A Novel Internal Model-Based Tracking Control for a Class of Linear Time-Varying Systems

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Zhen Zhang ◽  
Zongxuan Sun
Keyword(s):  
Internal Model ◽  
Linear Time ◽  
Implementation Process ◽  
Automatic Generation ◽  
Feedback Mechanism ◽  
Control Input ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Model Based ◽  
Time Varying Systems

This paper provides a novel method of constructing an internal model-based design of reference tracking and/or disturbance rejection for a class of linear time-varying plants with a known linear time invariant (LTI) exosystem. It is shown how the realization of an appropriate time-varying internal model can be constructed by means of a novel feedback mechanism. The design of the internal model consists of two ingredients: (1) a time-varying system immersion of the exosystem, and (2) an automatic generation of the desired control input to render the error-zeroing subspace invariant, based on the complete knowledge of the plant model. The important features of the proposed method lie in that the tracking problem setup and the proposed feedback mechanism allow us to avoid explicitly calculating the desired input, which keeps the regulated error identically at zero. Moreover the time-varying immersion is guaranteed to hold for the class of plant models under consideration. These features significantly broaden the range of applications of the proposed method, and simplify the control implementation process.

An Internal Model-Based Tracking Control for a Class of Uncertain Linear Time-Varying Systems

2010 ◽  
Author(s):  
Zhen Zhang ◽  
Zongxuan Sun ◽  
Peiqing Ye
Keyword(s):  
Tracking Control ◽  
Internal Model ◽  
Linear Time ◽  
Design Method ◽  
Uncertain System ◽  
Feedback Gain ◽  
Time Varying ◽  
Linear Parameter Varying ◽  
Model Based ◽  
Time Varying Systems

In this paper, we extend previous results for a novel internal model-based tracking control with a class of known LTV plant models driven by LTI exosystems to uncertain LTI plant models driven by LTV exosystems. The augmented time-varying system to be stabilized becomes uncertain. Moreover, the time-varying fashion under consideration renders the augmented uncertain system linear parameter-varying (LPV). By means of an output-feedback gain-scheduling design, the augmented uncertain LTV system is stabilized. Simulation results illustrate the proposed design method.

Floquet Experimental Modal Analysis for System Identification of Linear Time-Periodic Systems

2007 ◽  
Author(s):  
Matthew S. Allen
Keyword(s):  
System Identification ◽  
Linear Time ◽  
Time Varying ◽  
Response Model ◽  
State Matrix ◽  
Linear Time Invariant ◽  
Response Data ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Periodic

A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with time or Linear Time-Periodic (LTP). Examples include anisotropic rotorbearing systems, wind turbines, satellite systems, etc… A number of powerful techniques have been presented in the past few decades, so that one might expect to model or control an LTP system with relative ease compared to time varying systems in general. However, few, if any, methods exist for experimentally characterizing LTP systems. This work seeks to produce a set of tools that can be used to characterize LTP systems completely through experiment. While such an approach is commonplace for LTI systems, all current methods for time varying systems require either that the system parameters vary slowly with time or else simply identify a few parameters of a pre-defined model to response data. A previous work presented two methods by which system identification techniques for linear time invariant (LTI) systems could be used to identify a response model for an LTP system from free response data. One of these allows the system’s model order to be determined exactly as if the system were linear time-invariant. This work presents a means whereby the response model identified in the previous work can be used to generate the full state transition matrix and the underlying time varying state matrix from an identified LTP response model and illustrates the entire system-identification process using simulated response data for a Jeffcott rotor in anisotropic bearings.

scholarly journals Finite-Time Stability and Stabilization of Switched Linear Time-Varying Systems with Time-Varying Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Lulu Feng ◽  
Ping Zhao
Keyword(s):  
Finite Time ◽  
Linear Time ◽  
Average Dwell Time ◽  
Control Input ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Time Varying Systems ◽  
Varying Delay

This paper deals with the finite-time stability (FTS) of switched linear time-varying (SLTV) systems with time-varying delay. Firstly, based on Lyapunov–Krasovskii functional technique and average dwell time (ADT) approach, a sufficient criterion on FTS for SLTV systems with time-varying delay is obtained. For the SLTV system with delay and control input, based on the criterion, a state feedback controller is designed such that the closed-loop system is finite-time stable (FTS). Finally, an example is employed to illustrate the validity of our results.

Repetitive Control for Linear Time Varying Systems

2002 ◽  
Author(s):  
Zongxuan Sun ◽  
Tsu-Chin Tsao
Keyword(s):  
Discrete Time ◽  
Time Domain ◽  
Linear Time ◽  
Repetitive Control ◽  
Time Varying ◽  
Asymptotic Performance ◽  
Linear Time Invariant ◽  
Time Varying Systems ◽  
Periodic Signals ◽  
Linear Time Invariant System

Repetitive control that asymptotically tracks or rejects periodic signals has been widely used in many applications. For linear time invariant system, this problem has been thoroughly studied and solved. This paper presents the analysis and synthesis of repetitive control algorithms to track or reject periodic signals for linear time varying systems. Both continuous and discrete time domain results will be presented. A time varying internal model is embedded in the feedback loop to ensure asymptotic performance. It is shown that asymptotic performance can’t be achieved with a finite dimensional controller in the continuous time domain, while it is possible in the discrete time domain. Simulation results demonstrate the effectiveness of the proposed algorithms.

Asymptotic Stabilization of Fractional Permanent Magnet Synchronous Motor

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Yuxiang Guo ◽  
Baoli Ma
Keyword(s):  
Nonlinear Dynamics ◽  
Asymptotic Stability ◽  
Permanent Magnet ◽  
Linear Time ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Time Varying Systems ◽  
The Stability

This paper is mainly concerned with asymptotic stability for a class of fractional-order (FO) nonlinear system with application to stabilization of a fractional permanent magnet synchronous motor (PMSM). First of all, we discuss the stability problem of a class of fractional time-varying systems with nonlinear dynamics. By employing Gronwall–Bellman's inequality, Laplace transform and its inverse transform, and estimate forms of Mittag–Leffler (ML) functions, when the FO belongs to the interval (0, 2), several stability criterions for fractional time-varying system described by Riemann–Liouville's definition is presented. Then, it is generalized to stabilize a FO nonlinear PMSM system. Furthermore, it should be emphasized here that the asymptotic stability and stabilization of Riemann–Liouville type FO linear time invariant system with nonlinear dynamics is proposed for the first time. Besides, some problems about the stability of fractional time-varying systems in existing literatures are pointed out. Finally, numerical simulations are given to show the validness and feasibleness of our obtained stability criterions.

Finite-time control with H-infinity constraints of linear time-invariant and time-varying systems

2013 ◽  
Vol 11 (2) ◽  
pp. 165-172 ◽  
Author(s):  
Yang Guo ◽  
Yu Yao ◽  
Shicheng Wang ◽  
Baoqing Yang ◽  
Kai Liu ◽  
...  
Keyword(s):  
Finite Time ◽  
Linear Time ◽  
Time Varying ◽  
H Infinity ◽  
Linear Time Invariant ◽  
Time Control ◽  
Time Varying Systems ◽  
Time Invariant
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