Related Experiment Video
Updated: Jul 7, 2026
08:05
Design and Analysis for Fall Detection System Simplification
Published on: April 6, 2020
Observers for Takagi-Sugeno fuzzy systems
P Bergsten1, R Palm, D Driankov
1Dept. of Technol., Orebro Univ.
Summary
This study presents novel sliding mode observers for Takagi-Sugeno (TS) fuzzy systems, enhancing nonlinear observer design for systems with state-dependent weighting functions and model mismatches.
Area of Science:
- Control Systems Engineering
- Fuzzy Logic Systems
- Nonlinear System Analysis
Background:
- Dynamic Takagi-Sugeno (TS) fuzzy systems approximate nonlinear systems using multiple affine local linear models.
- Accurate state estimation is crucial for observing nonlinear systems, especially when model uncertainties exist.
- Existing observer designs often struggle with state-dependent weighting functions in TS fuzzy systems.
Purpose of the Study:
- To develop and analyze two novel sliding mode observers for dynamic Takagi-Sugeno (TS) fuzzy systems.
- To address challenges in observer design, including model/plant mismatches and state-dependent weighting functions.
- To provide robust nonlinear observer analysis and design methodologies.
Main Methods:
- Extension of sliding mode observer schemes to handle interpolated multiple local affine linear models.
- Analysis and design of observers specifically tailored for TS fuzzy system structures.
- Consideration of the complex scenario where TS fuzzy system weighting functions depend on the estimated state.
Main Results:
- Successful adaptation of sliding mode observer principles for TS fuzzy systems.
- Development of methods capable of effectively managing model/plant mismatches in nonlinear systems.
- Demonstration of observer design feasibility even when weighting functions are state-dependent.
Conclusions:
- The proposed sliding mode observers offer effective solutions for state estimation in dynamic TS fuzzy systems.
- The methodologies contribute to robust nonlinear observer design, particularly in the presence of uncertainties.
- This work advances the field by tackling complex TS fuzzy system observer challenges.
Related Concept Videos
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...
01:23Root Loci for Positive-Feedback Systems
The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
The construction rules for the root locus in positive feedback systems are similar to those in...
01:23Linear time-invariant Systems
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
01:20Second Order systems I
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
By reinterpreting the system, one can derive the closed-loop transfer function, which...
01:21Transfer Function in Control Systems
The transfer function is a fundamental concept in the analysis and design of linear time-invariant (LTI) systems. It offers a concise way to understand how a system responds to different inputs in the frequency domain. It serves as a bridge between the time-domain differential equations that describe system dynamics and the frequency-domain representation that facilitates easier manipulation and analysis.
To derive the transfer function, consider a general nth-order linear time-invariant...
To derive the transfer function, consider a general nth-order linear time-invariant...
01:18Second Order systems II
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If ζ...
If ζ...