scholarly journals Forced Sliding Mode Control for Chaotic Systems Synchronization

2021 ◽  
Author(s):  
Andrey A. Kuz'menko
Keyword(s):  
Robust Control ◽  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Engineering Problem ◽  
Control Laws ◽  
Mode Control ◽  
Performance Indexes ◽  
Chattering Effect ◽  
Method Of Design

Abstract Synchronization of chaotic systems is considered to be a common engineering problem. However, the proposed laws of synchronization control do not always provide robustness towards the parametric perturbations. The purpose of this article is to show the use of synergy-cybernetic approach for the construction of robust law for Arneodo chaotic systems synchronization. As the main method of design of robust control, the method of design of control with forced sliding mode of the synergetic control theory is considered. To illustrate the effectiveness of the proposed law it's compared in this article with the classical sliding mode control. The distinctive features of suggested robust control law are the more good compensation of parametric perturbations (better performance indexes --- the root-mean-square error, average absolute value of error) without designing perturbation observers, the ability to exclude the chattering effect, less energy-consuming and a simpler analysis of the stability of a closed-loop system. Offered approach will allow a new consideration for the design of robust control laws for chaotic systems, taking into account the ideas of directed self-organization and robust control. It can be used for synchronization other chaotic systems.Mathematics Subject Classification (2020) 93B35 · 93B52 · 93C30 · 93D21 · 34H10

scholarly journals THE USE OF FORCED SLIDING MODE CONTROL FOR CHAOTIC SYSTEMS SYNCHRONI-ZATION

2021 ◽  
pp. 101-113
Author(s):  
A.A. Kuz’menko ◽  
Keyword(s):  
Robust Control ◽  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Self Organization ◽  
Control Laws ◽  
Mode Control

The article demonstrates the application of the forced sliding mode control to the construction of ro-bust control laws for chaotic systems synchronization. The proposed method will allow a new ap-proach to the synthesis of robust control laws for chaotic systems, taking into account the ideas of di-rected self-organization and robust control.

Application of adaptive sliding mode control (sigma adaption method) for an uncertain three-story benchmark structure

2019 ◽  
Vol 23 (3) ◽  
pp. 497-509
Author(s):  
Javad Katebi ◽  
Jafar Jangara
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Gain Control ◽  
Adaptive Sliding Mode Control ◽  
Control Effort ◽  
Adaptive Sliding Mode ◽  
Mode Control ◽  
Performance Indexes ◽  
Control Gain ◽  
Chattering Effect

This study develops the application of adaptive sliding mode control to earthquake-excited uncertain structures. Adaptive sliding mode control is useful as it only requires the boundness feature of uncertainties and disturbances to determine control gain (and not the amplitude of bounds). Moreover, the amplitude of chattering effect, the main drawback of sliding mode control, attenuates while stability and robustness are preserved. For this purpose, two adaptive-gain control algorithms are considered. In addition, a time-varying boundary layer is considered to increase the accuracy. In order to examine the feasibility of the applied method, a three-story benchmark structure is considered. Furthermore, performance indexes are used to evaluate the effectiveness of adaptive sliding mode control in comparison to sliding mode control and fuzzy sliding mode control. Comparison of the simulation results in accordance to performance indexes demonstrates that adaptive sliding mode control not only attenuates the amplitude of control effort (i.e. chattering amplitude) but also makes the control of the maximum response of the structure applying adaptive sliding mode control more convenient. It is shown that displacement and drift performance indexes of adaptive sliding mode control are equal to or less than ones of sliding mode control, while root mean square of the control effort of adaptive sliding mode control is attenuated around 50%.

Robust Control of Permanent Magnet Synchronous Motor: Synergetic Approach

2020 ◽  
Vol 21 (8) ◽  
pp. 480-488
Author(s):  
A. A. Kuz’menko
Keyword(s):  
Robust Control ◽  
Sliding Mode Control ◽  
Permanent Magnet ◽  
Sliding Mode ◽  
System Stability ◽  
Stability Conditions ◽  
Rotor Speed ◽  
Control Laws ◽  
Mode Control ◽  
The Stability

Permanent magnet synchronous motors (PMSM) are widely used in practice due to its high-energy efficiency, compactness, reliability and high regulation performance. When controlling a PMSM rotor speed, the main control principle is the principle of cascade control with PI-regulators, which includes an external control loop for speed and two internal loops for stator currents along the (d, q)-axes. There are attempts to eliminate the disadvantages of this principle using for the control laws synthesis of modern methods of nonlinear control such methods as linearization feedback, backstepping, predictive control, sliding mode control, methods of robust and adaptive control, fuzzy and neural network control, a combination of these methods etc. However, in most cases, the use of these methods are intended to by means of an appropriate method to synthesize a static or dynamic set points for the standard PI-controllers of rotor speed and currents. In this paper we propose to consider two approaches of synergetic control theory (SCT) to construct a robust control law of PMSM: a sliding mode control laws design by the SCT method with subsequent invariant manifolds aggregation and the principle of integral adaptation (PIA). These approaches implement vector control and are not guided by the standard structure of the principle of cascade regulation of PMSM. The proposed approaches simplify the stability analysis of the closed-loop system: stability conditions consist of stability conditions of functional equations of SCT and the stability conditions for finish decomposed system, which the dimension is substantially less than the dimension of the original system. From the results of the comparisons of synthesized the PMSM robust control laws, we can say that more preferable laws synthesized in accordance with the PIA. The theoretical positions of this paper are illustrated by the results of modeling, which are showing the fulfillment of the control tasks: the achievement of targets, robustness to the change of the PMSM load moment.

Fractional Dynamic Sliding Mode Control for uncertain chaotic systems Applied to a Chaotic Robot arm under dynamic load.

2020 ◽  
Vol 10 ◽  
Author(s):  
Sara Gholipour P ◽  
Sara Minagar ◽  
Javad Kazemitabar ◽  
Mobin Alizadeh
Keyword(s):  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Qualitative And Quantitative ◽  
Mode Control ◽  
Quantitative Characteristics ◽  
Dynamic Sliding Mode Control ◽  
Dynamic Sliding Mode ◽  
Qualitative And Quantitative Characteristics

Background: A novel type of control strategy is presented for control of chaotic systems particularly a chaotic robot in joint and workspace which is the result of applying fractional calculus to dynamic sliding mode control. Objectives: To guarantee the sliding mode condition, control law is introduced based on the Lyapunov stability theory. Methods: A control scheme is proposed for reducing the chattering problem in finite time tracking and robust in presence of system matched disturbances. Conclusion: Also, all of chaotic robot's qualitative and quantitative characteristics have been investigated. Numerical simulations indicate viability of our control method. Results: Qualitative and quantitative characteristics of the chaotic robot are all proven to be viable thru simulations.

Robust sliding mode control for a class of underactuated systems with mismatched uncertainties

2009 ◽  
Vol 223 (6) ◽  
pp. 785-795 ◽  
Author(s):  
D W Qian ◽  
X J Liu ◽  
J Q Yi
Keyword(s):  
Robust Control ◽  
Sliding Mode Control ◽  
Control Method ◽  
Sliding Mode ◽  
Underactuated Systems ◽  
Sliding Surface ◽  
Nominal System ◽  
Sliding Surfaces ◽  
Mode Control ◽  
Mismatched Uncertainties

Based on the sliding mode control methodology, this paper presents a robust control strategy for underactuated systems with mismatched uncertainties. The system consists of a nominal system and the mismatched uncertainties. Since the nominal system can be considered to be made up of several subsystems, a hierarchical structure for the sliding surfaces is designed. This is achieved by taking the sliding surface of one of the subsystems as the first-layer sliding surface and using this sliding surface and the sliding surface of another subsystem to construct the second-layer sliding surface. This process continues till the sliding surfaces of all the subsystems are included. A lumped sliding mode compensator is designed at the last-layer sliding surface. The asymptotic stability of all of the layer sliding surfaces and the sliding surface of each subsystem is proven. Simulation results show the validity of this robust control method through stabilization control of a system consisting of two inverted pendulums and mismatched uncertainties.

Global sliding mode control and application in chaotic systems

2008 ◽  
Vol 56 (1-2) ◽  
pp. 193-198 ◽  
Author(s):  
Leipo Liu ◽  
Zhengzhi Han ◽  
Wenlin Li
Keyword(s):  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Mode Control ◽  
Global Sliding Mode Control
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