Cramer–Rao Bound Development for Linear Time Periodic Systems

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Chris S. Schulz ◽  
Donald L. Kunz ◽  
Norman M. Wereley
Keyword(s):  
Linear Time ◽  
System Model ◽  
Periodic Systems ◽  
Accurate Representation ◽  
Linear Time Invariant ◽  
Lti System ◽  
Identification Techniques ◽  
Cramer Rao Bound ◽  
Time Invariant ◽  
Time Periodic

System identification techniques are often used to determine the parameters required to define a model of a linear time invariant (LTI) system. The Cramer–Rao bound can be used to validate those parameters in order to ensure that the system model is an accurate representation of the system. Unfortunately, the Cramer–Rao bound is only valid for LTI systems and is not valid for linear time periodic (LTP) systems such as a helicopter rotor in forward flight. This paper describes an extension of the Cramer–Rao bound to LTP systems and demonstrates the methodology for a simple LTP system.

scholarly journals On Fault Detection in Linear Discrete-Time, Periodic, and Sampled-Data Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-18 ◽  
Author(s):  
P. Zhang ◽  
S. X. Ding
Keyword(s):  
Fault Detection ◽  
Linear Time ◽  
Periodic Systems ◽  
Data Systems ◽  
Sampled Data ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Problem Formulations ◽  
Time Invariant ◽  
Time Periodic

This paper gives a review of some standard fault-detection (FD) problem formulations in discrete linear time-invariant systems and the available solutions. Based on it, recent development of FD in periodic systems and sampled-data systems is reviewed and presented. The focus in this paper is on the robustness and sensitivity issues in designing model-based FD systems.

Periodic controller for guaranteed simultaneous stabilization of two plants with robust zero error tracking

2018 ◽  
Vol 233 (5) ◽  
pp. 480-490
Author(s):  
Arindam Chakraborty ◽  
Jayati Dey
Keyword(s):  
Design Methodology ◽  
Linear Time ◽  
Pole Placement ◽  
Control Input ◽  
Efficient Design ◽  
Simultaneous Stabilization ◽  
Bounded Control ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Time Periodic

The guaranteed simultaneous stabilization of two linear time-invariant plants is achieved by continuous-time periodic controller with high controller frequency. Simultaneous stabilization is accomplished by means of pole-placement along with robust zero error tracking to either of two plants. The present work also proposes an efficient design methodology for the same. The periodic controller designed and synthesized for realizable bounded control input with the proposed methodology is always possible to implement with guaranteed simultaneous stabilization for two plants. Simulation and experimental results establish the veracity of the claim.

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.

A Higher-Order Method for Dynamic Optimization of Controllable LTI Systems

2011 ◽  
Author(s):  
Damiano Zanotto ◽  
Sunil K. Agrawal ◽  
Giulio Rosati
Keyword(s):  
Differential Equations ◽  
Dynamic Optimization ◽  
Linear Time ◽  
Traditional Approach ◽  
Linear Time Invariant ◽  
System P ◽  
Lti System ◽  
Higher Order Method ◽  
Time Invariant ◽  
Controllability Index

This work describes a new procedure for dynamic optimization of controllable Linear time-invariant (LTI) systems. Unlike the traditional approach, which results in 2n first order differential equations, the method proposed here yields a set of m differential equations, whose highest order is twice the controllability index of the system p. This paper generalizes the approach presented in a previous work [1] to any controllable LTI system.

Comparison of Poincaré Normal Forms and Floquet Theory for Analysis of Linear Time Periodic Systems

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
Susheelkumar C. Subramanian ◽  
Sangram Redkar
Keyword(s):  
Floquet Theory ◽  
Normal Forms ◽  
Linear Time ◽  
Mathieu Equation ◽  
Temporal Variations ◽  
Periodic Systems ◽  
Comparative Results ◽  
Time Invariant ◽  
Identity Transformations ◽  
Time Periodic

Abstract In this work, the authors draw comparisons between the Floquet theory and Normal Forms technique and apply them towards the investigation of stability bounds for linear time periodic systems. Though the Normal Forms technique has been predominantly used for the analysis of nonlinear equations, in this work, the authors utilize it to transform a linear time periodic system to a time-invariant system, similar to the Lyapunov–Floquet (L–F) transformation. The authors employ an intuitive state augmentation technique, modal transformation, and near identity transformations to facilitate the application of time-independent Normal Forms. This method provides a closed form analytical expression for the state transition matrix (STM). Additionally, stability analysis is performed on the transformed system and the comparative results of dynamical characteristics and temporal variations of a simple linear Mathieu equation are also presented in this work.

Basics to Multirate Systems

2009 ◽  
pp. 23-63
Author(s):  
Ljiljana Milic
Keyword(s):  
Linear Time ◽  
Sampling Rate ◽  
Multirate Systems ◽  
Linear Time Invariant ◽  
Lti System ◽  
Linear Time Invariant Systems ◽  
Time Invariant ◽  
The Given

Linear time-invariant systems operate at a single sampling rate i.e. the sampling rate is the same at the input and at the output of the system, and at all the nodes inside the system. Thus, in an LTI system, the sampling rate doesn’t change in different stages of the system. Systems that use different sampling rates at different stages are called the multirate systems. The multirate techniques are used to convert the given sampling rate to the desired sampling rate, and to provide different sampling rates through the system without destroying the signal components of interest. In this chapter, we consider the sampling rate alterations when changing the sampling rate by an integer factor. We describe the basic sampling rate alteration operations, and the effects of those operations on the spectrum of the signal.

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