Stability Analysis and Controller Design for Fuzzy Parameter Varying Systems Based on Fuzzy Lyapunov Function

2018 ◽  
Author(s):  
Xiaojun Ban ◽  
Hongyang Zhang ◽  
Fen Wu
Keyword(s):  
Lyapunov Function ◽  
Controller Design ◽  
Design Procedure ◽  
Handling Time ◽  
Feedback Gain ◽  
Time Varying ◽  
System A ◽  
Fuzzy Lyapunov Function ◽  
Parameter Varying ◽  
Fuzzy Parameter

The fuzzy parameter varying (FPV) system is a mathematical model proposed to handle nonlinear time-varying dynamical systems encountered in engineering, which has some essential advantages in handling time-varying models. In this article, a new relaxation approach is proposed for the analysis and controller design of the FPV system. Different from the current results on the FPV system, the proposed approach employs the fuzzy Lyapunov function and full block S-procedure to reduce the conservatism in analysis. Furthermore, the relaxation technique proposed in this article can be also used in solving controller synthesis problem effectively. As a result, a design procedure of non-PDC output feedback gain-scheduling controller is provided to ensure asymptotic stability of the closed-loop FPV system. A numerical example is provided to illustrate the proposed method.

scholarly journals Novel Approach of Robust Hinf Tracking Control for Uncertain Fuzzy Descriptor Systems Using Parametric Lyapunov Function

2020 ◽  
Vol 36 (1) ◽  
pp. 69-88
Author(s):  
Ho Pham Huy Anh ◽  
Cao Van Kien
Keyword(s):  
Lyapunov Function ◽  
Fuzzy System ◽  
Controller Design ◽  
Descriptor Systems ◽  
Descriptor System ◽  
System A ◽  
Novel Approach ◽  
Special Cases ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical Systems

This paper proposes a novel uncertain fuzzy descriptor system which is an extension from standard T-S fuzzy system. A fixed Lyapunov function-based approach is considered and controller design for this rich class of fuzzy descriptor systems is formulated as a problem of solving a set of LMIs. The design conditions for the descriptor fuzzy system are more complicated than the standard state-space-based systems. However, the descriptor fuzzy system-based approach has the advantage of possessing fewer number of matrix inequality conditions for certain special cases. Hence, it is suitable for complex systems represented in descriptor form which is often observed in nonlinear mechanical systems.

Constant Turning Force Adaptive Controller Design

1989 ◽  
Vol 111 (2) ◽  
pp. 125-132 ◽  
Author(s):  
Bor-Sen Chen ◽  
Yih-Fang Chang
Keyword(s):  
Control System ◽  
Force Feedback ◽  
Controller Design ◽  
Cutting Tools ◽  
Design Procedure ◽  
Adaptive Controller ◽  
Pi Controller ◽  
Cutting Process ◽  
Time Varying ◽  
Good Reliability

In the Constant Turning Force Adaptive Control system, the cutting process is nonlinear time-varying; besides, the stability cannot be assured by classical control theory since the cutting tools usually cut a workpiece at various cutting depths. In this paper, based on the small gain theorem, we propose a new method to design a PI controller with high robustness to stabilize the force feedback control system against the nonlinear time-varying gain perturbation in the cutting process. A simple design procedure will be presented and several illustrative simulation results are given. The practical experimental results of a converted lathe with the PI controller designed with this method also show a good robustness and good reliability.

ADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF PERTURBED NONLINEAR TIME-VARYING DELAYS SYSTEMS WITH UNKNOWN CONTROL DIRECTION

2013 ◽  
Vol 21 (04) ◽  
pp. 497-531 ◽  
Author(s):  
HONGYUN YUE ◽  
JUNMIN LI
Keyword(s):  
Controller Design ◽  
Adaptive Fuzzy Control ◽  
Small Neighborhood ◽  
Design Procedure ◽  
Time Varying ◽  
Adaptive Fuzzy ◽  
Control Scheme ◽  
Unknown Control ◽  
Unknown Control Direction ◽  
Control Direction

An adaptive fuzzy control scheme with only one adjusted parameter is developed for a class of nonlinear time-varying delays systems. Three kinds of uncertainties: time-varying delays, control directions, and nonlinear functions are all assumed to be completely unknown, which is different from the previous work. During the controller design procedure, appropriate Lyapunov-Krasovskii functionals are used to compensate the unknown time-varying delays terms and the Nussbaum-type function is used to detect the unknown control direction. It is proved that the proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood around zero. The two main advantages of the developed scheme are that (i) by combining the appropriate Lyapunov-Krasovskii functionals with the Nussbaum-gain technique, the control scheme is proposed for a class of nonlinear time-varying delays systems with unknown control directions, (ii) only one parameter needs to be adjusted online in controller design procedure, which reduces the computational burden greatly. Finally, two examples are used to show the effectiveness of the proposed approach.

scholarly journals Improved Results on Delay-Dependent Robust H ∞ Control of Uncertain Neutral Systems with Mixed Time-Varying Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Jingsha Zhang ◽  
Yongke Li ◽  
Xiaolin Ma ◽  
Zhilong Lin ◽  
Changlong Wang
Keyword(s):  
State Feedback ◽  
Controller Design ◽  
The State ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Time Varying ◽  
Neutral Systems ◽  
The Matrix ◽  
Left And Right ◽  
Delay Dependent

In this paper, the problem of the delay-dependent robust H ∞ control for a class of uncertain neutral systems with mixed time-varying delays is studied. Firstly, a robust delay-dependent asymptotic stability criterion is shown by linear matrix inequalities (LMIs) after introducing a new Lyapunov–Krasovskii functional (LKF). The LKF including vital terms is expected to obtain results of less conservatism by employing the technique of various efficient convex optimization algorithms and free matrices. Then, based on the obtained criterion, analyses for uncertain systems and H ∞ controller design are presented. Moreover, on the analysis of the state-feedback controller, different from the traditional method which multiplies the matrix inequality left and right by some matrix and its transpose, respectively, we can obtain the state-feedback gain directly by calculating the LMIs through the toolbox of MATLAB in this paper. Finally, the feasibility and validity of the method are illustrated by examples.

scholarly journals Optimal Robust LQI Controller Design for Z-Source Inverters

2020 ◽  
Vol 10 (20) ◽  
pp. 7260
Author(s):  
Amirhossein Ahmadi ◽  
Behnam Mohammadi-Ivatloo ◽  
Amjad Anvari-Moghaddam ◽  
Mousa Marzband
Keyword(s):  
Disturbance Rejection ◽  
Controller Design ◽  
Design Procedure ◽  
Bat Algorithm ◽  
Linear Quadratic ◽  
System A ◽  
Stability Robustness ◽  
Power Inverters ◽  
Quadratic Integral ◽  
The Stability

This paper investigates the linear quadratic integral (LQI)-based control of Z-source inverters in the presence of uncertainties such as parameter perturbation, unmodeled dynamics, and load disturbances. These uncertainties, which are naturally available in any power system, have a profound impact on the performance of power inverters and may lead to a performance degradation or even an instability of the system. A novel robust LQI-based design procedure is presented to preserve the performance of the inverter against uncertainties while a proper level of disturbance rejection is satisfied. The stability robustness of the system is also studied on the basis of the maximum sensitivity specification. Moreover, the bat algorithm is adopted to optimize the weighting matrices. Simulation results confirm the effectiveness of the proposed controller in terms of performance and robustness.

scholarly journals A Linear Parameter Varying Control Approach for DC/DC Converters in All-Electric Boats

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Soroush Azizi ◽  
Mohammad Hassan Asemani ◽  
Navid Vafamand ◽  
Saleh Mobayen ◽  
Mohammad Hassan Khooban
Keyword(s):  
Smart Grids ◽  
Control Method ◽  
Controller Design ◽  
Design Procedure ◽  
Energy Resources ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Boost Converters ◽  
Control Approach ◽  
Parameter Varying

Utilization of renewable energies in association with energy storage is increased in different applications such as electrical vehicles (EVs), electric boats (EBs), and smart grids. A robust controller strategy plays a significant role to optimally utilize the energy resources available in a power system. In this paper, a suitable controller for the energy resources of an EB which consists of a 5 kW solar power plant, 5 kW fuel cell, and 2 kW battery package is designed based on the linear parameter varying (LPV) controller design approach. Initially, all component dynamics are augmented, and by exploiting the sector-nonlinearity approach, the LPV representation is derived. Then, the LPV control method determines the suitable gains of the states’ feedbacks to provide the required pulse commands of the boost converters of the energy resources to regulate the DC-link voltage and supply the power of EB loads. Comparing with the state-of-the-art nonlinear control methods, the developed control approach assures the stability of the overall system, as it considers all component dynamics in the design procedure. The real-time simulation results demonstrate the performance of the designed controller in the creation of a constant DC-link voltage.

Robust H∞ Takagi–Sugeno fuzzy output-feedback control for differential speed steering vehicles

2020 ◽  
Vol 234 (12) ◽  
pp. 2822-2835 ◽  
Author(s):  
Paul Oke ◽  
Sing Kiong Nguang
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Electric Vehicles ◽  
Output Feedback ◽  
Controller Design ◽  
Output Feedback Control ◽  
Operating Conditions ◽  
Fuzzy Lyapunov Function ◽  
Takagi Sugeno ◽  
Differential Speed

This paper studied the modelling and control of four-wheel independently driven electric vehicles using differential speed steering. The Takagi–Sugeno fuzzy modelling approach represents the nonlinearities of the four-wheel independently driven electric vehicle state variables in several system models. The proposed controller design is a robust Takagi–Sugeno fuzzy output-feedback control based on a fuzzy Lyapunov function approach. More precisely, the Lyapunov function is chosen to be dependent on the membership functions. Sufficient conditions for the existence of the robust Takagi–Sugeno fuzzy controller are given in terms of linear matrix inequality constraints. The designed parameters are tested by simulating the four-wheel independently driven electric vehicles under varying operating conditions. The simulation results underscore the robustness and disturbance rejection importance of the proposed controller, which is then contrasted to better highlight the improved performance of the proposed approach over a fixed robust controller design.

scholarly journals Robust Finite-Timeℋ∞Control for Uncertain Systems Subject to Intermittent Measurements

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zhenghong Deng
Keyword(s):  
Finite Time ◽  
Controller Design ◽  
Design Method ◽  
Design Procedure ◽  
Linear Matrix ◽  
Finite Time Stability ◽  
System A ◽  
Controller Gain ◽  
Intermittent Measurements ◽  
Time Systems

This paper investigates the robust finite-timeℋ∞controller design problem of discrete-time systems with intermittent measurements. It is assumed that the system is subject to the norm-bounded uncertainties and the measurements are intermittent. The Bernoulli process is used to describe the phenomenon of intermittent measurements. By substituting the state-feedback controller into the system, a stochastic closed-loop system is obtained. Based on the analysis of the robust stochastic finite-time stability and theℋ∞performance, the controller design method is proposed. The controller gain can be calculated by solving a sequence of linear matrix inequalities. Finally, a numerical example is used to show the design procedure and the effectiveness of the proposed design methodology.

Observer-Based Robust Synchronization of Dynamical Systems

1998 ◽  
Vol 08 (11) ◽  
pp. 2243-2254 ◽  
Author(s):  
Alexander Pogromsky ◽  
Henk Nijmeijer
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Function ◽  
Frequency Domain ◽  
Design Procedure ◽  
Time Varying ◽  
Robust Synchronization ◽  
Error Dynamics

The paper deals with the problem of robust synchronization of dynamical systems. The design procedure is based on the concept of observers with absolutely stable error dynamics. In the general case of nonlinear time-varying error dynamics the procedure requires exact knowledge of a Lyapunov function while in case of the linearizable error dynamics frequency domain conditions which ensure existence of such a function can be employed. Two examples are considered: synchronization of two Lorenz systems and Rössler systems.

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