Abstract
This paper proposes a design method for a robust fractional-order PID (FOPID) controller for time-delay systems. A new Bode's ideal transfer function is introduced to tolerance the time-delay in loop. Robust stability is analyzed for the Bode's model in terms of gain and phase margins to help the parameter tuning. To simplify FOPID design from solving nonlinear equations, five unknown parameters are reduced to one in the Bode shaping by data fitting between a parametric model and the real plant. Then, the problem is simply solved by one-dimensional searching. Furthermore, the proposed FOPID controller design is extended to multi-input and multi-output (MIMO) systems by using disturbance observer (DOB). Finally, simulation results are presented to show the effectiveness of the proposed method.
Highlights
In the past decades, an increasing number of studies are focusing on the application of fractional calculus in many areas of industrial engineering
Bode shaping is an effective method for control system design in frequency domain [20]–[26] As a good open-loop model, Bode’s ideal transfer function is discussed in [22], which shows its stronger robustness against loop gain variation
We aim to propose a robust fractional-order PID (FOPID) controller design for time-delay systems by Bode shaping
Summary
An increasing number of studies are focusing on the application of fractional calculus in many areas of industrial engineering. Bode shaping is an effective method for control system design in frequency domain [20]–[26] As a good open-loop model, Bode’s ideal transfer function is discussed in [22], which shows its stronger robustness against loop gain variation. We aim to propose a robust FOPID controller design for time-delay systems by Bode shaping. To realize this goal, two problems are solved in this paper: VOLUME 8, 2020. This problem is seldom discussed in the current Bode shaping methods [37], [38] We solve this problem by investigating the gain and phase margins for the proposed time-delay Bode’s model.
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