Kontrol Stepsize Pada Integrasi Numerik Ekivalen Dengan Prinsip Aksi Kontroler PID Pada Sistem Kontrol
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Abstract
Differential equations with initial values are used as mathematical models to express problems in the fields of physics, engineering, biology or others. The achievement of differential equations solutions is mostly done through a numerical integration method approach. Stepsize control on numerical integration method will affect the accuracy and efficiency of the solution, and many stepsize control approaches are carried out proportionally and statically even though it is known that the problems reviewed are dynamic. That in the field of control systems there are P, PI, PD or PID controllers that can be static and dynamic and proportional action controls have the disadvantage of not being able to eliminate errors in steady-state conditions.
The problem between the stepsize control approach and the PID controller seems to be equivalence and this paper declares the existence of a close analogy of the two problems even though it is limited to theoretical and the numerical test cannot be explained because the research to be continues.
Persamaan diferensial dengan nilai awal (initial value problem) banyak digunakan sebagai model matematik untuk menyatakan permasalahan baik dalam bidang fisika, rekayasa, biologi atau lainnya. Pencapaian solusi persamaan diferensial tersebut banyak dilakukan melalui pendekatan metode integrasi numerik. Kontrol stepsize pada metode integrasi numerik akan mempengaruhi akurasi dan efisiensi dari solusi, dan banyak pendekatan kontrol stepsize dilakukan secara proporsional dan statik walaupun diketahui permasalahan yang ditinjau bersifat dinamik. Bahwa pada bidang sistem kontrol telah tersedia kontroler P, PI, PD atau PID yang dapat bersifat statik dan dinamik dan diketahui bahwa kontrol aksi proporsional mempunyai kelemahan tak dapat menghilangkan kesalahan pada kondisi steady-state. Permasalahan antara pendekatan kontrol stepsize dengan kontroler PID tampaknya ekivalen dan tulisan ini mendeklarasikan adanya analogi yang erat dari kedua permasalahan tersebut walaupun sebatas teoritis dan uji numeriknya belum dapat dipaparkan karena penelitiannya masih berlanjut.
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References
. K. Gustafsson, Stepsize Selection in Implicit Runge-Kutta Methods Viewed As A Control Problem. IFAC 12th Triennial World Congress. Sydney, Australia, 1993.
. Hairer, E., S.P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I - Nonstiff Problems, vol 8. Springer Series in Computational Mathematics. Springer-Verlag. 1987.
. K. Gustafsson, “Control of Error and Convergence in ODE Solver”, PhD Thesis, Departement of Automatic Control, Lund Institute of Technology, 1992.
. Karl Johan Astrom and Richard M. Murray, Feedback Systems : An Introduction for Scientists and Engineers, Princeton University Press, 2008.
. Bohdan T. Kulakowski, et al., Dynamic Modeling and Control of Engineering, Cambridge University Press, The Edinburgh Building, Cambridge CB2 8RU, UK, 2007.
. W. H. Press, et al., Numerical Recipes in C (Cambridge University Press, New York, 1988), Chap. 15.
. David F. Griffiths and Desmond J. Higham, Numerical Methods for Ordinary Differential Equations, Springer-Verlag London Limited, 2010.
. Higinio Ramos, et al., Solving First-order initial-value problems by using an explicit non-standard A-stable on-step method in variable step-size formulation, Applied Mathematics and Computation Jurnal 268, 2015.