Universal block diagram based modeling and simulation schemes for fractional-order control systems
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Updated: Mar 2, 2026

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Published on: November 24, 2021
Lu Bai1, Dingyü Xue2
1School of Information Science and Engineering, Northeastern University, Shenyang 110006, China; School of Information Engineering, Shenyang University, Shenyang 110044, China.
Abstract:
Universal block diagram based schemes are proposed for modeling and simulating the fractional-order control systems in this paper. A fractional operator block in Simulink is designed to evaluate the fractional-order derivative and integral. Based on the block, the fractional-order control systems with zero initial conditions can be modeled conveniently. For modeling the system with nonzero initial conditions, the auxiliary signal is constructed in the compensation scheme. Since the compensation scheme is very complicated, therefore the integrator chain scheme is further proposed to simplify the modeling procedures. The accuracy and effectiveness of the schemes are assessed in the examples, the computation results testify the block diagram scheme is efficient for all Caputo fractional-order ordinary differential equations (FODEs) of any complexity, including the implicit Caputo FODEs.
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