Abstract
This paper considers the control problem of a robotic manipulator with separately excited dc motor drives as actuators. An innovative method is proposed which achieves robot speed-control requirements, with simultaneous minimization of total electromechanical losses, while the drives follow the desired speed profiles of the robot joints under various loads and random load disturbances. If there is no demand for a specific speed profile, the optimal speed trajectory is determined by minimizing an electromechanical losses criterion. Controllable energy losses, such as armature copper losses, armature iron losses, field copper losses, stray load losses, brush load losses, friction and windage losses, can be expressed proportionally to the squares of the armature and the field (exciting) currents, the angular velocity and the magnetic field flux. The controllable energy loss term is also included in the optimal control integral quadratic performance index, defined for the whole operation period. Thus the appropriate control signals required for following the desired trajectory by simultaneous energy loss minimization for the whole operation interval are achieved. Two case studies of optimal robot control with and without minimization of actuator energy losses are presented and compared, showing the energy savings that can be achieved by the proposed methodology.
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Baines, P. J. and Mills, J. K.: Feedback linearized joint torque control of a geared, dc motor driven industrial robot, in: Proceedings, 1995 IEEE Robotics and Automation International Conference, Vol. 3, 1995, pp. 3129–3136.
Bazaraa, M. S., Sherali, H. D., and Shetty, C. M.: Nonlinear Programming - Theory and Algoritms, Wiley, New York, 1993.
Buhler, H.: Electronique de reglage et de commande, Dunod, 1979.
Cathey, J. J.: Reduction of dc traction motor armature cooper losses through optimal control, Elec. Mach. Electromech. (1979), 269–283.
Cordon, R., Sanz, E., and Vega, P.: Robust control in robotic manipulators with dc motors, in: Proceedings, 1998 5th International Workshop on Advanced Motion Control, AMC' 98-Coimbra, 1998, pp. 42–46.
Duff, I. S., Erisman, A.M., and Reid, J. K.: Direct Methods for Sparse Matrices, Monographs on Numerical Analysis, Clarendon Press, Oxford, 1992.
Egami, T. and Tsuchiya, T.: Efficiency optimized speed-control system synthesis method based on improved optimal regulator theory, IEEE Trans. Ind. Electron. IE-33(2) (1986), 114–125.
Egami, T. and Tsuchiya, T.: Efficiency optimized speed-control system with feed - forward compensation, IEEE Trans. Ind. Electron. IE-34(2) (1987), 216–226.
Egami, T., Wang, J., and Tsuchiya, T.: Efficiency optimized speed-control system synthesis method based on improved optimal regulator theory - application to seperately excited dc motor system, IEEE Trans. Ind. Electron. IE-32(4) (1985), 372–380.
Fitzerald, A. E., Kingsley, C., and Kusko, A.: Electric Machinery, McGraw-Hill, 1971.
Fletcher, R.: Practical Methods of Optimazation, Vol. 1, Unconstrained Optimization, and Vol. 2, Constrained Optimization, Wiley, 1980.
Gajendran, F. and George, S.: A simple linear adaptive speed control of energy efficient dc motor, in: Proceedings, Int. Conf. ElectricMachines and Drives, IEMD' 99, 1999, pp. 664–666.
Gill, P. E., Murray, W., and Wright, M. H.: Practical Optimization, Academic Press, London, 1981.
Han, S. P.: A globally convergent method for non-linear programming, J. Optim. Theory Appl. 22 (1977), 297.
Hock, W. and Schittowski, K.: A Comparative Performance Evaluation of 27 Nonlinear Programming Codes, Lecture Notes in Econom. Math. Systems 187, Vol. 30, Springer-Verlag, Berlin, 1983.
Hong, S. C. and Park, M. H.: Microprocessor - based optimal efficiency drive of separately excited dc motor, in: Proc. 1984 IEEE TENCON, 1984, pp. 126–128.
Hong, S. C. and Park, M. H.: Microprocessor-based optimal efficiency drive of separately excited dc motor, IEEE Trans. Ind. Electron. IE-34(4) (1987), 433–440.
Electro-Craft Corp.: dc Motor Speed Controls Servo Systems, 4th edn, Hopkins, MN, 1978.
Kirk, D. E.: Optimal Control Theory, Prentice-Hall, NJ, 1970.
Kostenko, M. and Piotrovsky, L.: Electrical Machines, Vol. I, Mir, Moscow, 1974.
Kusko, A. and Galler, D.: Control means for minimization of losses in ac and dc motor drives, IEEE Trans. Ind. Appl. IA-19 (1983), 561–570.
Kusko, A.: Solid-State dc Motor Drives, MIT Press, Cambridge, MA, 1969.
Leonard, W.: Control of Electrical Drives, Springer-Verlag, 1985.
Ma, S.: Real-time algorithm for quasi-minimum energy control of robotic manipulators, in: Proceedings, 1995 IEEE 21st International Conference on Industrial Electronics, Control, and Instrumentation (IECON), Vol. 2, 1995, pp. 1324–1329.
McDonald, A.: Robot Technology, Theory, Design and Application, Prentice-Hall, 1986.
Margaris, N.: Minimization of the Electrical Motor's Losses. I. dc Drives, Thessaloniki, 1989.
Nailen, R. L.: Can field tests prove motor efficiency? IEEE Trans. Ind. Appl. 25 (1989).
MATLAB Optimization Toolbox User's Guide, The MathWorks, Inc., MA, 1992.
Powell, M. J. D.: Variable metric methods for constrained optimization, in: A. Bachem, M. Grotschel and B. Korte (eds), Mathematical Programming: The State of the Art, Springer-Verlag, 1983, pp. 288–311.
Powell, M. J. D.: The convergence of variable metric methods for non-linearly constrained optimization calculations, in: O. L. Mangasarian, R. R. Meyer and S. M. Robinson (eds), Non-Linear Programming 3, Academic Press, 1978.
Powell, M. J. D.: A Fast Algorithm for Non-linearly Constrained Optimization Calculations, Numerical Analysis, Lecture Notes in Math. 630, Springer-Verlag, 1978.
Trzynadlowski, A. M.: Energy optimization of a certain class of incremental motion dc drives, IEEE Trans. Ind. Electron. 85 (1965), 34–43.
Tzafestas, S. and Stavrakakis, G.: Model reference adaptive control of industrial robots with actuator dynamics, J. Info, and Optim. Sci. 10(3) (1989), 423–444.
Wallace, R. S.: Miniature direct drive rotary actuators, II. Eye, finger and leg, in: Proceedings, IEEE International Conference on Robotics and Automation, Vol. 2, 1994, pp. 1496–1501.
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Sergaki, E.S., Stavrakakis, G.S. & Pouliezos, A.D. Optimal Robot Speed Trajectory by Minimization of the Actuator Motor Electromechanical Losses. Journal of Intelligent and Robotic Systems 33, 187–207 (2002). https://doi.org/10.1023/A:1014643401778
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DOI: https://doi.org/10.1023/A:1014643401778