Comparison of the simulation and measurement results

The measurement and simulation results are given in Figs. 5.9-5.10 for the position control and in Fig.(5.11) for the tracking control. As it can be observed from the figures, the automatic tuning gives otherwise acceptable response except the tail of the response, which approaches the reference value very slowly. This is probably caused by the fact that the controller cancels slow process poles with relatively large integration time constant (small integral part gain) in order to get sufficient response to the setpoint changes. On the other hand this results that the controller has a rather poor rejection of the constant disturbances such as the stiction in this system. Fig. 5.11 shows also that the offset error elimination by position tracking control is not enough effective, because it takes several seconds to decay. The position error has also intolerably large value for high precision systems. It can beconcluded that automatic tuning can be used only for pre-tuning of the

PID controller and controller parameters should be fine-tuned when applied on the real test setup.

Fig. 5.9. Step response for position control.

Fig. 5.10.Control signal from PID controller.

Fig. 5.11. Sinusoidal response for tracking position system.

In order to improve the performance of the belt-drive system the integral parts in both cases was increased. The experimental results with higher integrator gains are represented in Figs. 5.12 and 5.13 for the position controller and in Fig. 5.14 for the tracking controller.

Fig. 5.12. Step response for position control with increased integral term.

Fig. 5.13. Control signal from PID controller with increased integral term.

.

Figs. 5.12-5.13 represent the step response of the position control system. Now, it can be noticed that the steady state error has an allowable value of 2mm. The damping and the operating speed are also satisfactory. It can be concluded that the accurate position control requirements are attained.

Fig. 5.14. Sinusoidal response for tracking position system.

Fig. 5.14 shows that high accuracy of tracking control system is now achieved. The error is effectively eliminated. Thus, the control goal is attained. However, low damping of the system gives some oscillations in the beginning of the process as can be observed from Fig. 5.14.

6 Conclusions

As result of the work a model of the belt drive system and its PID control was developed.

The designed model describes the system behavior with adequate accuracy. Friction and belt elasticity phenomena impact was taken into account in the developed model. The correspondence of the model was demonstrated by experimental tests.

The PID control based on the position feedback was developed. This control was applied to the designed dynamic model to show its effectiveness by simulations. Using the developed model the pretuning of the controller with the help of MATLAB^® instruments can be performed.

Also the practical structure of PID control was constructed with taking into account the limitations of the actuator. In addition, the discretization of the PID controller was made for implementation it to the dSPACE™ system. The effectiveness of the developed controllers was proved by experimental tests.

The developed position control system ensures allowable error value. Also the damping and the operating speed of the closed loop system are satisfactory. As a conclusion, the specified position control requirements were attained.

High accuracy of the belt drive system is achieved with the help of tracking controller.

The position error is effectively eliminated. However, low damping of the system gives oscillations in the beginning of the process, which may present a limiting factor in some practical application. The position tracking control requires impovement in order to avoid the oscillations in the step response.

References:

[1] “Application Examples”: Parker Hannifin Corporation. 16 April 2007

<http://www.parkermotion.com/catalog_eng_ref.htm>

[2] Kerrkanen K., 2006. Dynamic analysis of belt-drives using the absolute nodal coordinate formulation. /PhD work Lappeenranta University of Technology. ISBN 952-214-193-3

[3] Hungles, A., 2003. Electric motors and drives: Fundamentals, types and applications.-Printed by Newnes, Manchester. ISBN 0-7506-1741-1

[4] Younkin, G., 2003. Industrial servo control systems: Fundamentals and applications.

[5] Drury, B., 2001. The Control Techniques Drives and Controls Handbook, Published by the Institution of Electrical Engineers, London. ISBN 0-85296-793-4

[6] Crowder R. M., 1995. Electric drives and their controls, Clarendon Press, Oxford.

ISBN 0-19-859371-6

[7] Toshihiro, S., Tsuneo, K., 2004. Motor drive technology: History and visions for the future. 35^th Annual IEEE Power Electronics Specialists Conference, p.2-9.

[8] Puranen, J., Induction motor versus permanent magnet synchronous motor in motion control applications: a comparative study. / PhD work Lappeenranta University of Technology. ISBN 952-214-296-4

[9] Mikerov A.G., Djankhotov V.V., 2002. Small electrical machines and drives. Saint-Petersburg Electrotechnical University “LETI”, Russia

[10] Pyrhonen J., 2006. Electrical Drives 2006/2007, Lecture notes, LUT, Finland.

[11] Barret J., Harned T., Monnich J. Linear motor basics. Parker Hannifin Corporation.

[12] Hace, A., Jezernik, K., Sabanovic, A., SMC with disturbance observer for a linear belt-drive, IEEE ISIE 2005, June 20-23, Dubrovnik, Croatia.

[13] Serway R.A., 1982.Physics: For scientists and engineers. ISBN 0-03-057903-1

[14] Armstrong –Helouvry, B, 1991. Control of machines with friction. Published by Kluwer Academic Publishers, Boston.

[15] Yu-Feng Li, Motion, 1999. Control Subject to Nonlinearities and Flexibility (A Overview based on friction and flexibility compensation), Technical report, Department of Machine Design, Royal Institute of Technology, Sweden

[16] Ge S.S., Lee T.H., Ren S.X., 1999.Adaptive Friction Compensation of Servo Mechanisms, IEEE, International Conference on Control Applications, USA

[17] Franklin G.F., Powell J.D., Workman M.L., 1998. Digital control of dynamic systems. Printed by Addison Wesley Longman Inc., USA. ISBN 0-201-33153-5

[18] Astrom K., Hagglund T., 1995. PID Controllers: Theory, design, tuning. USA. ISBN 1-55617-516-7

[19] Nonlinear Control Design Blockset User’s Guide, 1997.The MathWorks, Inc.

[20] Bortsov J.A., Sokolovskii G.G., 1992. Automated electrical drive with flexible connections. Printed by Energoatomizdat, Saint-Petersburg (in Russian). ISBN 5-283-04544-7

[21] Franklin G.F., Powell J.D., Emami-Naeini A., 1986. Feedback control of dynamic system. Printed by Addison-Wesley publishing company, USA. ISBN 0-201-11540-9

[22] Friedland B., 1986. Control system design: An introduction to state-space methods.

Printed by McGraw-Hill Book Company, USA. ISBN 0-07-022441-2

[23] Astrom K.J., Wittenmark B., 1997. Computer-controlled systems: theory and design.

Printed by Prentice Hall, USA. ISBN 0-13-314899-8

[24] Vtorov V.B, 2007. Advanced control engineering. Lecture slides.

[25] Bovicheva E.V., Vtorov V.B. On an approach to parametric design of model reference adaptive systems. (in Russian)

[26] Vtorov V.B., Kalmykov A.N. Some questions of design and practical implementation of signal type adaptation systems. (in Russian)

[27] Sliding mode control of a suspended pendulum. Tutorials of Drexel Autonomous System Lab, by Drexel University. 10 May 2007

http://www.pages.drexel.edu/~vn43/tutorials/sliding_mode_control/smcsp/smcsp.html

Appendices