satНАУКА и ТЕХНИКАScience & Technique2227-10312414-0392Belarusian National Technical University10.21122/2227-1031-2018-17-5-413-420sat-1870Research ArticleМАШИНОСТРОЕНИЕMECHANICAL ENGINEERINGОптимизация управления движением мостового кранаOptimization of Bridge Crane Movement ControlЛовейкинВ. С.LoveikinV. S.

Доктор технических наук, профессор 

Адрес для переписки: Ромасевич Юрий Александрович Национальный университет биоресурсов и природопользования Украины, ул. Героев Обороны, 12, 03041, г. Киев, Украина. Тел.: +380 44 527-87-34     romasevichyuriy@ukr.net

РомасевичЮ. А.RomasevichY. A.

Доктор технических наук, доцент

Address for correspondence: Romasevich Yuriy A. – National University of Life and Environmental Sciences of Ukraine, 12 Geroev Oborony str., 03041, Kiev, Ukraine. Tel.: +380 44 527-87-34    romasevichyuriy@ukr.net

Национальный университет биоресурсов и природопользования УкраиныУкраинаNational University of Life and Environmental Sciences of UkraineUkraine201812102018175413420Copyright © Ловейкин В.С., Ромасевич Ю.А., 20182018Ловейкин В.С., Ромасевич Ю.А.Loveikin V.S., Romasevich Y.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://sat.bntu.by/jour/article/view/1870

Переходные режимы движения мостовых кранов определяют их энергетические, динамические и электрические показатели, а также производительность и долговечность работы. На основе анализа показателей эффективности работы мостового крана решена задача оптимального управления его передвижением. В качестве критериев оптимизации выбраны терминальные и интегральный критерии, отображающие нежелательные динамические свойства крана. С помощью метода Лежандра установлена возможность достижения минимума интегрального критерия. Анализ уравнения Эйлера – Пуассона, которое является необходимым условием минимума интегрального критерия, показал, что аналитическое нахождение решения оптимизационной задачи невозможно. Для нахождения приближенного решения оптимизационной задачи использован метод дифференциальной эволюции. Приближенное (субоптимальное) решение было найдено в комплексной области, которая является конъюнкцией ограниченных областей динамических параметров и фазовых координат системы. Ограничение области фазовых координат системы (в статье использована полиномиальная базисная функция) дало возможность достичь абсолютных минимумов терминальных критериев задачи. Для установления эффективности реализации субоптимального управления проведено моделирование движения мостового крана с учетом динамической механической характеристики его электропривода. В процессе моделирования изменению подвергались частота и амплитуда питающего напряжения электропривода механизма передвижения крана (использован частотный скалярный метод изменения скорости асинхронного электропривода). Сравнительный анализ динамических, кинематических, электрических и энергетических показателей работы мостового крана при субоптимальном и S-образном (стандартном) законах изменения частоты и напряжения питания электропривода крана дал возможность установить улучшение эффективности его работы при субоптимальном управлении.

Transient modes of bridge cranes movement determine their energy, dynamic and electrical performance, as well as productivity and durability of work. An optimal control problem of its movement has been solved while making an analysis of indicators for efficient performance of a bridge crane. Terminal and integral criteria have been selected as optimization criteria. They represent undesirable dynamic properties of the crane. Legendre method has been used to determine the possibility for achieving minimum of the optimization criterion. An analysis of the Euler-Poisson equation, which is a necessary condition for the minimum of the integral criterion, has shown that it is impossible to find a solution for the optimization problem in an analytical form. A method of differential evolution has been used in order to find an approximate solution to the optimization problem. The approximate (suboptimal) solution has been found in the complex domain, which is a limited domain conjunction of dynamic parameters and phase coordinates of the system. Limitation in the domain of the system phase coordinates (a polynomial basis function has been used in the paper) provides the possibility to attain absolute minimums of terminal problem criteria. A simulation of the bridge crane motion has been carried out in order to establish an efficiency for implementation of the suboptimal control. During this process dynamic mechanical characteristics of its electric drive have been taken into account. While carrying out the simulation, a frequency and an amplitude of the electric drive voltage in the crane movement mechanism have been changed (frequency scalar method for speed changing of an asynchronous electric drive has been used). A comparative analysis of the dynamic, kinematic, electrical and energy performance indicators of the bridge crane under suboptimal and S-curved (standard) laws of frequency and voltage variations in the crane electric drive has made it possible to establish an improvement in the efficiency of its operation under suboptimal control.

мостовой краноптимальное управлениеинтегральный и терминальный критериимоделированиеколебаниядинамические нагрузкидифференциальная эволюцияbridge craneoptimal controlintegral and terminal criteriasimulationoscillationsdynamic loadsdifferential evolutionReferencesKomarov M. S. (1969) Dynamics of Load-Lifting Machines. Мoscow, Mashynostroenye Publ. 206 (in Russian).Komarov M. S. (1969) Dynamics of Load-Lifting Machines. Мoscow, Mashynostroenye Publ. 206 (in Russian).Kazak S. А. (1968) Dynamics of Overhead Cranes. Мoscow, Mashynostroenye Publ. 331 (in Russian).Kazak S. А. (1968) Dynamics of Overhead Cranes. Мoscow, Mashynostroenye Publ. 331 (in Russian).Gohberg М. М. (1969) Metal Constructions of Hoistingand-Transport Machines. Мoscow, Mashynostroenye Publ. 520 (in Russian).Gohberg М. М. (1969) Metal Constructions of Hoistingand-Transport Machines. Мoscow, Mashynostroenye Publ. 520 (in Russian).Gaidamaka V. F. (1989) Load-Lifting Machines. Кiev, Vyscha Shkola Publ. 328 (in Russian).Gaidamaka V. F. (1989) Load-Lifting Machines. Кiev, Vyscha Shkola Publ. 328 (in Russian).Sheffler M., Dresyh Kh., Kurt F. (1981) Load-Lifting Cranes. Book 2. Мoscow, Mashynostroenye Publ. 287 (in Russian).Sheffler M., Dresyh Kh., Kurt F. (1981) Load-Lifting Cranes. Book 2. Мoscow, Mashynostroenye Publ. 287 (in Russian).Lobov N. А. (1987) Dynamics of Load-Lifting Cranes, Мoscow, Mashynostroenye Publ. 160 (in Russian).Lobov N. А. (1987) Dynamics of Load-Lifting Cranes, Мoscow, Mashynostroenye Publ. 160 (in Russian).Budikov L. Ya. (1997) Multiparametric Analysis of Overhead-Type Crane Dynamics. Luhansk, Publishing house of East Ukrainian National University named after V. Dal. 210 (in Russian).Budikov L. Ya. (1997) Multiparametric Analysis of Overhead-Type Crane Dynamics. Luhansk, Publishing house of East Ukrainian National University named after V. Dal. 210 (in Russian).Loveikin V. S., Chovniuk Iu. V., Dikteruk M. H., Pastushenko S. I. (2004) Simulation of Dynamics for Lifting Machine Mechanisms. Kyiv-Mykolaiv, Mykolaiv National Agrarian University. 286 (in Ukrainian).Loveikin V. S., Chovniuk Iu. V., Dikteruk M. H., Pastushenko S. I. (2004) Simulation of Dynamics for Lifting Machine Mechanisms. Kyiv-Mykolaiv, Mykolaiv National Agrarian University. 286 (in Ukrainian).Loveikin V. S., Romasevych Yu. O. (2016) Dynamics and Optimization of Overhead Crane Movement. Kyiv, KOMPRINT Publ. 314 (in Ukrainian).Loveikin V. S., Romasevych Yu. O. (2016) Dynamics and Optimization of Overhead Crane Movement. Kyiv, KOMPRINT Publ. 314 (in Ukrainian).Blackburn D., Singhose W., Kitchen J., Patrangenaru P., Lawrence J. (2009) Command Shaping for Nonlinear Crane Dynamics. Journal of Vibration and Control, 16 (4), 477–501. https://doi.org/10.1177/1077546309106142.Blackburn D., Singhose W., Kitchen J., Patrangenaru P., Lawrence J. (2009) Command Shaping for Nonlinear Crane Dynamics. Journal of Vibration and Control, 16 (4), 477–501. https://doi.org/10.1177/1077546309106142.Naif B. Almutairi, Mohamed Zribi (2009) Sliding Mode Control of a Three-dimensional Overhead Crane. Journal of Vibration and Control, 15 (11). 1679–1730. https://doi.org/10.1177/1077546309105095.Naif B. Almutairi, Mohamed Zribi (2009) Sliding Mode Control of a Three-dimensional Overhead Crane. Journal of Vibration and Control, 15 (11). 1679–1730. https://doi.org/10.1177/1077546309105095.Moustafa Kamal A. F., Ebeid A. M. (1998) Nonlinear Modeling and Control of Overhead Crane Load Sway. Journal of Dynamic Systems, Measurement, and Control, 110 (3), 266–271. https://doi.org/10.1115/1.3152680.Moustafa Kamal A. F., Ebeid A. M. (1998) Nonlinear Modeling and Control of Overhead Crane Load Sway. Journal of Dynamic Systems, Measurement, and Control, 110 (3), 266–271. https://doi.org/10.1115/1.3152680.Sun N., Fang Yo (2014) Non-Linear Tracking Control of Under-Actuated Cranes with Load Transferring and Lowering: Theory and Experimentation. Automatica, 50 (9), 2350–2357. https://doi.org/10.1016/j.automatica.2014.07.023.Sun N., Fang Yo (2014) Non-Linear Tracking Control of Under-Actuated Cranes with Load Transferring and Lowering: Theory and Experimentation. Automatica, 50 (9), 2350–2357. https://doi.org/10.1016/j.automatica.2014.07.023.Tuan L. A., Lee S., Dang V. H., Moon S., Kim B. S. (2013). Partial Feedback Linearization Control of Three-Dimensional Overhead Crane. International Journal of Control, Automation, and Systems, 11 (4), 718–727. https://doi.org/10.1007/s12555-012-9305-z.Tuan L. A., Lee S., Dang V. H., Moon S., Kim B. S. (2013). Partial Feedback Linearization Control of Three-Dimensional Overhead Crane. International Journal of Control, Automation, and Systems, 11 (4), 718–727. https://doi.org/10.1007/s12555-012-9305-z.Singhose W., Kim D., Kenison M. (2008) Input Shaping Control of Double-Pendulum Bridge Crane Oscillations. Journal of Dynamic Systems, Measurement, and Control, 130 (3), 034504-1−034504-6. https://doi.org/10.1115/1.2907363.Singhose W., Kim D., Kenison M. (2008) Input Shaping Control of Double-Pendulum Bridge Crane Oscillations. Journal of Dynamic Systems, Measurement, and Control, 130 (3), 034504-1−034504-6. https://doi.org/10.1115/1.2907363.Herasymiak R. P., Leshchev. V. A. (2008) Analysis and Synthesis Crane Electro-Mechanical Systems. Оdessa, SMIL Publ. 192 (in Russian).Herasymiak R. P., Leshchev. V. A. (2008) Analysis and Synthesis Crane Electro-Mechanical Systems. Оdessa, SMIL Publ. 192 (in Russian).Budikov L. Ya. (1997) Multi-Parametric Analysis of Overhead-Type Crane Dynamics. Luhansk, Publishing House of East Ukrainian National University named after V. Dal. 210 (in Russian).Budikov L. Ya. (1997) Multi-Parametric Analysis of Overhead-Type Crane Dynamics. Luhansk, Publishing House of East Ukrainian National University named after V. Dal. 210 (in Russian).Grigorov O. V., Loveikin V. S. (1997) Optimal Control of Hoisting Machine Movement. Kiev, IZMN Publ. 264 (in Ukrainian).Grigorov O. V., Loveikin V. S. (1997) Optimal Control of Hoisting Machine Movement. Kiev, IZMN Publ. 264 (in Ukrainian).Singhose W., Porter L., Kenison M., Kriikku E. (2000) Effects of Hoisting on Input Shaping Control of Gantry Cranes. Control Engineering Practice, 8 (10), 1159–1165. https://doi.org/10.1016/s0967-0661(00)00054-x.Singhose W., Porter L., Kenison M., Kriikku E. (2000) Effects of Hoisting on Input Shaping Control of Gantry Cranes. Control Engineering Practice, 8 (10), 1159–1165. https://doi.org/10.1016/s0967-0661(00)00054-x.Dhanda A., Vaughan J., Singhose W. (2016) Vibration Reduction Using Near Time-Optimal Commands for Systems with Nonzero Initial Conditions. Journal of Dynamic Systems, Measurement, and Control, 138 (4), 041006-1−041006-9. https://doi.org/10.1115/1.4032064.Dhanda A., Vaughan J., Singhose W. (2016) Vibration Reduction Using Near Time-Optimal Commands for Systems with Nonzero Initial Conditions. Journal of Dynamic Systems, Measurement, and Control, 138 (4), 041006-1−041006-9. https://doi.org/10.1115/1.4032064.Ermidoro M., Formentin S., Cologni A., Previdi F., Savaresi S. M. (2014) On Time-Optimal Anti-Sway Controller Design for Bridge Cranes. American Control Conference (ACC). Portland, Oregon, USA. 2809–2814. https://doi.org/10. 1109/acc.2014.6858939.Ermidoro M., Formentin S., Cologni A., Previdi F., Savaresi S. M. (2014) On Time-Optimal Anti-Sway Controller Design for Bridge Cranes. American Control Conference (ACC). Portland, Oregon, USA. 2809–2814. https://doi.org/10. 1109/acc.2014.6858939.Hazriq I. J., Nursabillilah M. A., Mohamed Z., Selamat N. A., Abidin A. F. Z., Jamian J. J., Kassim A. M. (2013) Optimal Performance of Nonlinear Gantry Crane System via Priority-Based Fitness Scheme in Binary PSO Algorithm. 5th International Conference on Mechatronics (ICOM’13). IOP Conf. Series: Materials Science and Engineering, 53. 012011. https://doi.org/10.1088/1757-899x/53/1/012011.Hazriq I. J., Nursabillilah M. A., Mohamed Z., Selamat N. A., Abidin A. F. Z., Jamian J. J., Kassim A. M. (2013) Optimal Performance of Nonlinear Gantry Crane System via Priority-Based Fitness Scheme in Binary PSO Algorithm. 5th International Conference on Mechatronics (ICOM’13). IOP Conf. Series: Materials Science and Engineering, 53. 012011. https://doi.org/10.1088/1757-899x/53/1/012011.Manson G. A. (2007) Time-Optimal Control of Overhead Crane Model. Optimal Control Applications & Methods, 3 (2), 115–120. https://doi.org/10.1002/oca.4660030202.Manson G. A. (2007) Time-Optimal Control of Overhead Crane Model. Optimal Control Applications & Methods, 3 (2), 115–120. https://doi.org/10.1002/oca.4660030202.Solis C. U., Clempner J. B., Poznyak A. S. (2016) Designing Terminal Optimal Control with Integral Sliding Mode Component Using Saddle Point Method Approach: Cartesian 3D-Crane Application. Nonlinear Dynamics, 86 (2), 911–926. https://doi.org/10.1007/s11071-016-2932-9.Solis C. U., Clempner J. B., Poznyak A. S. (2016) Designing Terminal Optimal Control with Integral Sliding Mode Component Using Saddle Point Method Approach: Cartesian 3D-Crane Application. Nonlinear Dynamics, 86 (2), 911–926. https://doi.org/10.1007/s11071-016-2932-9.Smekhov A. A., Erofeev N. Y. (1975) Optimal Control of Lifting and Transporting Machines. Мoscow, Mashynostroenye Publ. 239 (in Russian).Smekhov A. A., Erofeev N. Y. (1975) Optimal Control of Lifting and Transporting Machines. Мoscow, Mashynostroenye Publ. 239 (in Russian).Loveikin V. S., Pochka K. I. (2017) Synthesis of Camshaft Driving Mechanism in Roller Molding Installation with Combined Motion Mode According to Acceleration of Third Order. Nauka i Tekhnika = Science & Technique, 16 (3), 206–214 (in Russian). https://doi.org/10.21122/2227-1031-2017-16-3-206-214.Loveikin V. S., Pochka K. I. (2017) Synthesis of Camshaft Driving Mechanism in Roller Molding Installation with Combined Motion Mode According to Acceleration of Third Order. Nauka i Tekhnika = Science & Technique, 16 (3), 206–214 (in Russian). https://doi.org/10.21122/2227-1031-2017-16-3-206-214.Loveikin V. S., Chovniuk Yu. V., Liashko A. P. (2014) Crane Vibrating Systems Controlled by Mechatronic Devices with Magneto-Rheological Fluid: the Nonlinear Mathematical Model of Behavior and Optimization of Work Regimes. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu = Scientific Bulletin of National Mining University , 6, 97–102 (in Russian).Loveikin V. S., Chovniuk Yu. V., Liashko A. P. (2014) Crane Vibrating Systems Controlled by Mechatronic Devices with Magneto-Rheological Fluid: the Nonlinear Mathematical Model of Behavior and Optimization of Work Regimes. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu = Scientific Bulletin of National Mining University , 6, 97–102 (in Russian).Loveikin V. S., Nesterov A. P. (2002) Dynamic Optimization of Hoisting Machines, Kharkiv, KhDADTU. 285 (in Ukrainian).Loveikin V. S., Nesterov A. P. (2002) Dynamic Optimization of Hoisting Machines, Kharkiv, KhDADTU. 285 (in Ukrainian).Kyrychenko Y., Samusia V., Kyrychenko V. (2012) Software Development for the Automatic Control System of DeepWater Hydro-Hoist. Geomechanical Processes During Underground Mining, 81–86. https://doi.org/10.1201/b13157-14.Kyrychenko Y., Samusia V., Kyrychenko V. (2012) Software Development for the Automatic Control System of DeepWater Hydro-Hoist. Geomechanical Processes During Underground Mining, 81–86. https://doi.org/10.1201/b13157-14.Petrov Iu. P. (1977) Variational Methods of Optimal Control Theory, Leningrad, Energia Publ. 280 (in Russian).Petrov Iu. P. (1977) Variational Methods of Optimal Control Theory, Leningrad, Energia Publ. 280 (in Russian).Loveikin V. S., Romasevich Yu. O., Loveikin Yu. V. (2012) Analysis of Direct Variational Methods for Solving Optimal Control Problems. Visnyk Natsionalnoho Universytetu “Lvivska Politekhnika”. Optymizatsiia Vyrobnychykh Protsesiv i Tekhnichnyi Kontrol u Mashynobuduvanni ta Pryladobuduvanni [Bulletin of the Lviv Polytechnic National University. Series: Optimization of Production Processes and Technical Control in Mechanical Engineering and Instrument Making], 729, 70–79 (in Ukrainian).Loveikin V. S., Romasevich Yu. O., Loveikin Yu. V. (2012) Analysis of Direct Variational Methods for Solving Optimal Control Problems. Visnyk Natsionalnoho Universytetu “Lvivska Politekhnika”. Optymizatsiia Vyrobnychykh Protsesiv i Tekhnichnyi Kontrol u Mashynobuduvanni ta Pryladobuduvanni [Bulletin of the Lviv Polytechnic National University. Series: Optimization of Production Processes and Technical Control in Mechanical Engineering and Instrument Making], 729, 70–79 (in Ukrainian).Bronshtein I. N., Semendyayev K. A., Musiol G., Mühlig H. (2015) Handbook of Mathematics. Springer. 799. https://doi.org/10.1007/978-3-662-46221-8.Bronshtein I. N., Semendyayev K. A., Musiol G., Mühlig H. (2015) Handbook of Mathematics. Springer. 799. https://doi.org/10.1007/978-3-662-46221-8.Storn R., Kenneth P. (1995). Differential Evolution – Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces. Technical Report TR-95-012. International Computer Science Institute. 15.Storn R., Kenneth P. (1995). Differential Evolution – Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces. Technical Report TR-95-012. International Computer Science Institute. 15.Mitsubishi Electric (2011) FR-E700. Frequency Inverter Instruction Manual. 524.Mitsubishi Electric (2011) FR-E700. Frequency Inverter Instruction Manual. 524.

The authors declare that there are no conflicts of interest present.