algorithm with CFE approximation on a laboratory test stand.
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