A Graphical Design Method of Fractional-Order Proportional-Derivative Controllers for Fractional-Order Integrating Systems with Time Delays

2021 ◽  
Author(s):  
Xu Li ◽  
Daqing Wang ◽  
Dun Hu ◽  
Qianqian Zhang ◽  
Lifu Gao
Keyword(s):  
Fractional Order ◽  
Time Delays ◽  
Design Method ◽  
Graphical Design

Observer design for positive fractional-order interconnected time-delay systems

2018 ◽  
Vol 41 (2) ◽  
pp. 378-391 ◽  
Author(s):  
Hieu Trinh ◽  
Dinh Cong Huong ◽  
Saeid Nahavandi
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Time Delays ◽  
Large Scale ◽  
Design Method ◽  
Observer Design ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Reduced Order ◽  
Necessary And Sufficient

This paper considers the problem of designing positive reduced-order distributed functional observers for positive fractional-order interconnected time-delay systems. The systems under consideration belong to a class of large-scale fractional-order systems where each system is formed by [Formula: see text] ([Formula: see text]) interconnected subsystems with heterogeneous time delays in the interconnections and the local state vectors. First, a necessary and sufficient condition to ensure the positivity of the considered system is derived. Based on this result, [Formula: see text] stand-alone reduced-order positive distributed functional observers for the system are designed. These observers are always nonnegative at any time and they converge asymptotically to the true functional state vectors of the system. The designed observer for each subsystem is based on the local outputs and additional outputs from other subsystems but without the need to exchange the state estimates among the observers. Conditions for the existence of such positive distributed functional observers are derived and they are translated into a linear programming problem. Finally, the effectiveness of the proposed design method is supported by four numerical examples and simulation results.

Modified Posicast Control Design Method Based on the Parameters of a Fractional Order System

2021 ◽  
Vol 143 (4) ◽  
Author(s):  
Erhan Yumuk ◽  
Müjde Güzelkaya ◽  
İbrahim Eksin
Keyword(s):  
Real Time ◽  
Fractional Order ◽  
Control Method ◽  
Design Method ◽  
Order System ◽  
Half Cycle ◽  
Empirical Formulas ◽  
Real Time System ◽  
Novel Design ◽  
Better Than

Abstract In this study, a novel design method for half-cycle and modified posicast controller structures is proposed for a class of the fractional order systems. In this method, all required design variable values, namely, the input step magnitudes and their application times are obtained as functions of fractional system parameters. Moreover, empirical formulas are obtained for the overshoot values of the compensated system with half-cycle and modified posicast controllers designed utilizing this method. The proposed design methodology has been tested via simulations and ball balancing real-time system. It is observed that the derived formulas are in coherence with outcomes of the simulation and real-time application. Furthermore, the performance of modified posicast controller designed using proposed method is much better than other posicast control method.

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