Suboptimal Bilinear Routh Approximant for Discrete Systems

2004 ◽  
Vol 128 (3) ◽  
pp. 742-745 ◽  
Author(s):  
Younseok Choo
Keyword(s):  
Impulse Response ◽  
Approximation Method ◽  
Order Reduction ◽  
Original System ◽  
Discrete Systems ◽  
Reduced Model ◽  
The Stability

Recently an improved bilinear Routh approximation method has been suggested for the order reduction of discrete systems. In the method, the last α and β parameters of a reduced model were replaced by new parameters so that the impulse response energy of an original system is also preserved in the reduced model without destroying the stability preserving and time-moments matching properties. In this paper a new and simple improvement is proposed from which one can find a suboptimal bilinear Routh approximant. Compared to the previous result, the approach of this paper has an advantage that the improvement is always guaranteed.

Improved Bilinear Routh Approximation Method for Discrete-Time Systems

2000 ◽  
Vol 123 (1) ◽  
pp. 125-127 ◽  
Author(s):  
Younseok Choo
Keyword(s):  
Impulse Response ◽  
Discrete Time ◽  
Approximation Method ◽  
Original Model ◽  
Reduced Model ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems

Hwang and Shieh proposed a bilinear Routh approximation method for reducing the order of discrete-time systems. A reduced model derived by the method is not only stable whenever an original model is stable, but also fits the first few time-moments of the original one. This paper addresses the possibility of improving the method by letting the impulse response energy of the original model also be conserved in the reduced model without destroying the stability preserving and time-moments matching properties.

A New Consideration for Model Reduction Using Bilinear Schwarz Approximation for Discrete-Time Systems

2002 ◽  
Vol 124 (3) ◽  
pp. 475-477 ◽  
Author(s):  
Younseok Choo
Keyword(s):  
Model Reduction ◽  
Impulse Response ◽  
Discrete Time ◽  
Approximation Method ◽  
Original Model ◽  
Reduced Model ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems

A bilinear Schwarz approximation method has been proposed in the literature for reducing the order of discrete-time systems. The reduced model derived by the method preserves the stability and first few time-moments of the original one. This paper shows that the method can be modified so that the impulse response energy of the original model is also conserved in the reduced model without destroying the stability and time-moments preserving properties.

Conventional and Evolutionary Order Reduction Techniques for Complex Systems

2021 ◽  
Vol 16 (4) ◽  
pp. 74-98
Author(s):  
Abha Kumari ◽  
C. B. Vishwakarma
Keyword(s):  
Large Scale ◽  
Order Reduction ◽  
Original System ◽  
Conventional Technique ◽  
Stability Equation ◽  
Padé Approximations ◽  
Time Frequency ◽  
Reduction Techniques ◽  
Pade Approximations ◽  
The Stability

Order reduction of the large-scale linear dynamic systems (LSLDSs) using stability equation technique mixed with the conventional and evolutionary techniques is presented in the paper. The reduced system (RS) is obtained by mixing the advantages of the two methods. For the conventional technique, the numerator of the RS is achieved by using the Pade approximations and improved Pade approximations, whereas the denominator is obtained by the stability equation technique (SET). For the evolutionary technique, numerator of the RS is obtained by minimizing the integral square error (ISE) between transient responses of the original and the RS using the genetic algorithm (GA), and the denominator is obtained by the stability equation method. The proposed RS retains almost all the essential properties of the original system (OS). The viability of the proposed technique is proved by comparing its time, frequency responses, time domain specifications, and ISE with the new and popular methods available in the literature.

Model Reduction of a Parametrically Excited Drivetrain

2012 ◽  
Author(s):  
Thomas Pumhoessel ◽  
Peter Hehenberger ◽  
Klaus Zeman
Keyword(s):  
Stability Margin ◽  
Original System ◽  
Reduced Model ◽  
Parametrically Excited ◽  
System Parameters ◽  
Additional Stability ◽  
System Equations ◽  
The Difference ◽  
Set Up ◽  
The Stability

The complexity of engineering systems is continuously increasing, resulting in mathematical models that become more and more computationally expensive. Furthermore, in model based design, for example, system parameters are subject of change, and therefore, the system equations have to be evaluated repeatedly. Hence, there is a need for providing reduced models which are as compact as possible, but still reflect the properties of the original model in a satisfactory manner. In this contribution, the reduction of differential equations with time-periodic coefficients, termed as parametrically excited systems, is investigated using the method of Proper Orthogonal Decomposition (POD). A reduced model is set up based on the solution of the original system for a certain parametric combination resonance of the difference type, resulting in an additional stability margin of the trivial solution. It is shown that the POD reduced model approximates the stability behavior of the original system much better than a modally reduced model even if system parameters are subject of change.

SISO Continuous-System Reduction via Impulse Response Gramian by Iterative Formulae

2005 ◽  
Vol 128 (2) ◽  
pp. 391-393 ◽  
Author(s):  
Younseok Choo ◽  
Dongmin Kim
Keyword(s):  
Impulse Response ◽  
Linear Time ◽  
Order Reduction ◽  
Continuous System ◽  
Original System ◽  
Initial Time ◽  
Continuous Systems ◽  
System Matrix ◽  
Single Input Single Output ◽  
Single Output

This paper concerns the order reduction of single-input single-output (SISO) linear time-invariant continuous systems based on the impulse response Gramian. From the recursive relationship among the Gramians, a new formula is derived for computing the system matrix in controllability canonical form. The result is applied to the model reduction problem. Reduced models obtained approximate the reduced-order Gramians while preserving some initial time moments and Markov parameters of the original system.

scholarly journals State relevance for model order reduction applied to a microgrid

2021 ◽  
Author(s):  
Andrés Tomás-Martín ◽  
Aurelio García-Cerrada ◽  
Lukas Sigrist ◽  
Sauro Yagüe ◽  
Jorge Suárez-Porras
Keyword(s):  
Power Systems ◽  
Model Order Reduction ◽  
Ad Hoc ◽  
Stability Limit ◽  
Order Reduction ◽  
Original System ◽  
Reduced Model ◽  
State Variables ◽  
Nonlinear Simulation ◽  
Model Order

This paper presents a systematic model order reduction (MOR) algorithm based on state relevance applied to an islanded microgrid with electronic power generation. MOR of such islanded microgrids may not benefit, a priori, from the well-established time-scale separation usually applied to conventional power systems, and a systematic MOR is still an open issue. The proposed algorithm uses a balanced realization of the linear system, where state variables may not have physical meaning, to obtain the states' energies. It then calculates the relevance of the original system states from those energy values. The newly proposed ``state-relevance coefficient'' should help to choose which states to consider in a reduced model in each study case. Detailed nonlinear simulation results show that the proposed algorithm is able to find the relevant states to include in the reduced model systematically, even in operation points near the stability limit, where ad-hoc MOR techniques are likely to fail. The performance of the algorithm is illustrated in a system with grid-forming converters in various scenarios but can be easily applied to other systems.

State relevance for model order reduction applied to a microgrid

2021 ◽  
Author(s):  
Andrés Tomás-Martín ◽  
Aurelio García-Cerrada ◽  
Lukas Sigrist ◽  
Sauro Yagüe ◽  
Jorge Suárez-Porras
Keyword(s):  
Power Systems ◽  
Model Order Reduction ◽  
Ad Hoc ◽  
Stability Limit ◽  
Order Reduction ◽  
Original System ◽  
Reduced Model ◽  
State Variables ◽  
Nonlinear Simulation ◽  
Model Order

This paper presents a systematic model order reduction (MOR) algorithm based on state relevance applied to an islanded microgrid with electronic power generation. MOR of such islanded microgrids may not benefit, a priori, from the well-established time-scale separation usually applied to conventional power systems, and a systematic MOR is still an open issue. The proposed algorithm uses a balanced realization of the linear system, where state variables may not have physical meaning, to obtain the states' energies. It then calculates the relevance of the original system states from those energy values. The newly proposed ``state-relevance coefficient'' should help to choose which states to consider in a reduced model in each study case. Detailed nonlinear simulation results show that the proposed algorithm is able to find the relevant states to include in the reduced model systematically, even in operation points near the stability limit, where ad-hoc MOR techniques are likely to fail. The performance of the algorithm is illustrated in a system with grid-forming converters in various scenarios but can be easily applied to other systems.

scholarly journals Delay-dependent stability analysis for discrete-time systems with time varying state delay

2011 ◽  
Vol 17 (4) ◽  
pp. 497-503 ◽  
Author(s):  
Sreten Stojanovic ◽  
Dragutin Debeljkovic
Keyword(s):  
Original System ◽  
Discrete Systems ◽  
Mathematical Form ◽  
Time Varying ◽  
Time Varying Delay ◽  
Maximum Delay ◽  
The Stability ◽  
Delay Dependent ◽  
Time Systems ◽  
Delay Dependent Stability

The stability of discrete systems with time-varying delay is considered. Some sufficient delaydependent stability conditions are derived using an appropriate model transformation of the original system. The criteria are presented in the form of LMI, which are dependent on the minimum and maximum delay bounds. It is shown that the stability criteria are approximately the same conservative as the existing ones, but have much simpler mathematical form. The numerical example is presented to illustrate the applicability of the developed results.

scholarly journals Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case

2010 ◽  
Vol 2010 ◽  
pp. 1-23 ◽  
Author(s):  
Josef Diblík ◽  
Denys Ya. Khusainov ◽  
Irina V. Grytsay ◽  
Zdenĕk Šmarda
Keyword(s):  
Lyapunov Functions ◽  
Critical Case ◽  
Autonomous Systems ◽  
Discrete Systems ◽  
Simple Eigenvalue ◽  
Discrete Equations ◽  
The Matrix ◽  
The Stability ◽  
Important Characterization

Many processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalueλ=1of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.

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