scholarly journals Simplified Fractional Order Controller Design Algorithm

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1166 ◽  
Author(s):  
Eva-Henrietta Dulf
Keyword(s):  
Frequency Domain ◽  
Fractional Order ◽  
Closed Loop ◽  
Controller Design ◽  
Process Models ◽  
System Of Nonlinear Equations ◽  
Design Algorithm ◽  
Wide Range ◽  
Fractional Order Controller ◽  
Tuning Rules

Classical fractional order controller tuning techniques usually establish the parameters of the controller by solving a system of nonlinear equations resulted from the frequency domain specifications like phase margin, gain crossover frequency, iso-damping property, robustness to uncertainty, etc. In the present paper a novel fractional order generalized optimum method for controller design using frequency domain is presented. The tuning rules are inspired from the symmetrical optimum principles of Kessler. In the first part of the paper are presented the generalized tuning rules of this method. Introducing the fractional order, one more degree of freedom is obtained in design, offering solution for practically any desired closed-loop performance measures. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, using simple tuning-friendly equations. It can be applied to a wide range of process models, from integer order models to fractional order models. Simulation results are given to highlight these advantages.

Fractional order PI λ D μ controller design for satisfying time and frequency domain specifications simultaneously

2017 ◽  
Vol 68 ◽  
pp. 212-222 ◽  
Author(s):  
WeiJia Zheng ◽  
Ying Luo ◽  
XiaoHong Wang ◽  
YouGuo Pi ◽  
YangQuan Chen
Keyword(s):  
Frequency Domain ◽  
Fractional Order ◽  
Controller Design

scholarly journals The discrete-time tracking problem with H∞ model matching approach plus integral control

2019 ◽  
Vol 292 ◽  
pp. 01018
Author(s):  
Murat Akın ◽  
Tankut Acarman
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Controller Design ◽  
Model Matching ◽  
Matching Problem ◽  
Design Algorithm ◽  
Integral Control ◽  
Loop Transfer Function ◽  
Model Transfer ◽  
Static Output

In this study, the discrete-time H∞ model matching problem with integral control by using 2 DOF static output feedback is presented. First, the motivation and the problem is stated. After presenting the notation, the two lemmas toward the discrete-time H∞ model matching problem with integral control are proven. The controller synthesis theorem and the controller design algorithm is elaborated in order to minimize the H∞ norm of the closed-loop transfer function and to maximize the closed-loop performance by introducing the model transfer matrix. In following, the discrete-time H∞ MMP via LMI approach is derived as the main result. The controller construction procedure is implemented by using a well-known toolbox to improve the usability of the presented results. Finally, some conclusions are given.

scholarly journals Novel Optimum Magnitude Based Fractional Order Controller Design Method

2018 ◽  
Vol 51 (4) ◽  
pp. 912-917 ◽  
Author(s):  
Eva-H. Dulf ◽  
Mircea Șușcă ◽  
Levente Kovács
Keyword(s):  
Fractional Order ◽  
Controller Design ◽  
Design Method ◽  
Fractional Order Controller

Stability analysis of a discrete-time system with a variable-, fractional-order controller

2010 ◽  
Vol 58 (4) ◽  
pp. 613-619 ◽  
Author(s):  
P. Ostalczyk
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Discrete Time ◽  
Closed Loop ◽  
Control Strategies ◽  
Discrete Time System ◽  
Time System ◽  
Matrix Condition Number ◽  
Fractional Order Controller ◽  
Matrix Condition

Stability analysis of a discrete-time system with a variable-, fractional-order controllerVariable, fractional-order backward difference is a generalisation of commonly known difference or sum. Equations with these differences can be used to describe a variable-, fractional order digital control strategies. One should mention, that classical tools such as a state-space description and discrete transfer function cannot be used in the analysis and synthesis of such a type of systems. Equations describing a closed-loop system are proposed. They contain square matrices imitating the action of matrices in the system polynomial matrix description. This paper focuses on the stability analysis of a closed-loop SISO linear system with a controller described by the equations mentioned. A stability condition based on a transient denominator matrix condition number is proposed. Investigations are supported by two numerical examples.

scholarly journals Robust Synchronization Controller Design for a Class of Uncertain Fractional Order Chaotic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Lin Wang ◽  
Chunzhi Yang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Closed Loop System ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Lyapunov Stability Criterion ◽  
Theoretical Results

Synchronization problem for a class of uncertain fractional order chaotic systems is studied. Some fundamental lemmas are given to show the boundedness of a complicated infinite series which is produced by differentiating a quadratic Lyapunov function with fractional order. By using the fractional order extension of the Lyapunov stability criterion and the proposed lemma, stability of the closed-loop system is analyzed, and two sufficient conditions, which can enable the synchronization error to converge to zero asymptotically, are driven. Finally, an illustrative example is presented to confirm the proposed theoretical results.

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