Application of the "stretching" function for solving electrical circuits with differential-algebraic relations

• Autorzy: Drąg P. , Styczeń K.

Warianty tytułu

PL

Zastosowanie funkcji "rozciągających" do rozwiązywania obwodów elektrycznych z relacjami różniczkowo-algebraicznymi

• Języki publikacji: EN

Abstrakty

EN

In the article the problem of an accurately and effectively solving complex electrical circuits was considered. Application of the Kirchhoff’s laws enables us to model such circuits by both differential and algebraic equations. The presented approach is based on the direct shooting method. To preserve the continuity of the state variables and consistency of the initial conditions, in the nonlinear optimization problem the "stretching" function was applied. The presented method can be used to carry out the circuits simulation in a computationally efficient manner.

PL

W artykule poruszono problem dokładnego i skutecznego rozwiązywania złoz˙onych obwodów elektrycznych. Zastosowanie praw Kirchoffa umożliwia modelowanie takich obwodów zarówno przez równania różniczkowe jak i algebraiczne. Zaprezentowane podejście bazuje na bezpośredniej metodzie strzałów. Aby zapewnić ciągłość zmiennych stanu oraz spójne warunki początkowe, w zadaniu programowanie nieliniowego zastosowano funkcję "rozciągającą". Zaprezentowana metoda może być wykorzystana w symulowaniu obwodów w sposób wydajny obliczeniowo.

Słowa kluczowe

EN

electrical circuit simulation; differential-algebraic system; stretching function; inconsistent initial condition

PL

symulacja obwodów elektrycznych; równanie różniczkowe algebraiczne; funkcja rozciągająca; warunek początkowy

• Wydawca: Wydawnictwo SIGMA-NOT
• Czasopismo: Przegląd Elektrotechniczny
• Rocznik: 2015
• Tom: R. 91, nr 2
• Strony: 157--161
• Opis fizyczny: Bibliogr. 21 poz., wykr.

Twórcy

autor

Drąg P.

• Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Janiszewskiego 11-17, 50-372 Wrocław, Poland

autor

Styczeń K.

• Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Janiszewskiego 11-17, 50-372 Wrocław, Poland

Bibliografia

• [1] Biegler L.T., Campbell S., Mehrmann V.: DAEs, Control, and Optimization, SIAM, Philadelphia, 2012.
• [2] Bodestedt M., Tischendorf C.: PDAE models of integrated circuits and index analysis, Mathematical and Computer Modelling of Dynamical Systems, 13, pp. 1–17, 2007.
• [3] Boggs P.T., Tolle J.W.: Sequential Quadratic Programming, Acta Numerica, 4, pp. 1–51, 1995.
• [4] Brachtendorf H.G., Laur R.: On Consistent Initial Conditions for Circuit’s DAEs with Higher Index, IEEE Transactions on Circuits and Systems – I: Fundamental Theory and Applications, 48, pp. 606–612, 2001.
• [5] Brenan K.E., Campbell S.L., Petzold L.R.: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia, 1996.
• [6] Chen Q., Weng S.-H., Cheng C.-K.: A Practical Regularization Technique for Modified Nodal Analysis in Large- Scale Time-Domain Circuit Simulation, IEEE Transactions on Computer–Aided Design of Integrated Circuits and Systems, 31, pp. 1031–1040, 2012.
• [7] Diehl M., Bock H.G., Schlöder J.P., Findeisen R., Nagy Z., Allgöwer F.: Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations, Journal of Process Control, 12, pp. 577–585, 2002.
• [8] Drąg P., Styczeń K.: A Two-Step Approach for Optimal Control of Kinetic Batch Reactor with electroneutrality condition, Przegląd Elektrotechniczny, 6, pp. 176–180, 2012.
• [9] Fijnvandraat J.G., Houben S.H.M.J., ter Maten E.J.W., Peters J.M.F.: Time domain analog circuit simulation, Journal of Computational and Applied Mathematics, 185, pp. 441–459, 2006.
• [10] Günther M.: A Joint DAE/PDE Model for Interconnected Electrical Networks, Mathematical and Computer Modelling of Dynamical Systems, 6, pp. 114–128, 2000.
• [11] Günther M., Feldmann U.: The DAE-index in electric circuit simulation, Mathematics and Computers in Simulation, 39, pp. 573–582, 1995.
• [12] Günther M., Hoschek M.: ROW methods adapted to electric circuit simulation packages, Journal of Computational and Applied Mathematics, 82, pp. 159–170, 1997.
• [13] Hairer E., Lubich C., Roche M.: The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Lecture Notes in Mathematics, 1989.
• [14] Li Y.: A simulation-based evolutionary approach to LNA circuit design optimization, Applied Mathematics and Computation, 209, pp. 57–67, 2009.
• [15] März R., Schwarz D.E., Feldmann U., Sturtzel S., Tischendorf C.: Finding Beneficial DAE Structures in Circuit Simulation, Jäger W. et al. (eds.), Mathematics - Key Technology for the Future, Springer-Verlag Berlin Heidelberg, pp. 413–428, 2003.
• [16] Nocedal J., Wright S.J.: Numerical Optimization. Second Edition, Springer, New York, 2006.
• [17] Parsopoulos K.E., Plagianakos V.P., Mogoulas G.D., Vrahatis M.N.: Improving the particle swarm optimizer by function "stretching", in: Hadjisavvas N., Pardalos P.M. (eds.), Advances in Convex Analysis and Global Optimization, Kluwer Academic Publishers, pp. 445–457, 2001.
• [18] Parsopoulos K.E., Plagianakos V.P., Mogoulas G.D., Vrahatis M.N.: Objective function "stretching" to alleviate convergence to local minima, Nonlinear Analysis, 47, pp. 3419–3424, 2001.
• [19] Petzold L.: Differential-algebraic equations are not ode’s, SIAM J. Sci. Stat. Comput., 3, pp. 367–384, 1982.
• [20] Takamatsu M., Iwata S.: Index reduction for differentialalgebraic equations by substitution method, Linear Algebra and its Applications, 429, pp. 2268–2277, 2008.
• [21] Udave D.E.C., Ogrodzki J., de Anda M.A.G.: DC Large- Scale Simulation of Nonlinear Circuits on Parallel Processors, JET Intl Journal of Electronics and Telecommunications, 58, pp. 285–295, 2012.