Adaptive fuzzy sliding-mode controller of uncertain nonlinear systems
1Department of Electrical Engineering, National Central University, Chung-Li, 32001 Taiwan, ROC. s9541006@cc.ncu.edu.tw
ISA Transactions
|April 2, 2008
Summary
This study introduces adaptive fuzzy sliding-mode controllers for Takagi-Sugeno (T-S) fuzzy models. The Lyapunov function method designs fuzzy sliding surfaces and controllers, effectively handling uncertainties.
Area of Science:
- Control Engineering
- Fuzzy Systems
- Nonlinear Control Theory
Background:
- Takagi-Sugeno (T-S) fuzzy models are widely used for representing complex nonlinear systems.
- Sliding-mode control (SMC) offers robustness but can be sensitive to parameter uncertainties.
- Adaptive control strategies are needed to enhance performance in the presence of unknown dynamics.
Purpose of the Study:
- To design adaptive fuzzy sliding-mode controllers (SMCs) for T-S fuzzy models.
- To utilize Lyapunov functions for establishing stable fuzzy sliding surfaces.
- To address unknown parameter perturbations and external disturbances through an adaptive mechanism.
Main Methods:
- Design of fuzzy sliding surfaces using Lyapunov functions and linear matrix inequalities (LMIs).
- Development of adaptive fuzzy sliding-mode controllers integrated with the T-S fuzzy model framework.
- Application of an adaptive mechanism to compensate for system uncertainties and disturbances.
Main Results:
- Demonstrated the use of Lyapunov functions to derive fuzzy sliding surfaces via LMIs.
- Successfully designed adaptive fuzzy SMCs for T-S fuzzy systems.
- Validated the proposed adaptive mechanism's ability to handle unknown parameter perturbations and external disturbances.
Conclusions:
- The proposed Lyapunov-based approach effectively designs fuzzy sliding surfaces and adaptive controllers for T-S fuzzy models.
- The adaptive mechanism enhances robustness against uncertainties and disturbances.
- The presented methods are feasible, as illustrated by two practical examples.
Related Concept Videos
01:26Feedback control systems
Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
01:22Controller Configurations
Controller configurations are crucial in a car's cruise control system because they manage speed over time to maintain a consistent pace regardless of road conditions, thereby meeting design goals. In traditional control systems, fixed-configuration design involves predetermined controller placement. System performance modifications are known as compensation.
Control-system compensation involves various configurations, most commonly series or cascade compensation, in which the controller aligns...
Control-system compensation involves various configurations, most commonly series or cascade compensation, in which the controller aligns...
01:26PD Controller: Design
In automotive engineering, car suspension systems often employ Proportional Derivative (PD) controllers to enhance performance. PD controllers are utilized to adjust the damping force in response to road conditions. A controller, acting as an amplifier with a constant gain, demonstrates proportional control, with output directly mirroring input.
Designing a continuous-data controller requires selecting and linking components like adders and integrators, which are fundamental in Proportional,...
Designing a continuous-data controller requires selecting and linking components like adders and integrators, which are fundamental in Proportional,...
01:21Linear Approximation in Time Domain
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
01:07Time-Domain Interpretation of PD Control
Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
Consider the example of control of motor torque. Initially, a positive...
01:22Multi-input and Multi-variable systems
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
In the absence of...