Fractional PID controller designed for a CD pickup head position control to be used in optical microscopy

  • Paula Andrea Ortiz Valencia Instituto Tecnológico Metropolitano (ITM)
  • Lorena Cardona Rendón Universidad Nacional de Colombia
Keywords: Position tracking, Fractional control, Robust control, Optical microscopy, Optical mouse, CD


On this work a fractional PID controller is designed for a CD pickup head position control that is intended to use in the development of a motorized optical microscope. In such an application the disk or CD would be replaced by a plate with the sample to be studied, and the pickup head would be used to illuminate the sample. The controller is designed in such a way that there is no dependence on a CD written subcode to determine the position of the head, and for this, a computer mouse is used as a position sensor. We also look for the controller to improve the system performance and to be robust against model uncertainties of the plant, that is why we use a fractional controller PI^λ D^μ and adjust the parameters K_p, K_i, K_dλ and μ according to five robustness rules. For tuning the control we use the Matlab optimization toolbox together with fmincon function. At the end of the paper we present the simulation results, concluding about the resolution obtained, the robustness of the controller and the viability of the control system to be used in a microscope.


Download data is not yet available.

Author Biographies

Paula Andrea Ortiz Valencia, Instituto Tecnológico Metropolitano (ITM)

MSc. en Ingeniería área Automática, Universidad Pontificia Bolivariana. Docente Tiempo Completo, Investigador Grupo Automática y Electrónica, Instituto Tecnológico Metropolitano ITM, Medellín, Colombia

Lorena Cardona Rendón, Universidad Nacional de Colombia

PhD(c) Universidad Nacional de Colombia. MSc. en Ingeniería área Automática, Universidad Pontificia Bolivariana. Grupo Inteligencia Artificial en Educación, Universidad Nacional de Colombia, sede Medellín


[1] C. H. Lee, C. T. Chang, K. S. Fan and T. C. Chang. “An overview of recycling and treatment of scrap computers”.Journal of Hazardous Materials. Vol. 114, No. 1–3 pp. 93–100, 2004, ISSN: 0304–3894. DOI: 10.1016/j.jhazmat.2004.07.013.

[2] J. H. Zhang and L. Cai. “An autofocusing measurement system with a piezoelectric translator”.IEEE/ ASME Transactions on Mechatronics. Vol. 2, No. 3, pp. 213–216. 1997. ISSN:1083–4435. DOI: 10.1109/3516.622974.

[3] J. H. Zhang and L. Cai. “Profilometry using an optical stylus with interferometric readout”. Measurement Science & Technology.Vol. 8, No. 5, pp. 546–549, 1997. ISSN: 0957–0233. DOI: 10.1088/0957-0233/8/5/013.

[4] K. Ehrmann, A. Ho and K. Schindhelm.“A 3D optical profilometer using a compact disc reading head”. Measurement Science and Technology. Vol 9, No. 8, pp. 1259–1265, 1998. ISSN: 0957–0233. DOI: 10.1088/0957-0233/9/8/019.

[5] A. Bartoli, P. Poggi, F. Quercioli and B. Tiribilli. “Fast one dimensional profilometer with a compact disc pickup”. Applied Optics.Vol. 40, No. 7, pp. 1044–1048, 2001. ISSN: 2155–3165. DOI: 10.1364/AO.40.001044.

[6] A. Bartoli, P. Poggi, F. Quercioli, B. Tiribilli and M. Vassalli. “Optical profilometer with a standalone scanning sensor head”. Optical Engineering. Vol. 40, No. 12, pp. 2852–2859, 2001. ISSN: 00913286. DOI: 10.1117/1.1417494.

[7] K. C. Fan, C. L. Chu and J. I. Mou.“Development of a low-cost autofocusing probe for profile measurement”. Measurement Science and Technology. Vol. 12, No. 12, pp. 2137–2146, 2001. ISSN: 0957–0233.DOI: 10.1088/0957-0233/12/12/315.

[8] N. Islam, R. Parkin, M. Jackson and P. Mueller.“A novel surface profile measurement system”. AU Journal of Technology. Vol. 10, No. 3, pp. 203–209, 2007.

[9] J. Benschop and G. Rosmalen.“Confocal compact scanning optical microscope based on compact disc technology”. Applied Optics. Vol. 30, No. 10, pp. 1179–1184, 1991. ISSN: 2155-3165. DOI: 10.1364/ AO.30.001179.

[10] F. Quercioli, B. Tiribilli, C. Ascoli, P. Baschieri and C. Frediani.“Monitoring of an atomic force microscope cantilever with a compact disk pickup”. Review of Scientific Instruments. Vol. 70, No. 9, pp. 3620–3624, 1999. ISSN: 0034–6748. DOI: 10.1063/1.1149969.

[11] E. T. Hwu, K. Y. Huang, S. K. Hung and I. S. Hwang.“Measurement of cantilever displacement using a compact disk /digital versatile disk pickup head”. Japanese Journal of Applied Physics. Vol. 45, No. 3B, pp. 2368–2371, 2006. ISSN: 1347–4065. DOI: 10.1143/JJAP.45.2368

[12] E. T. Hwu, S. K. Hung, C. W. Yang and I. S. Hwang.“Simultaneous detection of translational and angular displacements of micromachined elements”.Applied Physics Letters, Vol. 91, No. 22, pp. 221908–221908-3, 2007. ISSN: 0003-6951. DOI: 10.1063/1.2817750.

[13] E. T. Hwu, S. K. Hung, C. W. Yang, K. Y. Huang and I. S. Hwang. “Real-time detection of linear and angular displacements with a modified DVD optical head”. Nanotechnology. Vol. 19, No. 11, pp. 115501–115507, 2008. ISSN: 0957-4484. DOI: 10.1088/0957- 4484/19/11/115501.

[14] E. T. Hwu, H. Illers, L. Jusko and H. U. Danzebrink. “A hybrid scanning probe microscope (SPM) module based on a DVD optical head”. Measurement Science and Technology. Vol. 20, No. 8, pp.1–8, 2009. ISSN: 0957- 0233. DOI: doi:10.1088/0957-0233/20/8/084005.

[15] F. Quercioli, A. Mannoni& B. Tiribilli. “Correlation optical velocimetry with a compact disk pickup”. Applied Optics.Vol. 36, No. 25, pp. 6372–6375, 1997. ISSN: 2155-3165. DOI: 10.1364/AO.36.006372.

[16] F. Quercioli, A. Mannoni& B. Tiribilli. “Laser Doppler velocimetry with a compact disc pickup”. Applied Optics. Vol.37, No. 25, pp. 5932–5937, 1998. ISSN: 2155- 316. DOI: 10.1364/AO.37.005932.

[17] F. Quercioli, B. Tiribilli and A. Bartoli. “Interferometry with optical pickups”. Optics Letters. Vol. 24, No. 10, pp. 670–672, 1999. ISSN: 1539-4794. DOI: 10.1364/OL.24.000670.

[18] K. C. Fan, C. L. Chu, J. L. Liao and J. I. Mou. “Development of a high-precision straightness measuring system with DVD pick-up head”. Measurement Science and Technology.Vol. 14, No. 1, pp. 47–54, 2003. ISSN: 0957–0233. DOI: 10.1088/0957-0233/14/1/307.

[19] K. C. Fan, Y. Fei and X. Yu. “Development of a microCMM”. Proceedings of the International Manufacturing Leaders Forum on Global Competitive Manufacturing. Adelaide, Australia. 27th February - 2nd March 2005.

[20] K. C. Fan, Z. F. Lai, P. Wu, Y. C. Chen, Y. Chen and G. Jäger. “A displacement spindle in a micro/nano level”. Measurement Science and Technology. Vol. 18, No. 6, pp. 1710–1717, 2007. ISSN: 0957–0233. DOI: 10.1088/0957-0233/18/6/S07.

[21] S. Morris, R. Pratt, M. Hughes, R. Kouzes, K. Pitts and E. Robinson. “DVD based electronic pulser”. IEEE Transactions on Nuclear Science.Vol. 53, No. 4, pp. 2303–2307, 2006. ISSN: 0018-9499. DOI: 10.1109/ TNS.2006.877859.

[22] C. L. Chu and C. H. Lin. “Development of an optical accelerometer with a DVD pick-up head”. Measurement Science and Technology.Vol. 16, No. 12, pp. 2498–2502, 2005. ISSN: 0957–0233. DOI: doi:10.1088/0957-0233/16/12/014.

[23] C. L. Chu, C. H. Lin and K. C. Fan. “Two-dimensional optical accelerometer based on commercial DVD pick-up head”. Measurement Science and Technology. Vol. 18, No. 1, pp. 265–274, 2007. ISSN: 0957–0233. DOI: 10.1088/0957-0233/18/1/033.

[24] C. L. Chu and C. Y. Chiu.“Development of a low-cost nanoscale touch trigger probe based on two commercial DVD pick-up heads”. Measurement Science and Technology. Vol. 18, No. 7, pp. 1831–1842, 2007. ISSN: 0957–0233. DOI: 10.1088/0957-0233/18/7/006.

[25] C. L. Jones. “Cryptographic hash functions and CD-based optical biosensors”. Problems of Nonlinear Analysis in Engineering Systems.Vol. 2, No. 23, pp. 17–36, 2005. ISSN: 1727-687X.

[26] A. Tibbe, B. De Grooth, J. Greve, C. Rao, G. Dolan and L. Terstappen. “Cell analysis system based on compact disk technology”. Cytometry.Vol. 47, No. 3, pp. 173–182, 2002. ISSN: 0196–4763. DOI: 10.1002/ cyto.10061.

[27] J. Kim, G. Liu and L. Lee. “Lens-scanning Raman microspectroscopy system using compact disc optical pickup technology”. Optics Express. Vol. 13, No. 12, pp. 4780–4785, 2005. ISSN: 1094–4087.DOI: 10.1364/OPEX.13.004780.

[28] S. Lange et al. “Measuring bimolecular binding events with a compact disc player device”. AngewandteChemie. Vol. 45, No. 2, pp. 270–273, 2005. ISSN: 1521- 3757.DOI: 10.1002/anie.200501243.

[29] S. Kostner and M. Vellekoop. “Particle and cell detection using a DVD pickup head”. Biennial Report of The Society for Micro- and Nanoelectronics, 2005–2006, pp. 401–404.

[30] S. Kostner and M. Vellekoop.“Low cost cytometer based on a DVD pickup head”. Eleventh International Conference on Miniaturized Systems for Chemistry and Life Sciences. Paris, France, 2007, pp. 739–741.

[31] S. Kostner and M. Vellekoop. “Cell analysis in a microfluidic cytometer applying a DVD pickup head”. Sensors and Actuators B Vol. 132, No. 2, pp. 512–517, 2008. ISSN: 0925-4005. DOI: 10.1016/j.snb.2007.11.038.

[32] V. Yim, S. Y. Lee, S. Kim and J. Y. Park. “Multipurpose DVD pick-up scanner for analysis of microfluidics and micromechanical structures”. 30th Annual International IEEE EMBS Conference.Vancouver, Canada, 2008. pp. 2749–2751.

[33] K. H. Kim, S. Y. Lee, S. Kim, S. H. Lee and S. G. Jeong. “A new DNA chip detection mechanism using optical pick-up actuators”. Microsystem Technologies. Vol. 13, No. 8–10, pp.1359–1369, 2007. ISSN: 1432–1858. DOI: 10.1007/s00542-006-0367-9.

[34] K. H. Kim, S. Y. Lee, S. Kim and S. G. Jeong. “DNA microarray scanner with a DVD pick-up head”. Current Applied Physics. Vol. 8, No. 6, pp. 687–69, 2008, ISSN: 1567-1739. DOI: 10.1016/j.cap.2007.04.047.

[35] K. H. Park et al. “Bio-information scanning technology using an optical pick-up head”. Ultramicroscopy. Vol. 108, No. 10, pp. 1319–1324, 2008. ISSN: 0304- 3991. DOI: 10.1016/j.ultramic.2008.04. 074.

[36] T. R. Armstrong and M. P. Fitzgerald. “An autocollimator based on the laser head of a compact disc player”. Measurement Science and Technology.Vol. 3, No. 11, pp. 1072–1076, 1992. ISSN: 0957–0233. DOI: 10.1088/0957-0233/3/11/009.

[37] M. Felton. “CD simplicity”.Analytical Chemistry.Vol. 75, No. 13, pp. 302A–306A, 2003. ISSN: 1520-6882. DOI: 10.1021/ac031357z.

[38] C. A. Monje, Y Chen, B. M. Vinagre, D.Xue, and V. Feliu, “Fractional-order systems and controls :fundamentals and applications”. Springer-Verlag.1st Edition. 415 p. London, England. ISBN: 978-1849963343. 2010.

[39] A. Oustaloup, P. Melchior, P. Lanusse, O. Coisand F. Dancla. “The CRONE toolbox for Matlab”. IEEE International Symposium on Computer-Aided Control System Design, CACSD 2000, Anchorage, USA, 2000.190– 195.

[40] C.Monje. “Tuning and Auto-tuning of Fractional Order Controllers for Industry Applications”. Control Engineering Practice. Vol. 16.No. 7. Pp.798-812. 2008.

[41] D. Valerio, J.S. Da Costa. “Tuning rules for fractional PIDs”. Advances in Fractional Calculus: Theoretical Developments and Applications.Springer 1st Ed. Pp.463–476. Dordrecht, The Neterlands. ISNB: 978-1- 4020-6041-0. 2007.

[42] N. Tan, Ö.F. Özgüven, y M.M. Özyetkin. “Robust stability analysis of fractional order interval polynomials” .ISA Transactions. Vol. 48, No. 2, 166–172, 2009. ISSN: 0019-0578. DOI: 10.1016/ j.isatra.2009.01.002.

[43] L. Meng, y D. Xue. ”Design of an optimal fractionalorder PID controller using Multi-Objective GA optimization”. IEEE Chinese Control and Decision Conference, 2009, 3849–3853.

[44] J.Y. Cao, y B.G. Cao. “Design of Fractional Order Controllers Based on Particle Swarm Optimization”.1st IEEE Conference on Industrial Electronics and Applications.Marina Mandarin, Singapore. 24-26 May 2006, pp. 1–6.

[45] C.H. Lee, y F.K Chang. “Fractional-order PID controller optimization via improved electromagnetism–like algorithm”. Expert Systems with Applications. Vol. 37, No. 12, 8871–8878, 2010. ISSN: 0957-4174. DOI:10.1016/ j.eswa.2010.06.009.

[46] N. Matsunaga, K. Sasano, and H. Okajima. “An Implementation of Fractional–order PID Controller with Dynamic Quantizer considering the Memory Constraint”. IEEE International Conference on Control Applications, Yokohama, Japan, 2010. Pp. 2409–2414.

[47] A. Pisano, M.R. Rapai, y E. Usai. “On second-order sliding-mode control of fractional-order dynamics”. American Control Conference, AACC. Baltimore, USA, 2010. Pp. 6680–6685.

[48] R. Zhang, y S. Yang, “Adaptive synchronization of fractional-order chaotic systems via a single driving variable”. Nonlinear Dynamics.Vol. 66, No. 4, pp. 831–837, 2011. ISSN: 1573-269X. DOI: 10.1007/s11071-011- 9944-2.

[49] F. Padula, A.Visioli,. “Tuning rules for optimal PID and fractional order PID controllers”. Journal of Process Control. Vol. 21, No. 1, 69–81, 2011. ISSN: 0959- 1524. DOI: 10.1016/j.jprocont.2010.10. 006.

[50] R. Dorf and R. Bishop. “Sistemas de control moderno”. Pearson Prentice Hall, 10a Ed. 882 p. Madrid, España. ISBN: 978–8420544014. 2005.

[51] P.Maybeck. Stochastic models, estimation and control, Vol 1. Academic Press, New York, 1979, 423 p.

[52] K. Iskakov, A. Albu-Schaeffer, M. Schedl, G. Hirzinger and V. Lopota. “Influence of sensor quantization on the control performance of robotics actuators”. Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.San Diego, CA, USA, Oct 29 - Nov 2, pp. 1085–1092.

[53] D. Valério and J. S. da Costa. “Ninteger: a non-integer control toolbox for Matlab”. Proccedings of the 1st IFAC Workshop on Fractional Differentiation and its Applications, FDA’06, Bordeaux, France, 2004, 6 p.

[54] P. Ortiz, J. Ramírez and L.Cardona. “Modelo matemá - tico y control de un sistema de fluidos”. 1a. edición. Medellín 2011: instituto tecnológico metropolitano. ISBN 978-958-8743-08-0.

[55] L. Cardona, P. Ortiz and A. Restrepo. “Modelado y control de posición de una unidad de CD para aplica - ciones en microscopia óptica” 3er Congreso interna - cional de Ingeniería mecatrónica. UNAB. Vol. 2, No 1. 2011.
How to Cite
Ortiz Valencia, P., & Cardona Rendón, L. (2012). Fractional PID controller designed for a CD pickup head position control to be used in optical microscopy. ITECKNE, 9(2), 106-117.
Research and Innovation Articles