Abstract
The fractional-order proportional-integral (FOPI) controller tuning rules based on the fractional calculus for the parallel cascade control systems are systematically proposed in this paper. The modified parallel cascade control structure (PCCS) with the Smith predictor is addressed for stable, unstable, and integrating process models with time delays. Normally, the PCCS consists of three controllers, including a stabilized controller, for a class of unstable and integrating models, a disturbance rejection controller in the secondary loop, and a primary servomechanism controller. Accordingly, the ideal controller is obtained by using the internal model control (IMC) approach for the inner loop. The proportional-derivative (PD) controller is suggested for the stabilized controller and is designed based on a stability criterion. Based on the fractional calculus, the analytical tuning rules of the FOPI controller for the outer loop can be established in the frequency domain. The simulation study is considered for three mentioned cases of process models and the results demonstrate the flexibility and effectiveness of the proposed method for the PCCS in comparison with the other methods. The robustness of the proposed method is also justified by perturbed process models with ±20% of process parameters including gain, time constant, and delay time.
Highlights
Cascade control is commonly used in industrial processes
The authors adopted a proportionalderivative (PD) controller to stabilize the unstable/integrating processes and used the internal model control (IMC) approach to design the controller for disturbance rejection in the secondary loop
Our aim is to design an analytic method of a generalized fractional-order proportional-integral (FOPI) controller for the primary loop of a parallel cascade control structure (PCCS) with a time delay to enhance the performances of designed systems
Summary
Cascade control is commonly used in industrial processes. It is adopted to reduce disturbance and improve the servo response of the closed-loop system. Our aim is to design an analytic method of a generalized FOPI controller for the primary loop of a PCCS with a time delay to enhance the performances of designed systems. It is mainly based on the concepts of fractional calculus and the IMC approach by using the frequency domain [18]. The tuning rule of the FOPI controller for primary processes can be derived directly without introducing any nonlinear objective function, and the proposed method can be applied for many typical process models including stable, unstable, and integrating primary processes
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