Mixed Method of Routh and ISE Criterion Approaches for Reduced-Order Modeling of Continuous-Time Systems

1984 ◽  
Vol 106 (4) ◽  
pp. 353-356 ◽  
Author(s):  
Chyi Hwang
Keyword(s):  
Mixed Method ◽  
Continuous Time ◽  
Reduced Order Model ◽  
System Response ◽  
Order Model ◽  
Reduced Order ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Continuous Time Systems ◽  
Time Systems

A mixed method using the advantages of Routh approximation method and integral-squared-error criterion is proposed for obtaining stable reduced-order models for high-order continuous-time systems. The reduced-order model tends to approximate the transient portion of the system response in the sense of minimum mean-squared-error, while the steady-state portion is matched exactly. Instead of actually evaluating time responses of the system and the reduced-order model, a matrix formula is used to calculate the integral-squared-error from the error transfer function.

scholarly journals Approximate Prediction-Based Control Method for Nonlinear Oscillatory Systems with Applications to Chaotic Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-21
Author(s):  
Thiago P. Chagas ◽  
Pierre-Alexandre Bliman ◽  
Karl H. Kienitz
Keyword(s):  
Continuous Time ◽  
Control Method ◽  
Nonlinear Dynamical Systems ◽  
System Response ◽  
Free System ◽  
Nonlinear Dynamical ◽  
Oscillatory Systems ◽  
Continuous Time Systems ◽  
Estimation Precision ◽  
Time Systems

The approximate Prediction-Based Control method (aPBC) is the continuous-time version of the well-known Prediction-Based Chaos Control method applied to stabilize periodic orbits of nonlinear dynamical systems. The method is based on estimating future states of the free system response of continuous-time systems using the solution from the Runge-Kutta implicit method in real time. Some aspects of aPBC are evaluated in the present work, particularly its robustness to low future states estimation precision is exemplified.

scholarly journals ON DISCRETE SAMPLING OF TIME-VARYING CONTINUOUS-TIME SYSTEMS

2009 ◽  
Vol 25 (4) ◽  
pp. 985-994 ◽  
Author(s):  
Peter M. Robinson
Keyword(s):  
Continuous Time ◽  
Time Varying ◽  
Order Model ◽  
First Order ◽  
Continuous Time Systems ◽  
Continuous Time Process ◽  
Time Systems ◽  
Over Time ◽  
Higher Order Models ◽  
Equal Spacing

We consider a multivariate continuous-time process, generated by a system of linear stochastic differential equations, driven by white noise, and involving coefficients that possibly vary over time. The process is observable only at discrete, but not necessarily equally-spaced, time points (though equal spacing significantly simplifies matters). Such settings represent partial extensions of ones studied extensively by A.R. Bergstrom. A model for the observed time series is deduced. Initially we focus on a first-order model, but higher-order models are discussed in the case of equally-spaced observations. Some discussion of issues of statistical inference is included.

Active and Passive Vibration Control Using Compact Damping Patches: Assessment of a Reduced Order Model for an Euler Beam

2015 ◽  
Author(s):  
Joseph Plattenburg ◽  
Jason T. Dreyer ◽  
Rajendra Singh
Keyword(s):  
Computational Models ◽  
Parametric Design ◽  
Reduced Order Model ◽  
System Response ◽  
Control Input ◽  
Passive Damping ◽  
Order Model ◽  
Euler Beam ◽  
Reduced Order ◽  
Developing Area

Concurrent placement of compact active and passive damping patches for vibration reduction is a developing area of research. Analytical and computational models to evaluate alternate patch configurations and structural geometries are not widely available. To overcome this void, this paper presents a simplified discrete-system model for vibrations of a beam-like structure. A disturbance input is included in the model, along with a control input from an active patch. Localized structural damping resulting from a passive patch is modeled with an equivalent loss factor. Results from the simplified model are verified using a more detailed analytical formulation, which is based on the Ritz approximation. Verification studies include the effect of a passive damping patch on modal loss factors and broadband attenuation. Finally, a few case studies are proposed which show the efficacy of the reduced-order model for parametric design studies. These studies include determining the effect of localized damping on the control system parameters that are required for attenuation of localized and global motions. The effect of patch locations on system response is also studied. This work has potential applications in industry since compact damping patches are attractive NVH treatments that add minimal weight and complexity.

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