### Design of a Matlab toolbox and GUI for minimal realizations

#### Abstract

Minimal realization for linear systems has been studied extensively in the literature. Techniques proposed differ in terms of the configuration of the state space form, the time efficiency of the algorithm and the reduction of memory storage. The minimal realization toolbox presented in this paper offers the possibility to test different methods and choose the most suitable form depending on the application. The given system can be represented by a transfer function or by raw (frequency or time domain) data. A graphical user interface (GUI) was implemented in order to ease the use of this toolbox and allow to rapidly test the methods and display the results.

#### Keywords

#### Full Text:

PDF#### References

C. B. Vishwakarma, "Modified Hankel Matrix Approach for Model Order Reduction in Time Domain," International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, vol. 8, p. 7, 2014.

Y. Shamash. (1975, Model reduction using minimal realisation algorithms. Electronics Letters 11(16), 385-387. Available: http://digitallibrary.theiet.org/content/journals/10.1049/el_19750293

C.-T. Chen, Linear System Theory and Design: Oxford University Press, Inc., 1995.

E. C. Abana, M. Pacion, R. Sordilla, D. Montaner, D. Agpaoa, and R. M. Allam, "Rakebot: a robotic rake for mixing paddy in sun drying," Indonesian journal of electrical engineering and computer science, vol. 14, 2019.

R. Pilla, S. Killari, and K. B. M. Sahu, "Design and Simulation of the Control System for Inverter-fed Permanent Magnet Synchronous Motor Drive," Indonesian journal of electrical engineering and computer science, vol. 12, 2018.

A. J. Mayo and A. C. Antoulas, "A framework for the solution of the generalized realization problem," Linear algebra and its applications, vol. 425, pp. 634-662, 2007.

B. Peherstorfer, S. Gugercin, and K. Willcox, "Data-Driven Reduced Model Construction with Time-Domain Loewner Models," SIAM Journal on Scientific Computing, vol. 39, pp. A2152-A2178, 2017.

Y. Yuan, A. Rai, E. Yeung, G.-B. Stan, S. Warnick, and J. Goncalves, "A minimal realization technique for the dynamical structure function of a class of LTI systems," IEEE Transactions on Control of Network Systems, pp. 1-1, 2015.

A. V. Evseev and V. N. Chetverikov, "Realizations and minimal realizations of input-output mappings of general form," Differential Equations, vol. 49, pp. 1609-1618, 2014.

C. W. Scherer and İ. E. Köse, "From transfer matrices to realizations: Convergence properties and parametrization of robustness analysis conditions," Systems & Control Letters, vol. 62, pp. 632-642, 2013.

P. Corke, "Robot Manipulator Capability in MATLAB: A Tutorial on Using the Robotics System Toolbox [Tutorial]," IEEE Robotics & Automation Magazine, vol. 24, pp. 165-166, 2017.

H. Qin, Z. Liu, Y. Liu, and H. Zhong, "An object-oriented MATLAB toolbox for automotive body conceptual design using distributed parallel optimization," Advances in Engineering Software, vol. 106, pp. 19-32, 2017.

J. R. Raj, S. M. K. Rahman, and S. Anand, "Microcontroller USB interfacing with MATLAB GUI for low cost medical ultrasound scanners," Engineering Science and Technology, an International Journal, vol. 19, pp. 964-969, 2016.

B. S. Ahmed, M. A. Sahib, and M. Y. Potrus, "Generating combinatorial test cases using Simplified Swarm Optimization (SSO) algorithm for automated GUI functional testing," Engineering Science and Technology, an International Journal, vol. 17, pp. 218-226, 2014.

X.-D. Sun, T. Clarke, and M. A. Maiza. (1996, A toolbox for minimal state space model realisation. IEE Proceedings - Control Theory and Applications 143(2), 152-158. Available: http://digital-library.theiet.org/content/journals/10.1049/ip-cta_19960360

B. D. Schutter, "Minimal state-space realization in linear system theory: an overview," Journal of Computational and Applied Mathematics, p. 24, 2000.

K. Cherifi and K. Hariche, "Review of MIMO minimal realization techniques and case study on SCARA robot manipulator " International review of automatic control, vol. 10, 2017.

Y. Yuan, A. Rai, E. Yeung, G. B. Stan, S. Warnick, and J. Gonçalves, "A Minimal Realization Technique for the Dynamical Structure Function of a Class of LTI Systems," IEEE Transactions on Control of Network Systems, vol. 4, pp. 301-311, 2017.

E.G.Gilbert, "Controllability and observability in multi-variable control systems," SIAM J. Control vol. 1, pp. 128–151, 1963.

R.E.Kalman, "Irreducible realizations and the degree of a rational matrix," J. Soc. Ind. Appl. Math, vol. 13, p. 24, 1965.

S. Tsay, Barnett, Structural analysis and design of multivariable control systems : an algebraic approac: Berlin ; New York : Springer-Verlag, 1988.

M. Sababha, M. Zohdy, and M. Kafafy, "Robust pole placement using firefly algorithm," International journal of electrical and computer engineering, vol. 9, 2019.

P. Benner, P. Losse, V. Mehrmann, and M. Voigt, "Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations," in Surveys in Differential-Algebraic Equations III, A. Ilchmann and T. Reis, Eds., ed Cham: Springer International Publishing, 2015, pp. 117-175.

S. Campbell, P. Kunkel, and V. Mehrmann, "Chapter 2: Regularization of Linear and Nonlinear Descriptor Systems," in Control and Optimization with Differential-Algebraic Constraints, ed: Society for Industrial and Applied Mathematics, 2012, pp. 17-36.

R. K. H. Galvão, K. H. Kienitz, and S. Hadjiloucas, "Conversion of descriptor representations to state-space form: an extension of the shuffle algorithm," International Journal of Control, pp. 1-15, 2017.

J. Sjöberg, "Descriptor Systems and Control Theory," Linköpings universitet, Department of Electrical Engineering2005.

A. Antoulas, S. Lefteriu, and A. Ionita, "Chapter 8: A Tutorial Introduction to the Loewner Framework for Model Reduction," in Model Reduction and Approximation, ed: Society for Industrial and Applied Mathematics, 2017, pp. 335-376.

A. Parvaresh and S. M. A. Mohammadi, "A Multi-Zone HVAC System for a Typical Building for MATLAB/SIMULINK Platform," Bulletin of Electrical Engineering and Informatics, vol. 2, p. 83~87, 2013.

A. Akinrinde, A. Swanson, and R. Tiako, "Effect of Ferroresonance on Wind Turbine: Comparison of Atp/Emtp and Matlab/Simulink," Indonesian journal of electrical engineering and computer science, vol. 14, 2019.

Q. G. Wang, Decoupling Control: Springer Berlin Heidelberg, 2003.

P. Benner, V. Mehrmann, V. Sima, S. Van Huffel, and A. Varga, "SLICOT - A Subroutine Library in Systems and Control Theory," in Applied and Computational Control, Signal and Circuits. vol. 1, ed, 1999, pp. 499-539.

T. Penzl, "Algorithms for model reduction of large dynamical systems," Linear algebra and its applications, vol. 415, pp. 322-343, 2006.

DOI: http://doi.org/10.11591/ijeecs.v17.i2.pp929-940

### Refbacks

- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.