scholarly journals Steady-State Response of Periodically Switched Linear Circuits via Augmented Time-Invariant Nodal Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Riccardo Trinchero ◽  
Igor S. Stievano ◽  
Flavio G. Canavero
Keyword(s):  
Steady State ◽  
Frequency Domain ◽  
Linear Time ◽  
Automatic Generation ◽  
Steady State Response ◽  
Linear Time Invariant ◽  
State Response ◽  
Linear Circuits ◽  
Circuit Components ◽  
Time Invariant

We focus on the simulation of periodically switched linear circuits. The basic notation and theoretical framework are presented, with emphasis on the differences between the linear time-invariant and the time-varying cases. For this important class of circuits and sources defined by periodic signals, the computation of their steady-state response is carried out via the solution of an augmented time-invariant MNA equation in the frequency-domain. The proposed method is based on the expansion of the unknown voltages and currents in terms of Fourier series and on the automatic generation of augmented equivalents of the circuit components. The above equivalents along with the information on circuit topology allow creating, via circuit inspection, a time-invariant MNA equation, the solution of which provides the coefficients of both the time- and the frequency-domain responses of the circuit. Analytical and numerical examples are used to stress the generality and benefits of the proposed approach.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

Novel Gaussian State Estimator based on H2 Norm and Steady-State Variance

2020 ◽  
Author(s):  
Alesi Augusto De Paula ◽  
Víctor Costa da Silva Campos ◽  
Guilherme Vianna Raffo ◽  
Bruno Otávio Soares Teixeira
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Estimation Error ◽  
Performance Criterion ◽  
Gaussian State ◽  
State Estimator ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Linear Time Invariant System ◽  
Time Invariant

This paper proposes a novel state estimator for discrete-time linear systems with Gaussian noise. The proposed algorithm is a fixed-gain filter, whose observer structure is more general than Kalman one for linear time-invariant systems. Therefore, the steady-state variance of the estimation error is minimized. For white noise stochastic processes, this performance criterion is reduced to the square H2 norm of a given linear time-invariant system. Then, the proposed algorithm is called observer H2 filter (OH2F). This is the standard Wiener-Hopf or Kalman-Bucy filtering problem. As the Kalman predictor and Kalman filter are well-known solutions for such a problem, they are revisited.

Steady-State Optimal State and Input Observer for Discrete Stochastic Systems

1989 ◽  
Vol 111 (2) ◽  
pp. 121-127 ◽  
Author(s):  
Y. Park ◽  
J. L. Stein
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Stochastic Systems ◽  
Linear Time ◽  
The State ◽  
Optimal State ◽  
Unknown Inputs ◽  
Linear Time Invariant ◽  
Error Covariance ◽  
Time Invariant

Model-based machine diagnostics techniques require the modeled states and machine inputs to be measured. Because measurement of all the states and inputs is not always possible or practical, a simultaneous state and input observer is required. Previous work has developed this type of acausal observer and shown it is susceptible to noise. This paper develops a steady-state optimal observer that minimizes the trace of the steady-state error covariance of the state and input estimates for discrete, linear, time-invariant, stochastic systems with unknown inputs. In addition, a method to distinguish the best measurement set among the available measurement sets is developed. Results from numerical simulations show that the optimal observer can greatly improve estimation results in some cases.

scholarly journals Steady-State Deflection of a Circular Plate Rotating Near Its Critical Speed

1999 ◽  
Vol 66 (4) ◽  
pp. 1015-1017 ◽  
Author(s):  
Jen-San Chen
Keyword(s):  
Steady State ◽  
Circular Plate ◽  
Critical Speed ◽  
Applied Load ◽  
Fixed Time ◽  
Steady State Response ◽  
Plate Model ◽  
State Response ◽  
Nonlinear Plate ◽  
Time Invariant

The steady-state response of a disk spinning near its critical speed and under space-fixed time-invariant load is analyzed by using von Karman’s nonlinear plate model. It is found that as the disk rotates beyond a modified critical speed there exist three steady-state deflections, among which only one is in the same direction as the applied load and is stable in the presence of space-fixed damping.

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