• ICROS
• /
• v.1 no.1
• /
• pp.50-50
• /
• 1995

It has been pointed out in the literature that the Routh approximation method for order reduction has limitations in treating transfer functions with the denominator-numerator order difference not equal to one. The purpose of this paper is to present a new algorithm based on the Routh approximation method that can be applied to general rational transfer functions, yielding reduced models with arbitrary order.

• Transactions on Control, Automation and Systems Engineering
• /
• v.1 no.1
• /
• pp.50-53
• /
• 1999

It has been pointed out in the literature that the Routh approximation method for order reduction has limitations in treating transfer functions with the denominator-numerator order difference not equal to one. The purpose of this paper is to present a new algorithm based on the Routh approximation method that can be applied to general rational transfer functions, yield ing reduced models with arbitrary order.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.36 no.8
• /
• pp.584-593
• /
• 1987

A new combined approximation method using Routh stability array and mean-square error (MSE) method is proposed for deriving reduced-order z-transter functions for discrete time systems. The Routh stability array is used to obtain the reduced-order denominator polynomial, and the numerator polynomial is obtained by minimizing the mean-square error between the unit step responses of the original system and reduced model. The advantages of the new combined approximation method are that the reduced model is always stable provided the original model is stable and the initial and steady-state characteristics of the original model can be preserved in the reduced model.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.33 no.10
• /
• pp.396-401
• /
• 1984

This paper present a method of using simplified models for deriving suboptimal controllers to the original higher-order systems. Routh approximation method is a very useful technique for reducing the order of a linear systems. This method dose not require a knowlege of system eigenvalues and eigenvectors and possesses many desirable features such as preservation of reduced order model stability and minimum computational requirements. These properties are utilized to derive suboptimal controllers in this paper. In order to implement htese ocntrollers on the original system, the relationship between the state vectors of the original system and the reduced order models is required. A procedure fir evaluating an approximate aggregation matrix is also developed. A numerical example is given for the illustration of this method, shich is compared with the existing Model aggregation method in the resultant figures.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.24 no.4
• /
• pp.583-589
• /
• 1987

A new approximation method is proposed for the linear model reduction of high order dynamic systems. This mehtod is based upon the denominator table(D-table) and time moment-matching technique. The denominator table(D-table) is used to obtain the denominator polynomial of reduced-order model, and the numerator polynomial is obtained by time moment-matching method. This proposed method does not require the calculation of the alpha-beta expansion and reciprocal transformation which should be calculadted by Routh approximation method. The advantages of the proposed method are that it is computationally every attractive better than Routh approximation method and the reduced model is stable Il the original system is stable.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.36 no.9
• /
• pp.660-669
• /
• 1987

Routh approximation method is the most computationally attractive. But this method may cause time-response error because this method does not match the time-response directly. In this paper a new mixed method for obtaining stable reduced-order models for high-order continuous-time systems is proposed. It makes use of the advantages of the Routh approximation method and the Minimization of Integral Squared Error(MISE) criterion approach. In this mixed method the characteristic polynomial of the reduced-order model is first obtained from that of original system by using the Auxiliary Denominator Polynomial(ADP). The numerator polynomial is then determined so as to minimize the intergral squared-error of unit step responses. The advantages of the propsed method are that the reduced models are always stable if the original system are stable and the frequency domain and time domain characteristic of the original system will be preserved in the reduced models.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.36 no.4
• /
• pp.280-286
• /
• 1987

A new method is presented for obtaining redced-order model for time-invariant systems. This method does not require the calculation of the reciprocal transformation, the alpha table, the beta-table and the alpha-beta expansion which should be calculated in Routh approximation method, hence it is computationally very attractive better than Routh approximation method, furthemore the stability of the reduced-order model is guaranted if the original system is stable. This method starts with the continued fraction espansion of auxiliary denominator polynomial give for the denominator polynomial of the reduced-order model. The coefficients of the numerator polynomial are then obtained by equating moment of the original and the reduced-order medel.

• Journal of Convergence for Information Technology
• /
• v.11 no.2
• /
• pp.124-129
• /
• 2021

In this paper, an optimal controller design that guarantees absolute stability is proposed. The order of application of the thesis determines whether the delay time is included, and if the delay time is included, the delay time is approximated through the Pade approximation method. Then, the open loop transfer function for the process model and the controller transfer function is obtained, and the absolute stability interval is calculated by the Routh-Hurwitz discrimination method. In the last step, the optimal Proportional and Integral and Derivative(PID) control parameter value is calculated using a genetic algorithm using the interval obtained in the previous step. As a result, it was confirmed that the proposed method guarantees stability and is superior to the existing method in performance index by designing an optimal controller. If we study the compensation method for the delay time in the future, it is judged that better performance indicators will be obtained.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.24 no.6
• /
• pp.948-955
• /
• 1987

The model reduction method of the high order linear time invariant systems is proposed. The continuous fraction expansion of Auxiliary denominator polynomial is used to obtain denominator polynomial of the reduced order model, and the numerator polynomial of the reduced order model is obtained by equating the first some moments of the original and the reduced order model, using simplified moment function. This methiod does not require the calculation of the reciprocal transformation which should be calculated in Routh approximation, furthemore the stability of the reduced order model is guaranted if original system is stable. Responses of this method showed us good characteristics.