scholarly journals Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Zaiyue Yang ◽  
C. W. Chan ◽  
Yiwen Wang
Keyword(s):  
Numerical Simulation ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Closed Loop ◽  
Robust Stabilization ◽  
Control Coefficient ◽  
Control Performance ◽  
Stabilization Problem ◽  
Asymptotic Stabilization

This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.

scholarly journals A Fuzzy Approach to Robust Control of Stochastic Nonaffine Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Ting-Ting Gang ◽  
Jun Yang ◽  
Qing Gao ◽  
Yu Zhao ◽  
Jianbin Qiu
Keyword(s):  
Nonlinear Systems ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Dynamic Feedback ◽  
Stabilization Problem ◽  
Fuzzy Models ◽  
Quadratic Lyapunov Functions ◽  
Affine Nonlinear Systems ◽  
Semiglobal Stabilization ◽  
Approximation Capability

This paper investigates the stabilization problem for a class of discrete-time stochastic non-affine nonlinear systems based on T-S fuzzy models. Based on the function approximation capability of a class of stochastic T-S fuzzy models, it is shown that the stabilization problem of a stochastic non-affine nonlinear system can be solved as a robust stabilization problem of the stochastic T-S fuzzy system with the approximation errors as the uncertainty term. By using a class of piecewise dynamic feedback fuzzy controllers and piecewise quadratic Lyapunov functions, robust semiglobal stabilization condition of the stochastic non-affine nonlinear systems is formulated in terms of linear matrix inequalities. A simulation example illustrating the effectiveness of the proposed approach is provided in the end.

scholarly journals Global Finite-Time Stabilization Problem of Affine Nonlinear Systems with Unknown Functions

2021 ◽  
Author(s):  
Fujin Jia ◽  
Junwei Lu ◽  
Yong-Min Li ◽  
Fangyuan Li
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Control Algorithm ◽  
Lyapunov Analysis ◽  
Stabilization Problem ◽  
Analysis Method ◽  
Control Approach ◽  
Affine Nonlinear Systems ◽  
Simulation Results ◽  
Finite Time Stabilization

In this paper, the global finite-time stabilization (FTS) of nonlinear systems with unknown functions (UFs) is studied. Firstly, in order to deal with UFs, a Lemma is proposed to avoid the Assumptions of UFs. Secondly, based on this Lemma, the control algorithm designed by using backstepping has no partial derivative of virtual controllers, so it avoids the “differential explosion” problem of backstepping. Thirdly, by using Lyapunov analysis method, backstepping and FTS method, a global FTS control algorithm of nonlinear systems with UFs is proposed. Finally, the feasibility of developed control approach is illustrated by the simulation results of a manipulator.

Uniform robust exact differentiator based adaptive robust control for a class of nonlinear systems

2017 ◽  
Vol 40 (9) ◽  
pp. 2901-2911 ◽  
Author(s):  
Zhangbao Xu ◽  
Dawei Ma ◽  
Jianyong Yao
Keyword(s):  
Robust Control ◽  
Nonlinear Systems ◽  
Closed Loop ◽  
Lyapunov Method ◽  
Adaptive Robust Control ◽  
Experimental Results ◽  
Closed Loop System ◽  
Robust Controller ◽  
Performance Simulation ◽  
The Stability

In this paper, an adaptive robust controller with uniform robust exact differentiator has been proposed for a class of nonlinear systems with structured and unstructured uncertainties. The adaptive robust controller is integrated with an uniform robust differentiator to handle the problem of the incalculable part of the derivative of virtual controls and the differential explosion happened in backstepping techniques. The stability of the closed loop system is demonstrated via Lyapunov method ensuring a prescribed transient and tracking performance. Simulation and experimental results are carried out to verify the advantages of the proposed method.

A novel multivariable nonlinear robust control design for turbofan engines

2021 ◽  
pp. 014233122110396
Author(s):  
Dingding Cheng ◽  
Lijun Liu ◽  
Zhen Yu
Keyword(s):  
Robust Control ◽  
Closed Loop ◽  
Control Method ◽  
Operating Conditions ◽  
Large Region ◽  
Control Performance ◽  
Nonlinear Robust Control ◽  
Turbofan Engines ◽  
Robust Control Design ◽  
Nonlinear Robust

Traditional steady-state control methods are applied to turbofan engines operating in the small region near certain operating conditions, which need to switch controllers for operating in the large region and then may lead to instability and performance degradation of the closed-loop system. In this paper, a novel multivariable nonlinear robust control method for turbofan engines is proposed to improve the control performance within the large region. To enlarge the controllable region, a polynomial state-space model describes the nonlinear characteristics of turbofan engines. Based on the analysis of the closed-loop control system, by using the Lyapunov function theorems, a polynomial robust controller is designed to ensure the stability and desired nonlinear control performance of turbofan engines. Compared with the classical PI, mixed sensitivity, and H∞ control, simulation results show that the proposed method has better transient responses, disturbance rejection, and other control performance for the turbofan engine within the large region.

Robust Control of a Gas Turbine With Variable Power Offtake

2006 ◽  
Author(s):  
Shahid Mahmood ◽  
Ian A. Griffin ◽  
Peter J. Fleming
Keyword(s):  
High Pressure ◽  
Robust Control ◽  
Gas Turbine ◽  
Disturbance Rejection ◽  
Closed Loop ◽  
Inverse Model ◽  
Conventional Approach ◽  
Control Performance ◽  
Variable Power ◽  
Improved Performance

The conventional approach to Rolls-Royce Inverse Model closed loop fuel control is to represent the inverse high-pressure (HP) spool dynamics within the controller. In this paper, the options of configuring the controller to represent either the intermediate (IP) or the low pressure (LP) dynamics of a 3-spool engine are also analysed. Control performance is assessed as the engine is subjected to step changes in power offtake. For each controller, power offtake is extracted from each of the three shafts in turn giving a total of 9 engine/controller configurations. For any given power offtake configuration applied to the engine, the results suggest that the controller based upon LP or IP dynamics offers more robustness measured in terms of phase margins and improved performance with regard to power offtake disturbance rejection.

Stabilization of polynomial systems in ℝ3 via homogeneous feedback

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Hamadi Jerbi ◽  
Thouraya Kharrat ◽  
Fehmi Mabrouk
Keyword(s):  
Nonlinear Systems ◽  
Closed Loop ◽  
Polynomial Systems ◽  
Stabilization Problem ◽  
Odd Degree

Abstract In this paper, we study the stabilization problem of a class of polynomial systems of odd degree in dimension three. The constructed stabilizing feedback is homogeneous and guarantee the homogeneity of the closed loop system.mynotered In the end of the paper, we show the efficiency of such a study in the local stabilization of nonlinear systems affine in control.

scholarly journals Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1110 ◽  
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Quanmin Zhu ◽  
Maamar Bettayeb ◽  
Giuseppe Fusco ◽  
...  
Keyword(s):  
Robust Control ◽  
Lyapunov Function ◽  
Chaotic System ◽  
Finite Time ◽  
Input Saturation ◽  
Robust Stabilization ◽  
Control Law ◽  
Robust Controller ◽  
Control Lyapunov Function ◽  
Error Variable

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

scholarly journals Adaptive Fuzzy Robust Control for a Class of Nonlinear Systems via Small Gain Theorem

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Xingjian Wang ◽  
Shaoping Wang
Keyword(s):  
Adaptive Control ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Closed Loop ◽  
Design Procedure ◽  
Control Law ◽  
Fuzzy Logic Systems ◽  
Adaptive Fuzzy ◽  
Small Gain Theorem ◽  
Small Gain

Practical nonlinear systems can usually be represented by partly linearizable models with unknown nonlinearities and external disturbances. Based on this consideration, we propose a novel adaptive fuzzy robust control (AFRC) algorithm for such systems. The AFRC effectively combines techniques of adaptive control and fuzzy control, and it improves the performance by retaining the advantages of both methods. The linearizable part will be linearly parameterized with unknown but constant parameters, and the discontinuous-projection-based adaptive control law is used to compensate these parts. The Takagi-Sugeno fuzzy logic systems are used to approximate unknown nonlinearities. Robust control law ensures the robustness of closed-loop control system. A systematic design procedure of the AFRC algorithm by combining the backstepping technique and small-gain approach is presented. Then the closed-loop stability is studied by using small gain theorem, and the result indicates that the closed-loop system is semiglobally uniformly ultimately bounded.

scholarly journals Finite-time stochastic input-to-state stability and observer-based controller design for singular nonlinear systems

2020 ◽  
Vol 25 (6) ◽  
pp. 980-996
Author(s):  
Feng Zhao ◽  
Xiangyong Chen ◽  
Jinde Cao ◽  
Ming Guo ◽  
Jianlong Qiu
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Linear Matrix ◽  
Stochastic Nonlinear Systems ◽  
Sufficient Condition ◽  
Exogenous Disturbance ◽  
Stochastic Input

This paper investigated observer-based controller for a class of singular nonlinear systems with state and exogenous disturbance-dependent noise. A new sufficient condition for finite-time stochastic input-to-state stability (FTSISS) of stochastic nonlinear systems is developed. Based on the sufficient condition, a sufficient condition on impulse-free and FTSISS for corresponding closed-loop error systems is provided. A linear matrix inequality condition, which can calculate the gains of the observer and state-feedback controller, is developed. Finally, two simulation examples are employed to demonstrate the effectiveness of the proposed approaches.

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