lyapunov stability theory
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Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 171
Author(s):  
Jiguang Hou ◽  
Xianteng Cao ◽  
Changshu Zhan

Suspension is an important part of intelligent and safe transportation; it is the balance point between the comfort and handling stability of a vehicle under intelligent traffic conditions. In this study, a control method of left-right symmetry of air suspension based on H∞ theory was proposed, which was verified under intelligent traffic conditions. First, the control stability caused by the active suspension control system running on uneven roads needs to be ensured. To address this issue, a 1/4 vehicle active suspension model was established, and the vertical acceleration of the vehicle body was applied as the main index of ride comfort. H∞ performance constraint output indicators of the controller contained the tire dynamic load, suspension dynamic stroke, and actuator control force limit. Based on the Lyapunov stability theory, an output feedback control law with H∞-guaranteed performance was proposed to constrain multiple targets. This way, the control problem was transformed into a solution to the Riccati equation. The simulation results showed that when dealing with general road disturbances, the proposed control strategy can reduce the vehicle body acceleration by about 20% and meet the requirements of an ultimate suspension dynamic deflection of 0.08 m and a dynamic tire load of 1500 N. Using this symmetrical control method can significantly improve the ride comfort and driving stability of a vehicle under intelligent traffic conditions.


Actuators ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 18
Author(s):  
Fahimeh Shiravani ◽  
Patxi Alkorta ◽  
Jose Antonio Cortajarena ◽  
Oscar Barambones

In this paper, an enhanced Integral Sliding Mode Control (ISMC) for mechanical speed of an Induction Motor (IM) is presented and experimentally validated. The design of the proposed controller has been done in the d-q synchronous reference frame and indirect Field Oriented Control (FOC). Global asymptotic speed tracking in the presence of model uncertainties and load torque variations has been guaranteed by using an enhanced ISMC surface. Moreover, this controller provides a faster speed convergence rate compared to the conventional ISMC and the Proportional Integral methods, and it eliminates the steady-state error. Furthermore, the chattering phenomenon is reduced by using a switching sigmoid function. The stability of the proposed controller under parameter uncertainties and load disturbances has been provided by using the Lyapunov stability theory. Finally, the performance of this control method is verified through numerical simulations and experimental tests, getting fast dynamics and good robustness for IM drives.


Electronics ◽  
2022 ◽  
Vol 11 (2) ◽  
pp. 179
Author(s):  
Jun Dai ◽  
Yi Zhang ◽  
Hua Deng

Existing hybrid force/position control algorithms mostly explicitly contain a dynamic model. Moreover, force and position controllers will be switched frequently. To solve the above problems, a novel voltage-based weighted hybrid force/position control algorithm is proposed for redundant robot manipulators. Firstly, mapping between voltage and terminal position and orientation is established so that the designed controller can be simplified by adopting the motor current as the feedback to replace the tedious calculation of the dynamic model. Secondly, a voltage-based weighted hybrid force/position control algorithm is proposed to eliminate the selection matrix. Force and position control laws are summed directly through a weighted way to avoid the problems of space decomposition and switching. Thirdly, the stability is proven using Lyapunov stability theory, then the selection method for weighted coefficient is provided. Fourthly, comparative simulations are performed. Results show that the proposed algorithm is suitable for impedance control and hybrid force/position control and can compensate for their deficiencies. Lastly, the transport experiment in the YZ plane is conducted. Results show that position and force accuracies in the Y- and Z-axis directions are 3.489 × 10−4 and 7.313 × 10−4 m and 1.238 × 10−1 and 1.997 × 10−1 N, respectively. Accordingly, it can effectively improve the operation capability and control accuracy.


2022 ◽  
Vol 9 ◽  
Author(s):  
Shunjie Li ◽  
Yawen Wu ◽  
Gang Zheng

In this paper, the adaptive control design is investigated for the chaos synchronization of two identical hyperchaotic Liu systems. First, an adaptive control law with two inputs is proposed based on Lyapunov stability theory. Secondly, two other control schemes are obtained based on a further analysis of the proposed adaptive control law. Finally, numerical simulations are presented to validate the effectiveness and correctness of these results.


2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ahmed S. Al-Obeidi ◽  
Saad Fawzi Al-Azzawi ◽  
Abdulsattar Abdullah Hamad ◽  
M. Lellis Thivagar ◽  
Zelalem Meraf ◽  
...  

In this study, a novel 7D hyperchaotic model is constructed from the 6D Lorenz model via the nonlinear feedback control technique. The proposed model has an only unstable origin point. Thus, it is categorized as a model with self-excited attractors. And it has seven equations which include 19 terms, four of which are quadratic nonlinearities. Various important features of the novel model are analyzed, including equilibria points, stability, and Lyapunov exponents. The numerical simulation shows that the new class exhibits dynamical behaviors such as chaotic and hyperchaotic. This paper also presents the hybrid synchronization for a novel model via Lyapunov stability theory.


2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Abdulsattar Abdullah Hamad ◽  
M. Lellis Thivagar ◽  
Jalawi Alshudukhi ◽  
Talal Saad Alharbi ◽  
Saud Aljaloud ◽  
...  

Chaotic systems are one of the most significant systems of the technological period because their qualities must be updated on a regular basis in order for the speed of security and information transfer to rise, as well as the system’s stability. The purpose of this research is to look at the special features of the nine-dimensional, difficult, and highly nonlinear hyperchaotic model, with a particular focus on synchronization. Furthermore, several criteria for such models have been examined; Hamiltonian, synchronizing, Lyapunov expansions, and stability are some of the terms used. The geometrical requirements, which play an important part in the analysis of dynamic systems, are also included in this research due to their importance. The synchronization and control of complicated networks’ most nonlinear control is important to use and is based on two major techniques. The linearization approach and the Lyapunov stability theory are the foundation for attaining system synchronization in these two ways.


2021 ◽  
Author(s):  
Shiju Yang ◽  
Chuandong Li ◽  
Yu Li ◽  
Ting Yang ◽  
Bo Li

Abstract In this paper, the fixed-time bipartite synchronization problem for coupled delayed neural networks with signed graphs is discussed. Different from traditional neural networks, the interactions between nodes of delayed neural networks can be either collaborative or antagonistic. Furthermore, compared with the initial-condition based finite-time synchronization, the settling time is bounded by a constant within fixedtime regardless of the initial condition. It is worth noting that the fixed-time stable network for bipartite synchronization in this paper achieves more faster convergence than most existing publications. By applying constructing comparison system method, Lyapunov stability theory and inequality techniques, some sufficient criteria for fixed-time bipartite synchronization are obtained. Finally, two numerical examples are granted to display the performance of the obtained results.


Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3281
Author(s):  
Shunjie Li ◽  
Yawen Wu ◽  
Xuebing Zhang

In this paper, a new four-dimensional hyperchaotic system with an exponential term is presented. The basic dynamical properties and chaotic behavior of the new attractor are analyzed. It can be shown that this system possesses either a line of equilibria or a single one. The existence of hyperchaos is confirmed by its Lyapunov exponents. Moreover, the synchronization problem for the hyperchaotic system is studied. Based on the Lyapunov stability theory, an adaptive control law with two inputs is proposed to achieve the global synchronization. Numerical simulations are given to validate the correctness of the proposed control law.


2021 ◽  
Vol 4 (1) ◽  
pp. 16-24
Author(s):  
Laith Ahmed Najam ◽  
Ayman Al Sawalha

This article addresses control for the chaos anti-synchronization of a high frequency oscillator nuclear spin generator (NSG), which generates and controls the oscillations of the motion of a nuclear magnetization vector in a magnetic field. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical (NSG) asymptotically anti-synchronized with uncertain parameters. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos anti-synchronization scheme .


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