A test for stability robustness of linear time-varying systems utilizing the linear time-invariant ν-gap metric

2009 ◽  
Vol 19 (9) ◽  
pp. 986-1015 ◽  
Author(s):  
Wynita M. Griggs ◽  
Alexander Lanzon ◽  
Brian D. O. Anderson
Keyword(s):  
Linear Time ◽  
Time Varying ◽  
Gap Metric ◽  
Linear Time Invariant ◽  
Stability Robustness ◽  
Time Varying Systems ◽  
Time Invariant

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.

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

scholarly journals Control of Constrained Linear-Time Varying Systems via Kautz Parametrization of Model Predictive Control Scheme

2017 ◽  
Vol 1 (2) ◽  
pp. 65 ◽  
Author(s):  
Massoud Hemmasian Ettefagh ◽  
José De Doná ◽  
Mahyar Naraghi ◽  
Farzad Towhidkhah
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Linear Time ◽  
Optimal Solution ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Decision Variables ◽  
Time Varying Systems ◽  
Kautz Network ◽  
Time Invariant

Kautz parametrization of the Model Predictive Control (MPC) method has shown its ability to reduce the number of decision variables in Linear Time Invariant (LTI) systems. This paper devotes to extend Kautz network to be used in MPC Algorithm for linear time-varying systems. It is shown that Kautz network enables us to maintain a satisfactory performance while the number of decision variables are reduced considerably. Stability of the algorithm is studied under the framework of the optimal solution. The proposed method is validated by an illustrative example. In this regard, the performance of unconstrained systems as well as constrained ones is compared.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

scholarly journals FE Analysis of Communications Systems for Drive-Thru Restaurants in a Business Dispute Over Specifications and Design Process

2021 ◽  
Vol 38 (1) ◽  
Author(s):  
Robert Peruzzi
Keyword(s):  
Communication System ◽  
Communication Systems ◽  
Linear Time ◽  
Forensic Analysis ◽  
Time Varying ◽  
Audio Quality ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Quick Service ◽  
Time Invariant

Forensic analysis in this case involves the design of a communication system intended for use in Quick Service Restaurant (QSR) drive-thru lanes. This paper provides an overview of QSR communication system components and operation and introduces communication systems and channels. This paper provides an overview of non-linear, time-varying system design as contrasted with linear, time-invariant systems and discusses best design practices. It also provides the details of how audio quality was defined and compared for two potentially competing systems. Conclusions include that one of the systems was clearly inferior to the other — mainly due to not following design techniques that were available at the time of the project.

Linear Approximations for Swing Leg Motion During Gait

1984 ◽  
Vol 106 (2) ◽  
pp. 137-143 ◽  
Author(s):  
W. H. Lee ◽  
J. M. Mansour
Keyword(s):  
Linear Systems ◽  
System Analysis ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
State Variables ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Leg Motion ◽  
Time Invariant

The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.

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