lyapunov method
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2022 ◽  
pp. 107754632110421
ShengChao Zhen ◽  
MuCun Ma ◽  
XiaoLi Liu ◽  
Feng Chen ◽  
Han Zhao ◽  

In this paper, we design a novel robust control method to reduce the trajectory tracking errors of the SCARA robot with uncertainties including parameters such as uncertainty of the mechanical system and external disturbance, which are time-varying and nonlinear. Then, we propose a deterministic form of the model-based robust control algorithm to deal with the uncertainties. The proposed control algorithm is composed of two parts according to the assumed upper limit of the system uncertainties: one is the traditional proportional-derivative control, and the other is the robust control based on the Lyapunov method, which has the characteristics of model-based and error-based. The stability of the proposed control algorithm is proved by the Lyapunov method theoretically, which shows the system can maintain uniformly bounded and uniformly ultimately bounded. The experimental platform includes the rapid controller prototyping cSPACE, which is designed to reduce programming time and to improve the efficiency of the practical operation. Moreover, we adopt different friction models to investigate the effect of friction on robot performance in robot joints. Finally, numerical simulation and experimental results indicate that the control algorithm proposed in this paper has desired control performance on the SCARA robot.

2022 ◽  
Vol 355 ◽  
pp. 03063
Run Lu ◽  
Guichen Zhang ◽  
Jianqiang Shi

A stable adaptive control scheme for multi-point mooring system (MPMS) with uncertain dynamics is proposed in this paper. The control scheme is designed by a hybrid controller based on RBF (Radial Basis Function) NN (Neural Network) and SMC (Sliding Mode Control), which learns the MPMS dynamic changes, and the compensation of external disturbances is realized through adaptive RBFNN control. Meanwhile the RBF-SMC control parameters are adapted by the Lyapunov method to minimize squares dynamic positioning (DP) error. The convergence of the hybrid controller is proved theoretically, and the proposed mooring control scheme is applied to the “Kantan3” mooring simulation system. Finally, the simulation results are compared with the traditional PID controller and standard RBF controller to demonstrate the effective mooring positioning performance of the control scheme for the MPMS.

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Abdulsattar Abdullah Hamad ◽  
M. Lellis Thivagar ◽  
Malik Bader Alazzam ◽  
Fawaz Alassery ◽  
Muayyad Mahmood Khalil ◽  

Hybrid synchronization is one of the most significant aspects of a dynamic system. We achieve nonlinear control unit results to synchronize two comparable 7D structures in this study. Many dynamic systems are directly connected to health care and directly enhance health. We employed linearization and Lyapunov as analytical methods, and since the linearization method does not need updating the Lyapunov function, it is more successful in achieving synchronization phenomena with better outcomes than the Lyapunov method. The two methods were combined, and the result was a striking resemblance to the dynamic system’s mistake. The mathematical system with control and error of the dynamic system was subjected to digital emulation. The digital good outcomes were comparable to the two methods previously stated. We compared the outcomes of three hybrid synchronizations based on Lyapunov and linearization methods. Finally, we used the existing system, presenting it in a new attractor and comparing the findings to those of other similar systems.

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3139
Mireya Cabezas-Olivenza ◽  
Ekaitz Zulueta ◽  
Ander Sánchez-Chica ◽  
Adrian Teso-Fz-Betoño ◽  
Unai Fernandez-Gamiz

There is presently a need for more robust navigation algorithms for autonomous industrial vehicles. These have reasonably guaranteed the adequate reliability of the navigation. In the current work, the stability of a modified algorithm for collision-free guiding of this type of vehicle is ensured. A lateral control and a longitudinal control are implemented. To demonstrate their viability, a stability analysis employing the Lyapunov method is carried out. In addition, this mathematical analysis enables the constants of the designed algorithm to be determined. In conjunction with the navigation algorithm, the present work satisfactorily solves the localization problem, also known as simultaneous localization and mapping (SLAM). Simultaneously, a convolutional neural network is managed, which is used to calculate the trajectory to be followed by the AGV, by implementing the artificial vision. The use of neural networks for image processing is considered to constitute the most robust and flexible method for realising a navigation algorithm. In this way, the autonomous vehicle is provided with considerable autonomy. It can be regarded that the designed algorithm is adequate, being able to trace any type of path.

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1631
Gani Stamov ◽  
Ivanka Stamova ◽  
Cvetelina Spirova

In this paper we study an impulsive delayed reaction-diffusion model applied in biology. The introduced model generalizes existing reaction-diffusion delayed epidemic models to the impulsive case. The integral manifolds notion has been introduced to the model under consideration. This notion extends the single state notion and has important applications in the study of multi-stable systems. By means of an extension of the Lyapunov method integral manifolds’ existence, results are established. Based on the Lyapunov functions technique combined with a Poincarè-type inequality qualitative criteria related to boundedness, permanence, and stability of the integral manifolds are also presented. The application of the proposed impulsive control model is closely related to a most important problems in the mathematical biology—the problem of optimal control of epidemic models. The considered impulsive effects can be used by epidemiologists as a very effective therapy control strategy. In addition, since the integral manifolds approach is relevant in various contexts, our results can be applied in the qualitative investigations of many problems in the epidemiology of diverse interest.

Haris Calgan

Purpose This study aims to design and implement a novel tilt integral sliding mode controller and observer for sensorless speed control of a permanent magnet synchronous motor (PMSM). Design/methodology/approach A control strategy combining the tilt integral derivative (TID) with sliding mode control (SMC) is proposed to determine the tilt integral sliding mode manifold. Using this manifold, tilt integral sliding mode controller (TISMC) and observer (TISMO) are designed. The stabilities are verified by using Lyapunov method. To prove the effectiveness and robustness of proposed methods, sensorless speed control of PMSM is performed for various operating conditions such as constant and variable speed references, load disturbance injection, parameter perturbation, whereas sensor noises are not taken into account. The performance of proposed method is compared with TID controller, proportional integral derivative controller and conventional SMO. Findings Simulation results demonstrate that TISMC and TISMO have better performance in all operating conditions. They are robust against parameter uncertainties and disturbances. TISM based sensorless control of PMSM is well guaranteed with superior performance. Originality/value The proposed method has not been tackled in the literature. By combining TID and SMC, novel tilt integral sliding manifold is presented and used in designing of the controller and observer. It is proven by Lyapunov method that errors converge to zero.

Andrii Hnatov ◽  
Shchasiana Arhun ◽  
Ruslan Bagach ◽  
Hanna Hnatova ◽  
Valentina Tarasova ◽  

Problem. There are many methods for determining the stability of the energy system. In normal operating condition (normal rated mode), the power system must reliably ensure the consumption of electricity of normalized quality. However, in addition to the normal state, there are emergency and transient states caused by various transients. This is due to the fact that the energy system is constantly changing its parameters. Such changes are determined by variations in the amount of power produced and consumed, as well as the changes in system configuration. Goal. The goal is studying the possibilities of various methods of determining the power systems stability and drawing up the general algorithm of actions for maintenance of their stability. Methodology. When determining the stability of energy systems by the Lyapunov method, two methods can be used: the direct method and the first approximation method. Lyapunov direct method refers to differential methods. To conclude about the stability of the system we do not find a general or particular solution of differential equations, but with their help we find a mathematical function, the complete derivative of which over time allows to obtain a conclusion about the stability of the system. Results. Many methods can be used to determine whether a sustainable energy system is stable or not. The most common are the Lyapunov methods and the Moiseev method. It is determined that the direct Lyapunov method refers to differential methods. The application of the direct Lyapunov method for energy problems is limited. Currently, it can be used only for some individual cases. The method of the first approximation (Lyapunov first method) has received wider application in the solution of power problems. When applying this method, which belongs to the group of methods of full integration, the right-hand sides of the equations are decomposed into power series. Originality. It is determined that one of the perspective directions of increasing the efficiency of the mathematical device work is using the methods of the second order in modeling and optimization of operating modes of electric power systems. This allows you to increase the speed and reliability of the convergence of iterative processes. Practical value. Based on the analysis of various existing methods for solving the problems of stability of energy systems, an algorithm of actions is proposed and developed, which will help to solve the problem of stability in practice.

Ubong D. Akpan

In this paper, the effects of circulatory forces on undamped gyroscopic systems have been studied. The stability or otherwise of arising MGKN systems have been analysed using eigenvalue method and Lyapunov method. Bottema-Lakhadanov-Karapetyan theorem is also employed to further analyze the systems. Examples are given to illustrate the use of these methods in determining the stability or otherwise of undamped gyroscopic circulatory systems.

2021 ◽  
Yufei Guo ◽  
Baolin Hou ◽  
Shengyue Xu ◽  
Ruilin Mei ◽  
Zhigang Wang ◽  

Abstract Oscillatory base manipulators (OBMs) are a kind of mechanical systems suffering from unexpected base oscillations. The oscillations affect tremendously system stability. Various control methods have been explored, but most of them require measurement or prediction of the oscillations. This study is concerned with a novel OBM-the autoloader, which are used in modern, autonomous main battle tanks. The base oscillation of the autoloader is hard to be obtained in practice. Furthermore, control synthesis for autoloaders is complicated with intrinsic payload uncertainty and actuator saturation. To address these issues, a novel robust control scheme is proposed in this work relying on the implicit Lyapunov method. Moreover, a novel two-Degree-of-Freedom manipulator operating on a vibrating base is constructed to realize the proposed control. To the best of the authors' knowledge, this is the first study considering both control and hardware implementation for the OBM-like autoloaders. Experimental results demonstrate that, although without prior information of the base oscillation, the proposed controller exhibits good robustness against the base oscillation and payload uncertainty.

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