A finite-time adaptive order estimation approach for non-integer order nonlinear systems
S Sepehr Tabatabaei1, Mahdi Tavakoli2, Heidar Ali Talebi3
1Department of Electrical Engineering, Shahreza Campus, University of Isfahan, Iran.
ISA Transactions
|September 11, 2021
Summary
This study introduces novel methods for estimating the order of nonlinear systems, even those with non-integer orders. These techniques ensure bounded estimation errors using only a compact time interval.
Area of Science:
- Control Theory
- Nonlinear Systems Analysis
- System Identification
Background:
- Estimating the order of nonlinear systems is crucial for accurate modeling and control.
- Existing methods often struggle with systems exhibiting time-varying or non-integer orders.
Purpose of the Study:
- To develop novel methods for estimating the order of nonlinear systems, particularly those with non-integer orders.
- To address the challenge of estimating orders in time-varying and multivariable systems.
- To design estimators for systems with unknown pseudo-states.
Main Methods:
- Analysis of stability for time-varying order systems.
- Development of an estimation scheme for multivariable systems with time-varying incommensurate orders.
- Design of an order/pseudo-state estimator for nonlinear systems with unknown pseudo-states.
Main Results:
- A method is proposed to approximate the order of multivariable systems with time-varying incommensurate orders.
- An order/pseudo-state estimator is designed for a class of nonlinear systems.
- The proposed methods are shown to be extendable to other nonlinear system classes.
Conclusions:
- The developed methods provide effective means for estimating the order of complex nonlinear systems.
- A key advantage is the ability to guarantee bounded estimation error within a compact time interval.
- The research contributes to advancing system identification and control of nonlinear systems.
Related Concept Videos
01:21First Order Systems
208
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
208
01:21Linear Approximation in Time Domain
164
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,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
164
01:18Second Order systems II
211
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.
211
01:26Linear Approximation in Frequency Domain
185
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
185
01:23Linear time-invariant Systems
533
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...
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...
533
01:20Second Order systems I
288
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...
288