Auto-Tuning by Using Double Extended Kalman-Bucy Filter: An Application to Dc Motor for Controlling Speed

Yıl 2021, Cilt: 25 Sayı: 1, 163 - 174, 01.02.2021

Hakan Kızmaz

Öz

In this study, a modified adaptive control algorithm is proposed and investigated. The algorithm consists of a controller, an estimator and an auxiliary model like in model reference adaptive control strategy. PID controller is used to provide controlling. The controller includes adjustable parameters. Traditional PID controller parameters are usually set to fulfil the reference behaviour criterion. In this study, minimum-time criterion is chosen. Extended Kalman-Bucy estimator is employed for estimating controller parameters to make system behave like auxiliary model. The estimator adjusts the controller parameters so that system output can catch the reference input at minimum time. The study may call as the minimization of the settling time problem. The controller and estimator of the system are operated simultaneously. The achievement of the proposed algorithm is proved by simulation results including a simple dc motor model.

Anahtar Kelimeler

Dc motor, Extended Kalman-Bucy Filter, parameter estimation, PID control, speed control, adaptive control

Kaynakça

• [1] K. V. C. R. V Rajasekhar, “Design and Analysis of DC Motor With PID Controller - A State Space Approach,” ITSI Trans. Electr. Electron. Eng., vol. 1, no. 3, pp. 11–14, 2013.
• [2] P. M. Meshram and R. G. Kanojiya, “Tuning of PID Controller using Ziegler-Nichols Method for Speed Control of DC Motor,” in 2013 IEEE International Conference on Control Applications (CCA), 2012, pp. 117–122.
• [3] Y. Yang, Y. Wang, and P. Jia, “Adaptive robust control with extended disturbance observer for motion control of DC motors,” Electron. Lett., vol. 51, no. 22, pp. 1761–1763, 2015, doi: 10.1049/el.2015.1009.
• [4] H. Chu, B. Gao, W. Gu, and H. Chen, “Low-Speed Control for Permanent-Magnet DC Torque Motor Using Observer-Based Nonlinear Triple-Step Controller,” IEEE Trans. Ind. Electron., vol. 64, no. 4, pp. 3286–3296, 2017, doi: 10.1109/TIE.2016.2598298.
• [5] O. Prem, “Intelligent Speed Control of DC Servo Motor Drive,” pp. 3029–3033, 2018.
• [6] S. Rakhonde and V. Kulkarni, “Sliding mode controller (SMC) governed speed control of DC motor,” 2018 3rd IEEE Int. Conf. Recent Trends Electron. Inf. Commun. Technol. RTEICT 2018 - Proc., pp. 1657–1662, 2018, doi: 10.1109/RTEICT42901.2018.9012572.
• [7] M. Mallareddy, “Application of Bio geography based Fractional order PID controller in DC motor drive speed control,” 2020.
• [8] L. Samir, G. Said, and S. Youcef, “PID Control of DC Servo Motor using a Single Memory Neuron,” no. October, pp. 25–27, 2018.
• [9] W. G. M. Elnaim and S. F. Babiker, “Comparative study on the speed of DC motor using PID and FLC,” in Proceedings of 2016 Conference of Basic Sciences and Engineering Studies, SGCAC 2016, 2016, pp. 24–29, doi: 10.1109/SGCAC.2016.7458001.
• [10] Y. Ma, Y. Liu, and C. Wang, “Design of parameters self-tuning fuzzy PID control for DC motor,” 2010, vol. 2, pp. 345–348, doi: 10.1109/ICINDMA.2010.5538300.
• [11] S. K. Suman and V. K. Giri, “Speed Control of DC Motor Using Different Optimization Techniques Based PID Controller,” IEEE Int. Conf. Eng. Technol., vol. 2, no. 7, pp. 6488–6494, 2012.
• [12] P. A. Adewuyi, “DC Motor Speed Control: A Case between PID Controller and Fuzzy Logic Controller,” Int. J. Multidiscip. Sci. Eng., vol. 4, no. 4, pp. 36–40, 2013.
• [13] M. Jaiswal and M. P. H. O. D. Ex, “Speed Control of DC Motor Using Genetic Algorithm Based PID Controller,” vol. 3, no. 7, pp. 247–253, 2013.
• [14] M. D. Amanullah, M. Jain, P. Tiwari, S. Gupta, and G. Kumari, “Optimization of PID Parameter for Position Control of DC-Motor using Multi-Objective Genetic Algorithm,” Int. J. Innov. Res. Electr. Instrum. Control Eng., vol. 2, no. 6, pp. 1644–1650, 2014.
• [15] B. Hekimoglu, “Optimal Tuning of Fractional Order PID Controller for DC Motor Speed Control via Chaotic Atom Search Optimization Algorithm,” IEEE Access, vol. 7, pp. 38100–38114, 2019, doi: 10.1109/ACCESS.2019.2905961.
• [16] S. Ekinci, D. Izci, and B. Hekimoğlu, “PID Speed Control of DC Motor Using Harris Hawks Optimization Algorithm,” 2020 Int. Conf. Electr. Commun. Comput. Eng., vol. 2, no. June, pp. 3–8, 2020, doi: 10.1109/ICECCE49384.2020.9179308.
• [17] L. Harnefors, S. E. Saarakkala, and M. Hinkkanen, “Speed control of electrical drives using classical control methods,” IEEE Trans. Ind. Appl., vol. 49, no. 2, pp. 889–898, 2013, doi: 10.1109/TIA.2013.2244194.
• [18] J. Han, “From PID to active disturbance rejection control,” IEEE Trans. Ind. Electron., vol. 56, no. 3, pp. 900–906, 2009, doi: 10.1109/TIE.2008.2011621.
• [19] A. Damiano, G. L. Gatto, I. Marongiu, and A. Pisano, “Second-order sliding-mode control of dc drives,” IEEE Trans. Ind. Electron., vol. 51, no. 2, pp. 364–373, 2004, doi: 10.1109/TIE.2004.825268.
• [20] Y. Shao and J. Li, “Modeling and Switching Tracking Control for a Class of Cart-Pendulum Systems Driven by DC Motor,” IEEE Access, vol. 8, pp. 44858–44866, 2020, doi: 10.1109/ACCESS.2020.2978269.
• [21] J. Yao, Z. Jiao, and D. Ma, “Adaptive robust control of dc motors with extended state observer,” IEEE Trans. Ind. Electron., vol. 61, no. 7, pp. 3630–3637, 2014, doi: 10.1109/TIE.2013.2281165.
• [22] S. A. Hamoodi, I. I. Sheet, and R. A. Mohammed, “A Comparison between PID controller and ANN controller for speed control of DC Motor,” 2nd Int. Conf. Electr. Commun. Comput. Power Control Eng. ICECCPCE 2019, pp. 221–224, 2019, doi: 10.1109/ICECCPCE46549.2019.203777.
• [23] N. Y. R. J.G. Ziegler, N.B. Nichols, “Optimum Settings for Automatic Controller,” Trans. A.S.M.E, pp. 759–768, 1942, doi: 10.1115/1.2899060.
• [24] K. J. Åström and T. Hägglund, “Automatic Tuning of Simple Regulators with Specificaiotns on Phase and Amplitude Margins,” Automatica, vol. 20, no. 5, pp. 645–651, 1984.
• [25] T. S. Schei, “A method for closed loop automatic tuning of PID controllers,” Automatica, vol. 28, no. 3, pp. 587–591, 1992, doi: 10.1016/0005-1098(92)90182-F.
• [26] A. A. Voda and I. D. Landau, “A method for the auto-calibration of PID controllers,” Automatica, vol. 31, no. 1, pp. 41–53, 1995, doi: 10.1016/0005-1098(94)00067-S.
• [27] É. Poulin, A. Pomerleau, A. Desbiens, and D. Hodouin, “Development and evaluation of an auto-tuning and adaptive PID controller,” Automatica, vol. 32, no. 1, pp. 71–82, 1996, doi: 10.1016/0005-1098(95)00105-0.
• [28] R. E. Kalman, “A new approach to linear filtering and prediction problems,” Trans. ASME-Journal Basic Eng., vol. 82, no. Series D, pp. 35–45, 1960, doi: 10.1115/1.3662552.
• [29] R. E. Kalman and R. S. Bucy, “New results in linear filtering and prediction theory,” J. Basic Eng., vol. 83, no. 1, pp. 95–108, 1961, doi: 10.1115/1.3658902.
• [30] P. Deshpande and A. Deshpande, “Inferential control of DC motor using Kalman Filter,” 2012 2nd Int. Conf. Power, Control Embed. Syst., pp. 1–5, 2012, doi: 10.1109/ICPCES.2012.6508056.
• [31] A. Khalid and A. Nawaz, “Sensor less control of DC motor using Kalman filter for low cost CNC machine,” 2014 Int. Conf. Robot. Emerg. Allied Technol. Eng., pp. 180–185, 2014, doi: 10.1109/iCREATE.2014.6828362.
• [32] Z. Aydogmus and O. Aydogmus, “A comparison of artificial neural network and extended Kalman filter based sensorless speed estimation,” Measurement, vol. 63, pp. 152–158, 2015, doi: 10.1016/j.measurement.2014.12.010.
• [33] A. H. Z. Farnaz, H. S. Sajith, P. J. Binduhewa, M. P. B. Ekanayake, and B. G. L. T. Samaranayake, “Low cost torque estimator for DC servo motors,” 2015 IEEE 10th Int. Conf. Ind. Inf. Syst. ICIIS 2015 - Conf. Proc., pp. 187–192, 2016, doi: 10.1109/ICIINFS.2015.7399008.
• [34] G. M. Siouris, An Engineering Approach to Optimal Control and Estimation Theory. New York: John Wiley & Sons, 1996.
• [35] P. C. Krause, O. Wasynczuk, and S. D. Sudhoff, Analysis of Electric Machinery and Drive Systems, 2nd ed. New York: John Wiley & Sons, 2002.