Optimization of Bridge Crane Movement Control

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.

1. Komarov M. S. (1969) Dynamics of Load-Lifting Machines. Moscow, Mashynostroenye Publ. 206 (in Russian).

2. Kazak S. A. (1968) Dynamics of Overhead Cranes. Moscow, Mashynostroenye Publ. 331 (in Russian).

3. Gohberg M. M. (1969) Metal Constructions of Hoistingand-Transport Machines. Moscow, Mashynostroenye Publ. 520 (in Russian).

4. Gaidamaka V. F. (1989) Load-Lifting Machines. Kiev, Vyscha Shkola Publ. 328 (in Russian).

5. Sheffler M., Dresyh Kh., Kurt F. (1981) Load-Lifting Cranes. Book 2. Moscow, Mashynostroenye Publ. 287 (in Russian).

6. Lobov N. A. (1987) Dynamics of Load-Lifting Cranes, Moscow, Mashynostroenye Publ. 160 (in Russian).

7. 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).

8. 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).

9. Loveikin V. S., Romasevych Yu. O. (2016) Dynamics and Optimization of Overhead Crane Movement. Kyiv, KOMPRINT Publ. 314 (in Ukrainian).

10. 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.

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. Herasymiak R. P., Leshchev. V. A. (2008) Analysis and Synthesis Crane Electro-Mechanical Systems. Odessa, SMIL Publ. 192 (in Russian).

17. 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).

18. Grigorov O. V., Loveikin V. S. (1997) Optimal Control of Hoisting Machine Movement. Kiev, IZMN Publ. 264 (in Ukrainian).

19. 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.

20. 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.

21. 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.

22. 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.

23. 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.

24. 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.

25. Smekhov A. A., Erofeev N. Y. (1975) Optimal Control of Lifting and Transporting Machines. Moscow, Mashynostroenye Publ. 239 (in Russian).

26. 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.

27. 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).

28. Loveikin V. S., Nesterov A. P. (2002) Dynamic Optimization of Hoisting Machines, Kharkiv, KhDADTU. 285 (in Ukrainian).

29. 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.

30. Petrov Iu. P. (1977) Variational Methods of Optimal Control Theory, Leningrad, Energia Publ. 280 (in Russian).

31. 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).

32. 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.

33. 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.

34. Mitsubishi Electric (2011) FR-E700. Frequency Inverter Instruction Manual. 524.