Order Reduction of Linear Dynamic Systems by Improved Routh Approximation Method

REFERENCES

• E. R. Samuel , L. Knockaert , and T. Dhaene , “Matrix-interpolation-based parametric model order reduction for multi-conductor transmission lines with delays,” IEEE Trans. Circ. Syst. II: Express Briefs , Vol. 62, no. 3, pp. 276–80, Mar. 2015.
   Web of Science ®Google Scholar
• L. Feng , J. G. Korvink , and P. Benner , “A fully adaptive scheme for model order reduction based on moment matching,” IEEE Trans. Compon. Packag. Manuf. Technol. , Vol. 5, no. 12, pp. 1872–84, Dec. 2015.
   Web of Science ®Google Scholar
• T.-S. Nguyen , T. L. Duc , T.-S. Tran , J.-M. Guichon , O. Chadebec , and G. Meunier , “Adaptive multipoint model order reduction scheme for large-scale inductive PEEC circuits,” IEEE Trans. Electromagn. Compat. , Vol. 59, no. 4, pp. 1143–51, Aug. 2017.
   Web of Science ®Google Scholar
• G. Scarciotti , and A. Astolfi , “Model reduction of neutral linear and nonlinear time-invariant time-delay systems with discrete and distributed delays,” IEEE Trans. Autom. Control , Vol. 61, no. 6, pp. 1438–51, Jun. 2016.
   Web of Science ®Google Scholar
• Y. Ni , C. Li , Z. Du , and G. Zhang , “Model order reduction based dynamic equivalence of a wind farm,” Int. J. Electr. Power Energy Syst. , Vol. 83, pp. 96–103, Dec. 2016.
   Web of Science ®Google Scholar
• G. Scarciotti , and A. Astolfi , “Data-driven model reduction by moment matching for linear and nonlinear systems,” Automatica , Vol. 79, pp. 340–51, May 2017.
   Web of Science ®Google Scholar
• C. Y. Jin , K. H. Ryu , S. W. Sung , J. Lee , and I.-B. Lee , “PID auto-tuning using new model reduction method and explicit PID tuning rule for a fractional order plus time delay model,” J. Process Control , Vol. 24, no. 1, pp. 113–28, Jan. 2014.
   Web of Science ®Google Scholar
• L. C. Hibbeler , M. M. C. See , J. Iwasaki , K. E. Swartz , R. J. O'Malley , and B. G. Thomas , “A reduced-order model of mould heat transfer in the continuous casting of steel,” Appl. Math. Model. , Vol. 40, no. 19–20, pp. 8530–51, Oct. 2016.
   Web of Science ®Google Scholar
• Z.-H. Xiao , and Y.-L. Jiang , “Multi-order Arnoldi-based model order reduction of second-order time-delay systems,” Int. J. Syst. Sci. , Vol. 47, no. 12, pp. 2925–34, Oct. 2016.
   Web of Science ®Google Scholar
• H. F. Vanlandingham , and B. Z. Yang , “Model order reduction using a nonlinear model strategy,” Int. J. Model. Simul. , Vol. 12, no. 2, pp. 34–8, Sep. 2016.
   Google Scholar
• A. Birouche , B. Mourllion , and M. Basset , “Model order-reduction for discrete-time switched linear systems,” Int. J. Syst. Sci. , Vol. 43, no. 9, pp. 1753–63, Feb. 2012.
   Web of Science ®Google Scholar
• M. Imran , A. Ghafoor , and V. Sreeram , “A frequency weighted model order reduction technique and error bounds,” Automatica , Vol. 50, pp. 3304–9, Dec. 2014.
   Web of Science ®Google Scholar
• S. Timme , K. J. Badcock , and A. Da Ronch , “Gust analysis using computational fluid dynamics derived reduced order models,” J. Fluids Struct ., Vol. 71, pp. 116–25, May 2017.
   Web of Science ®Google Scholar
• S. S. Sazhin , E. Shchepakina , and V. Sobolev , “Order reduction in models of spray ignition and combustion,” Combust. Flame , Vol. 187, pp. 122–8, Jan. 2018.
   Web of Science ®Google Scholar
• D. Kumar , and S. K. Nagar , “Reducing power system models by Hankel norm approximation technique,” Int. J. Model. Simul. , Vol. 33, no. 3, pp. 139–43, 2013.
   Google Scholar
• S. Ghosh , and N. Senroy , “Balanced truncation approach to power system model order reduction,” Electric Power Compon. Syst. , Vol. 41, no. 8, pp. 747–64, Jan. 2013.
   Web of Science ®Google Scholar
• N. Singh , R. Prasad , and H. O. Gupta , “Reduction of power system model using balanced realization, Routh and Padé approximation methods,” Int. J. Model. Simul. , Vol. 28, no. 1, pp. 57–63, Jan. 2008.
   Google Scholar
• A. Ramirez , A. Mehrizi-Sani , D. Hussein , M. Matar , M. Abdel-Rahman , J. Jesus Chavez , A. Davoudi , and S. Kamalasadan , “Application of balanced realizations for model-order reduction of dynamic power system equivalents,” IEEE Trans. Power Deliv. , Vol. 31, no. 5, pp. 2304–12, Oct. 2016.
   Web of Science ®Google Scholar
• H. Jardón-Kojakhmetov , and J. M. A. Scherpen , “Model order reduction and composite control for a class of slow-fast systems around a non-hyperbolic point,” IEEE Control Syst. Lett. , Vol. 1, no. 1, pp. 68–73, Jul. 2017.
   Google Scholar
• F. Donida , F. Casella , and G. Ferretti , “Model order reduction for object-oriented models: A control systems perspective,” Math. Comput. Model. Dyn. Syst. , Vol. 16, no. 3, 269–84, Jul. 2010.
   Web of Science ®Google Scholar
• W. Chen , and X. Li , “Model predictive control based on reduced order models applied to belt conveyor system,” ISA Trans. , Vol. 65, pp. 350–60, Nov. 2016.
   PubMed Web of Science ®Google Scholar
• A. Narwal , and R. Prasad , “Optimization of LTI systems using modified clustering algorithm,” IETE Tech. Rev. , Vol. 34, no. 2, pp. 201–13, Apr. 2017.
   Web of Science ®Google Scholar
• Y. Shamash , “Stable reduced-order models using Padé-type approximations,” IEEE Trans. Autom. Control , Vol. 19, pp. 615–6, Oct. 1974.
   Web of Science ®Google Scholar
• V. V. Krishnamurthy , and V. Seshadri , “Model reduction using the Routh stability criterion,” IEEE Trans. Autom. Control , Vol. 23, no. 3, pp. 729–31, Aug. 1978.
   Web of Science ®Google Scholar
• M. F. Hutton , and B. Friedland , “Routh approximations for reducing order of linear, time-invariant systems,” IEEE Trans. Autom. Control , Vol. 20, no. 3, pp. 329–37, Jun. 1975.
   Web of Science ®Google Scholar
• T. C. Chen , and C. Y. Chang , “Reduction of transfer functions by the stability-equation method,” J. Franklin Inst. , Vol. 308, no. 4, pp. 389–404, Oct. 1979.
   Web of Science ®Google Scholar
• A. K. Sinha , and J. Pal , “Simulation based reduced order modelling using a clustering technique,” Comput. Electr. Eng. , Vol. 16, no. 3, pp. 159–69, May 1990.
   Web of Science ®Google Scholar
• N. Ashoor , and V. Singh , “A note on lower order modeling,” IEEE Trans. Autom. Control , Vol. 27, no. 5, pp. 1124–6, Oct. 1982.
   Web of Science ®Google Scholar
• F. J. Alexandro Jr. , “Stable partial Padé approximations for reduced-order transfer functions,” IEEE Trans. Autom. Control , Vol. 29, pp. 159–62, Jun. 1983.
   Web of Science ®Google Scholar
• L. Fortuna , G. Nunnari , and A. Gallo , Model order reduction techniques with applications in electrical engineering , London, UK : Springer, 1992.
   Google Scholar
• Y. Shamash , “Model reduction using the Routh stability criterion and the Padé approximation technique,” Int. J. Control , Vol. 21, no. 3, pp. 475–84, Sep. 1975.
   Web of Science ®Google Scholar
• J. Pal , “Stable reduced-order Padé approximants using the Routh-Hurwitz array,” Electr. Lett. , Vol. 15, no. 8, pp. 225–6, Apr. 1979.
   Web of Science ®Google Scholar
• T. C. Chen , C. Y. Chang , and K. W. Han , “Stable reduced-order Padé approximants using stability-equation method,” Electr. Lett. , Vol. 16, no. 9, pp. 345–6, Apr. 1980.
   Web of Science ®Google Scholar
• T. C. Chen , C. Y. Chang , and K. W. Han , “Model reduction using the stability-equation method and the Padé approximation method,” J. Franklin Inst. , Vol. 309, no. 6, pp. 473–90, Jun. 1980.
   Web of Science ®Google Scholar
• B.-W. Wan , “Linear model reduction using Mihailov criterion and Padé approximation technique,” Int. J. Control , Vol. 33, no. 6, pp. 1073–89, Dec. 1981.
   Web of Science ®Google Scholar
• O. Ismail , B. Bandyopadhyay , and R. Gorez , “Discrete interval system reduction using Padé approximation to allow retention of dominant poles,” IEEE Trans. Circ. Syst.—I Fund. Theory Appl. , Vol. 44, no. 11, pp. 1075–78, Nov. 1997.
   Google Scholar
• C. B. Vishwakarma , and R. Prasad , “Clustering method for reducing order of linear system using Padé approximation,” IETE J. Res. , Vol. 54, no. 5, pp. 326–30, Sep. 2008.
   Web of Science ®Google Scholar
• C. B. Vishwakarma , “Order reduction using modified pole clustering and Pade approximations,” Int. J. Electr., Comput., Energy, Electron. Commun. Eng. , Vol. 5, no. 8, pp. 998–1002, Aug. 2011.
   Google Scholar
• V. Singh , “Non-uniqueness of model reduction using the Routh approach,” IEEE Trans. Autom. Control , Vol. 24, no. 4, pp. 650–1, Aug. 1979.
   Web of Science ®Google Scholar
• Y. Shamash , “Failure of the Routh-Hurwitz method of reduction,” IEEE Trans. Autom. Control , Vol. 25, no. 2, pp. 313–4, Apr. 1980.
   Web of Science ®Google Scholar
• D. P. Papadopoulo , and D. V. Bandekas , “Routh approximation method applied to order reduction of linear MIMO systems,” Int. J. Syst. Sci. , Vol. 55, no. 4, pp. 203–10, Apr. 1993.
   Google Scholar
• C.-S. Hsieh , and C. Hwang , “Reduced-order modeling of MIMO discrete systems using bilinear block Routh approximants,” J. Chin. Inst. Eng. , Vol. 12, no. 4, pp. 529–38, Feb. 1989.
   Google Scholar
• B. Bandyopadhyay , A. Upadhye , and O. Ismail , “γ-δ Routh approximation for interval systems,” IEEE Trans. Autom. Control , Vol. 42, no. 8, pp. 1127–30, Aug. 1997.
   Web of Science ®Google Scholar
• G. Langholz , and D. Feinmesser , “Model order reduction by Routh approximations,” Int. J. Syst. Sci. , Vol. 9, no. 5, pp. 493–6, Apr. 1978.
   Web of Science ®Google Scholar
• R. Prasad , “Padé type model order reduction for multivariable systems using Routh approximation,” Comput. Electr. Eng. , Vol. 26, no. 6, pp. 445–59, Aug. 2000.
   Web of Science ®Google Scholar
• C. Hwang , and K.-Y. Wang , “Optimal Routh approximations for continuous time systems,” Int. J. Syst. Sci. , Vol. 15, no. 3, pp. 249–59, May 1984.
   Web of Science ®Google Scholar
• C. Hwang , T.-Y. Guo , and L.-S. Sheih , “Model reduction using new optimal Routh approximant technique,” Int. J. Control , Vol. 55, no. 4, pp. 989–1007, Apr. 1992.
   Web of Science ®Google Scholar
• S. R. Desai , and R. Prasad , “A novel order diminution of LTI systems using Big Bang Big Crunch optimization and Routh approximation,” Appl. Math. Model. , Vol. 37, pp. 8016–28, Sep. 2013.
   Web of Science ®Google Scholar
• G. V. K. R. Sastry , and V. Krishnamurthy , “Relative stability using simplified Routh approximation method (SRAM),” IETE J. Res. , Vol. 33, no. 3, pp. 99–101, Jun. 1987.
   Google Scholar
• G. V. K. R. Sastry , and V. Krishnamurthy , “Biased model reduction by simplified Routh approximation method,” Electr. Lett. , Vol. 23, no. 20, pp. 1045–7, Sep. 1987.
   Web of Science ®Google Scholar
• Y. Shamash , “Stable biased reduced order models using the Routh method of reduction,” Int. J. Syst. Sci. , Vol. 11, no. 5, pp. 641–54, May 1980.
   Web of Science ®Google Scholar
• B. Bandyopadhyay , O. Ismail , and R. Gorez , “Routh-Pade approximation for interval systems,” IEEE Trans. Autom. Control , Vol. 39, no. 12, pp. 2454–6, Dec. 1994.
   Web of Science ®Google Scholar
• B. C. Moore , “Principal component analysis in control system: controllability, observability, and model reduction,” IEEE Trans. Autom. Control , Vol. 26, no. 1, pp. 17–36, Feb. 1981.
   Web of Science ®Google Scholar
• P. V. Kokotovik , R. E. O'Malley , and P. Sannuti , “Singular perturbation and order reduction in control theory-an overview,” Automatica , Vol. 12, pp. 123–32, Mar. 1976.
   Web of Science ®Google Scholar
• M. Avoki , “Control of large dynamic system by aggregation,” IEEE Trans. Autom. Control , Vol. 13, pp. 246–56, Jun. 1968.
   Google Scholar
• E. J. Grimme , “Krylov projection methods for model reduction,” Ph.D. thesis, ECE Dept., U. Illinois, Urbana , 1997.
   Google Scholar
• L. Pernebo , and L. M. Silverman , “Model reduction via balanced state space representations,” IEEE Trans. Autom. Control , Vol. 27, no. 2, pp. 382–7, Apr. 1982.
   Web of Science ®Google Scholar
• U. M. Al. Saggaf , “Approximate balanced-truncation model reduction for large scale systems,” Int. J. Control , Vol. 56, no. 6, pp. 1263–73, Jun. 1992.
   Web of Science ®Google Scholar
• V. Sreeram , S. Sahlan , W. M. W. Muda , T. Fernando, and H. H. C. Iu , “A generalized partial-fraction-expansion based frequency weighted balanced truncation technique,” Int. J. Control , Vol. 86, no. 5, pp. 833–43, Jan. 2013.
   Web of Science ®Google Scholar
• H. Sandberg , and A. Rantzer , “Balanced truncation of linear time-varying systems,” IEEE Trans. Autom. Control , Vol. 49, no. 2, pp. 217–29, Feb. 2004.
   Web of Science ®Google Scholar
• H. S. Abbas , and H. Werner , “Frequency-weighted discrete-time LPV model reduction using structurally balanced truncation,” IEEE Trans. Control Syst. Technol. , Vol. 19, no. 1, pp. 140–7, Jan. 2011.
   Web of Science ®Google Scholar
• P. Wittmuess , C. Tarin , A. Keck , E. Arnold , and O. Sawodny , “Parametric model order reduction via balanced truncation with Taylor series Representation,” IEEE Trans. Autom. Control , Vol. 61, no. 11, pp. 3438–51, Nov. 2016.
   Web of Science ®Google Scholar
• B. Besselink , N. Van De Wouw , J. M. A. Scherpen , and H. Nijmeijer , “Model reduction for nonlinear systems by incremental balanced truncation,” IEEE Trans. Autom. Control , Vol. 59, no. 10, pp. 2739–53, Oct. 2014.
   Web of Science ®Google Scholar
• K. Perev , and B. Shafai , “Balanced realization and model reduction of singular systems,” Int. J. Syst. Sci. , Vol. 25, no. 6, pp. 1039–52, May 1994.
   Web of Science ®Google Scholar
• G. Kotsalis , and A. Rantzer , “Balanced truncation for discrete time Markov jump linear systems,” IEEE Trans. Autom. Control , Vol. 55, no. 11, pp. 2606–11, Nov. 2010.
   Web of Science ®Google Scholar
• M. Farhood , and C. L. Beck , “On the balanced truncation and coprime factors reduction of Markovian jump linear systems,” Syst. Control Lett. , Vol. 96, pp. 96–106, Feb. 2014.
   Google Scholar
• Y. Zhu , L. Zhang , V. Sreeram , W. Shammakh , and B. Ahmad , “Resilient model approximation for Markov jump time-delay systems via reduced model with hierarchical Markov chains,” Int. J. Syst. Sci. , Vol. 47, no. 14, pp. 3496–507, Oct. 2015.
   Web of Science ®Google Scholar
• B. K. Kushwaha , and A. Narain , “Controller design for Cuk converter using model order reduction,” in 2nd International Conference on Power, Control and Embedded Systems, Allahabad, India, 17–19 Dec. 2012, pp. 1–5.
   Google Scholar
• E. Vuthchhay , P. Unnat , and C. Bunlaksananusorn , “Modeling of a sepic converter operating in continuous conduction mode,” in 6th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), Pattaya, Thailand, 6–9 May 2009, pp. 136–9.
   Google Scholar
• R. D. Middlebook , and S. Cuk , “A general unified approach to modeling switching-converter power stages,” Int. J. Electr. , Vol. 42, no. 6, pp. 521–50, Jan. 1977.
   Web of Science ®Google Scholar
• B. C. Kuo , Automatic control systems , 7th ed. Upper Saddle River, NJ: Prentice Hall Inc., 1995.
   Google Scholar
• A. Narwal , and R. Prasad , “A novel order reduction approach for LTI systems using cuckoo search optimization and stability equation,” IETE J. Res. , Vol. 62, no. 2, pp. 154–63, Aug. 2015. doi:10.1007/s10845-017-1309-3
   Web of Science ®Google Scholar
• A. Sikander , and R. Prasad , “Reduced order modelling based control of two wheeled mobile robot,” J. Intell. Manuf. , pp. 1–11, Feb. 2017.
   Web of Science ®Google Scholar
• A. Sikander , and R. Prasad , “Linear time-invariant system reduction using a mixed methods approach,” Appl. Math. Model. , Vol. 39, pp. 4848–58, Aug. 2015.
   Web of Science ®Google Scholar
• Y. Shamash , “Linear system reduction using Padé approximation to allow retention of dominant modes,” Int. J. Control , Vol. 21, no. 2, pp. 257–72, Mar. 1975.
   Web of Science ®Google Scholar
• Y. Shamash , “Truncation method of reduction: A viable alternative,” Electron. Lett. , Vol. 17, pp. 79–98, Jan. 1981.
   Web of Science ®Google Scholar
• A. Lepschy , and U. Viaro , “An improvement in the Routh-Padé approximation techniques,” Int. J. Control , Vol. 36, no. 4, pp. 643–61, May 1982.
   Web of Science ®Google Scholar
• N. Singh , R. Prasad , and H. O. Gupta , “Reduction of linear dynamic systems using Routh Hurwitz array and factor division method,” IETE J. Educ. , Vol. 47, no. 1, pp. 25–9, Mar. 2006.
   Google Scholar
• D. Kranthi Kumar , S. K. Nagar , and J. P. Tiwari , “A new algorithm for model order reduction of interval systems,” Bonfring Int. J. Data Min. , Vol. 3, no. 1, pp. 6–11, Mar. 2013.
   Google Scholar
• P. Gutman , C. Mannerfelt , and P. Molander , “Contributions to the model reduction problem,” IEEE Trans. Autom. Control , Vol. 27, no. 2, pp. 454–5, Apr. 1982.
   Web of Science ®Google Scholar
• Y. Bistritz , and U. Shaked , “Minimal Padé model reduction for multivariable systems,” J. Dyn. Syst., Meas. Control , Vol. 106, no. 4, pp. 293–9, Dec. 1984.
   Web of Science ®Google Scholar
• G. Parmar , S. Mukherjee , and R. Prasad , “System reduction using factor division algorithm and Eigen spectrum analysis,” Appl. Math. Model. , Vol. 31, no. 11, pp. 2542–52, Nov. 2007.
   Web of Science ®Google Scholar
• G. Parmar , R. Prasad , and S. Mukherjee , “Order reduction of linear dynamic systems using stability equation method and GA,” Int. J. Electr. Comput. Eng. , Vol. 1, no. 2, pp. 236–42, Jan. 2007.
   Google Scholar