scholarly journals Stability Analysis of Systems with Fuzzy PI Controllers Applied to Electric Drives

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1246
Author(s):  
Constantin Voloşencu
Keyword(s):  
Stability Analysis ◽  
Control Systems ◽  
Fuzzy Controller ◽  
Stability Domain ◽  
Input Output ◽  
Electric Drives ◽  
Output Stability ◽  
Pi Controllers ◽  
The Stability ◽  
Internal And External Stability

This paper analyzes the stability of fuzzy control systems with applications for electric drives. Ensuring the stability of these systems is a necessity in practice. The purpose of the study is the analysis of the dynamic characteristics of the speed control systems of electric drives based on fuzzy PI controllers in the context of performing stability analyses, both internal and input–output, finding solutions to stabilize these systems and provide guidance on fuzzy regulator design. The main methods of treatment applied are as follows: framing the control system in the theory of stability of multivariable non-linear systems, application of Lyapunov’s theory, performing an input–output stability analysis, and verification of the stability domain. The article presents the conditions for correcting the fuzzy controller to ensure internal and external stability, determines the limits of the stability sector, and gives indications for choosing the parameters of the controller. The considerations presented can be applied to various structures for regulating the speed of electric drives which use various PI fuzzy controllers.

scholarly journals Iterative stability analysis for general polynomial control systems

2021 ◽  
Author(s):  
Bo Xiao ◽  
Hak-Keung Lam ◽  
Zhixiong Zhong
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Control Systems ◽  
Polynomial System ◽  
Stability Conditions ◽  
General Polynomial ◽  
Main Challenge ◽  
Detailed Simulation ◽  
Feasible Solutions ◽  
The Stability

AbstractThe main challenge of the stability analysis for general polynomial control systems is that non-convex terms exist in the stability conditions, which hinders solving the stability conditions numerically. Most approaches in the literature impose constraints on the Lyapunov function candidates or the non-convex related terms to circumvent this problem. Motivated by this difficulty, in this paper, we confront the non-convex problem directly and present an iterative stability analysis to address the long-standing problem in general polynomial control systems. Different from the existing methods, no constraints are imposed on the polynomial Lyapunov function candidates. Therefore, the limitations on the Lyapunov function candidate and non-convex terms are eliminated from the proposed analysis, which makes the proposed method more general than the state-of-the-art. In the proposed approach, the stability for the general polynomial model is analyzed and the original non-convex stability conditions are developed. To solve the non-convex stability conditions through the sum-of-squares programming, the iterative stability analysis is presented. The feasible solutions are verified by the original non-convex stability conditions to guarantee the asymptotic stability of the general polynomial system. The detailed simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed approach is more capable to find feasible solutions for the general polynomial control systems when compared with the existing ones.

Lyapunov approach based design of a gain adaptive interval type-2 fuzzy controller for servo systems

2020 ◽  
pp. 1-19
Author(s):  
Ritu Rani De (Maity) ◽  
Rajani K. Mudi ◽  
Chanchal Dey
Keyword(s):  
Fuzzy Logic ◽  
Stability Analysis ◽  
Fuzzy Controller ◽  
Rule Base ◽  
Performance Study ◽  
Servo Systems ◽  
Lyapunov Approach ◽  
The Stability ◽  
Interval Type

This paper focuses on the development of a stable Mamdani type-2 fuzzy logic based controller for automatic control of servo systems. The stability analysis of the fuzzy controller has been done by employing the concept of Lyapunov. The Lyapunov approach results in the derivation of an original stability analysis that can be used for designing the rule base of our proposed online gain adaptive Interval Type-2 Fuzzy Proportional Derivative controller (IT2-GFPD) for servo systems with assured stability. In this approach a Quadratic positive definite Lyapunov function is used and sufficient stability conditions are satisfied by the adaptive type-2 fuzzy logic control system. Illustrative simulation studies with linear and nonlinear models as well as experimental results on a real-time servo system validate the stability and robustness of the developed intelligent IT2-GFPD. A comparative performance study of IT2-GFPD with other controllers in presence of noise and disturbance also proves the superiority of the proposed controller.

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