Development of a Digital Autotuning PI for First Order Plant Using RLS-PZC

Sidik Nurcahyo, Fitri Fitri, Sungkono Sungkono

Abstract


The fact that a real plant can be estimated as a first order and its parameters vary due to the environment has motivated this article to discuss the development of a digital autotuning PI for a first-order plant using Recursive Least Square (RLS) and Pole Zero Cancellation (PZC). Although the focus is only on first order, the methods discussed here hopefully become a basis for developing higher-order plants. Firstly, formulas for calculating PI parameters are derived using PZC and tested by simulation to verify their effectiveness. Then it is organized serially with the RLS and digital PI to form an autotuning PI algorithm. The RLS periodically reads plant input-output to estimate plant parameters. These resulting parameters are fed to PZC and finally, PZC outputs are used by digital PI to control the plant. This design is verified by Matlab simulation, where the controller is realized as an m-function containing a program code for RLS, PZC, and digital PI algorithm. The test was conducted by varying plant parameters, including DC gain and time constant. Verifying controller parameters and their response shows that RLS-PZC can effectively re-tune the digital PI parameters, proved by its response having zero steady-state error and its settling time is maintained. The proposed algorithm can also ensure that the PI controller output is always within the specified maximum limits hence the actual response does not deviate from the designed response.

Keywords


Autotuning PI; Recursive Least Square; Pole-Zero Cancelation; First-Order Plant; Matlab.

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References


G. Mendonça, F. Afonso, and F. Lau, “Model order reduction in aerodynamics: Review and applications,” Proc Inst Mech Eng G J Aerosp Eng, vol. 233, no. 15, pp. 5816–5836, 2019, doi: 10.1177/0954410019853472.

K. Lu et al., “Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems,” Mech Syst Signal Process, vol. 123, pp. 264–297, 2019, doi: 10.1016/j.ymssp.2019.01.018.

T. Hai, J. Zhou, and K. Muranaka, “An efficient fuzzy-logic based MPPT controller for grid-connected PV systems by farmland fertility optimization algorithm,” Optik (Stuttg), vol. 267, Oct. 2022, doi: 10.1016/j.ijleo.2022.169636.

N. Priyadarshi, M. Bhaskar, P. Modak, and N. Kumar, “Hybrid Firefly-PSO MPPT Based Single Stage Induction Motor for PV Water Pumping With Deep Fuzzy-Neural Network Learning,” IEEE International Conference on Power Electronics, Drives and Energy Systems, pp. 1-5, 2022, doi: 10.1109/pedes56012.2022.10080780.

S. Ferahtia et al., “Optimal adaptive gain LQR-based energy management strategy for battery–supercapacitor hybrid power system,” Energies (Basel), vol. 14, no. 6, 2021, doi: 10.3390/en14061660.

A. Ma’arif and A. Çakan, “Simulation and arduino hardware implementation of dc motor control using sliding mode controller,” Journal of Robotics and Control (JRC), vol. 2, no. 6, pp. 582–587, 2021, doi: 10.18196/jrc.26140.

R. N. Hasanah et al., “Design of PI sliding mode control for Zeta DC–DC converter in PV system,” Bulletin of the Polish Academy of Sciences: Technical Sciences, vol. 70, no. 3, pp. 1–8, 2022, doi: 10.24425/bpasts.2022.140952.

R. Rajesh and S. N. Deepa, “Design of direct MRAC augmented with 2 DoF PIDD controller: An application to speed control of a servo plant,” Journal of King Saud University - Engineering Sciences, vol. 32, no. 5, pp. 310–320, 2020, doi: 10.1016/j.jksues.2019.02.005.

S. Ciba, I. Iskender, and H. A. Ariani, “Comparing control performances of mrac and pid applied on a brushless dc motor,” International Journal on Technical and Physical Problems of Engineering, vol. 12, no. 3, pp. 10–15, 2020.

A. Latif, A. Z. Arfianto, H. A. Widodo, R. Rahim, and E. T. Helmy, “Motor DC PID system regulator for mini conveyor drive based-on matlab,” Journal of Robotics and Control (JRC), vol. 1, no. 6, pp. 185–190, 2020, doi: 10.18196/jrc.1636.

L. H. Woldeamanuel and A. Ramaveerapathiran, “Design of Multivariable PID Control Scheme for Humidity and Temperature Control of Neonatal Incubator,” IEEE Access, vol. 12, pp. 6051–6062, 2024, doi: 10.1109/ACCESS.2024.3349426.

I. M. M. Eltigani and U. Nangia, “Intelligent PSO- PID Controller Based Maximum Power Point Tracking (MPPT) for Photovoltaic System,” 2022 International Virtual Conference on Power Engineering Computing and Control: Developments in Electric Vehicles and Energy Sector for Sustainable Future (PECCON), pp. 1-6, 2022, doi: 10.1109/peccon55017.2022.9851173.

P. Sarhadi, A. R. Noei, and A. Khosravi, “Model reference adaptive PID control with anti-windup compensator for an autonomous underwater vehicle,” Rob Auton Syst, vol. 83, pp. 87–93, 2016, doi: 10.1016/j.robot.2016.05.016.

H. Gai, X. Li, F. Jiao, X. Cheng, X. Yang, and G. Zheng, “Application of a new model reference adaptive control based on pid control in cnc machine tools,” Machines, vol. 9, no. 11, 2021, doi: 10.3390/machines9110274.

A. Gaga and B. El, “Iow cost PID controller implementation of SEPIC Converter using 8-bits Microcontroller Target for Photovoltaic Applications,” J. Electrical Systems, vol. 18, no. 2, pp. 288-3–3, 2022.

N. Roongmuanpha, J. Satansup, T. Pukkalanun, and W. Tangsrirat, “Design of Mixed-Mode Analog PID Controller with CFOAs,” Sensors, vol. 24, no. 10, p. 3125, 2024, doi: 10.3390/s24103125.

S. Mahata, N. Herencsar, and G. Maione, “Optimal approximation of analog PID controllers of complex fractional-order,” Fract Calc Appl Anal, vol. 26, no. 4, pp. 1566–1593, 2023, doi: 10.1007/s13540-023-00168-x.

A. H. Akbar, A. Ma, C. Rekik, A. J. Abougarair, and A. Molla, “Implementing PID Control on Arduino Uno for Air Temperature Optimization,” Buletin Ilmiah Sarjana Teknik Elektro, vol. 6, no. 1, pp. 1–13, 2024, doi: 10.12928/biste.v6i1.9725.

B. F. Zhou and J. L. Zhang, “Design of DC Motor PID Control System Based on STM32 Single Chip Microcomputer,” International Core Journal of Engineering, vol. 6, no. 7, pp. 62–67, 2020, doi: 10.6919/ICJE.202007.

A. F. M. Sulaiman, I. Siradjuddin, and N. R. Dzakiyullah, “The Design of a Microcontroller-based Self Balancing Robot Employing PID Control and Kalman Filter,” Webology, vol. 19, no. 1, pp. 1194–1206, 2022, doi: 10.14704/web/v19i1/web19081.

K. Sozański, “Low Cost PID Controller for Student Digital Control Laboratory Based on Arduino or STM32 Modules,” Electronics (Switzerland), vol. 12, no. 15, 2023, doi: 10.3390/electronics12153235.

J. Kulisz and F. Jokiel, “A Hardware Implementation of the PID Algorithm Using Floating-Point Arithmetic,” Electronics, vol. 13, no. 8, p. 1598, 2024, doi: 10.20944/preprints202401.17.

I. Sukma, A. D. Suseno, P. Bakti, W. Ardiatna, and I. Supono, “Design and development of automatic voltage regulator using Ziegler-Nichols PID for electrical irons testing,” Bulletin of Electrical Engineering and Informatics, vol. 13, no. 6, pp. 3938–3947, 2024, doi: 10.11591/eei.v13i6.7326.

P. H. G. Coelho, J. F. M. Amaral, Y. C. Bacelar, E. N. Rocha, M. Bentes, and T. S. Souza, “Tuning Analog PID Controllers by Multi-Objective Genetic Algorithms with Fuzzy Aggregation,” International Conference on Enterprise Information Systems, ICEIS - Proceedings, vol. 1, pp. 563–571, 2023, doi: 10.5220/0011976900003467.

S. Mallick and U. Mondal, “MRAC based intelligent PID controller design technique for a class of dynamical systems,” Sadhana - Academy Proceedings in Engineering Sciences, vol. 49, no. 2, 2024, doi: 10.1007/s12046-024-02457-4.

E. Mendez et al., “ANN based MRAC-PID controller implementation for a furuta pendulum system stabilization,” Advances in Science, Technology and Engineering Systems, vol. 5, no. 3, pp. 324–333, 2020, doi: 10.25046/aj050342.

J. Jallad and O. Badran, “Firefly algorithm tuning of PID position control of DC motor using parameter estimator toolbox,” Bulletin of Electrical Engineering and Informatics, vol. 13, no. 2, pp. 916–929, 2024, doi: 10.11591/eei.v13i2.6216.

A. Dhanda and D. Niwas, “Comparison of Ziegler - Nichols, Cohen - Coon and Fuzzy Logic Controllers for Heat Exchanger Model: A Review,” International Journal of Engineering, Management, Humanities and Social Sciences Paradigms (IJEMHS), vol. 15, no. 01, pp. 1–7, 2015.

R. P. Borase, D. K. Maghade, S. Y. Sondkar, and S. N. Pawar, “A review of PID control, tuning methods and applications,” Int J Dyn Control, vol. 9, no. 2, pp. 818–827, 2021, doi: 10.1007/s40435-020-00665-4.

M. Hofreiter, “Relay identification using shifting method for pid controller tuning,” Energies (Basel), vol. 14, no. 18, 2021, doi: 10.3390/en14185945.

J. Sánchez Moreno, S. Dormido Bencomo, and J. M. Díaz Martínez, “Fitting of generic process models by an asymmetric short relay feedback experiment—The n-shifting method,” Applied Sciences, vol. 11, no. 4, p. 1651, 2021.

Y. Urakawa, “Vibration suppression in position control system by pole zero cancellation using limited pole placement method,” IEEJ Journal of Industry Applications, vol. 8, no. 2, pp. 256–262, 2019, doi: 10.1541/ieejjia.8.256.

Y. Wang, S. Deng, and W. Lu, “Zero-Pole Cancellation Based Iterative Learning Control Method for Speed Ripple Suppression of Single Rolling Rotor Compressor,” IEEE Access, vol. 12, pp. 55587–55599, 2024, doi: 10.1109/ACCESS.2024.3390091.

O. Miguel-Escrig and J. A. Romero-Pérez, “Improving the identification from relay feedback experiments,” Automatica, vol. 135, p. 109987, 2022, doi: 10.1016/j.automatica.2021.109987.

J. A. Romero-Pérez, O. Miguel-Escrig, J. Sánchez-Moreno, and S. Dormido-Bencomo, “Improving the relay feedback identification by using a gain-changing non-linearity,” IFAC-PapersOnLine, vol. 58, no. 7, pp. 418–423, 2024, doi: 10.1016/j.ifacol.2024.08.098.

K. J. Åström, T. Hägglund, C. C. Hang, and W. K. Ho, “Automatic tuning and adaptation for PID controllers - a survey,” Control Eng Pract, vol. 1, no. 4, pp. 699–714, 1993, doi: 10.1016/0967-0661(93)91394-C.

M. Moučka and M. Hofreiter, “PID controller with an autotuning function,” IEEE Access, vol. PP, p. 1, 2024, doi: 10.1109/ACCESS.2024.3462090.

N. Bouarroudj et al., “A new tuning rule for stabilized integrator controller to enhance the indirect control of incremental conductance MPPT algorithm: Simulation and practical implementation,” Optik (Stuttg), vol. 268, p. 169728, Oct. 2022, doi: 10.1016/j.ijleo.2022.169728.

A. Rehan, I. Boiko, and Y. Zweiri, “Autotuning of PID controller using the modified relay feedback test and optimization under uncertainty principle for robotic manipulators,” IET Control Theory and Applications, vol. 18, no. 5, pp. 581–602, 2024, doi: 10.1049/cth2.12592.

R. De Keyser, I. Birs, and C. Ionescu, “A performant PID autotuner based on a short relay test ?,” IFAC PapersOnLine, vol. 58, no. 7, pp. 328–333, 2024, doi: 10.1016/j.ifacol.2024.08.080.

D. Pavković, D. Lisjak, D. Kolar, and M. Cipek, “PI/PID Controller Relay Experiment Auto-Tuning with Extended Kalman Filter and Second-Order Generalized Integrator as Parameter Estimators,” Tehnicki Vjesnik, vol. 30, no. 3, pp. 715–723, 2023, doi: 10.17559/TV-20221003112627.

R. S. Patil, S. P. Jadhav, M. D. Patil, N. Mumbai, and C. Author, “Review of Intelligent and Nature-Inspired Algorithms-Based Methods for Tuning PID Controllers in Industrial Applications,” Journal of Robotics and Control (JRC), vol. 5, no. 2, pp. 336–358, 2024, doi: 10.18196/jrc.v5i2.20850.

E. W. Suseno, A. Ma’arif, and R. D. Puriyanto, “Tuning Parameter Pengendali PID dengan Metode Algoritma Genetik pada Motor DC,” TELKA - Telekomunikasi Elektronika Komputasi dan Kontrol, vol. 8, no. 1, pp. 1–13, 2022, doi: 10.15575/telka.v8n1.1-13.

S. B. Joseph, E. G. Dada, A. Abidemi, D. O. Oyewola, and B. M. Khammas, “Metaheuristic algorithms for PID controller parameters tuning: review, approaches and open problems,” Heliyon, vol. 8, no. 5, p. e09399, 2022, doi: https://doi.org/10.1016/j.heliyon.2022.e09399.

Y. S. Arikusu and N. Bayhan, “Design of a Novel PID Controller Based on Machine Learning Algorithm for a Micro-Thermoelectric Cooler of the Polymerase Chain Reaction Device,” IEEE Access, vol. 12, no. April, pp. 61959–61977, 2024, doi: 10.1109/ACCESS.2024.3392734.

S. Cheng et al., “DiffTune: Auto-Tuning through Auto-Differentiation,” IEEE Transactions on Robotics, vol. 40, pp. 4085–4101, 2024, doi: 10.1109/TRO.2024.3429191.

W. V Jahnavi, J. N. C. Sekhar, and A. S. Reddy, “A Review on PID Controller Tuning Using Modern Computational Algorithms,” Journal of Emerging Technologies and Innovative Research, vol. 10, no. 8, pp. 160–168, 2023.

I. A. Abbas and K. Mustafa, “A review of adaptive tuning of PID-controller: Optimization techniques and applications,” Int. J. Nonlinear Anal. Appl. In Press, vol. 6822, pp. 2008–6822, 2023.

M. J. Hasan and M. Y. Hellan, “Control and Modeling of PSO-PID based MPPT,” Int J Comput Appl, 2022, doi: 10.5120/ijca2022922112.

S. B. Joseph, E. G. Dada, A. Abidemi, D. O. Oyewola, and B. M. Khammas, “Metaheuristic algorithms for PID controller parameters tuning: review, approaches and open problems,” Heliyon, vol. 8, no. 5, p. e09399, 2022, doi: 10.1016/j.heliyon.2022.e09399.

C. Aoughlis, A. Belkaid, I. Colak, O. Guenounou, and M. A. Kacimi, “Automatic and Self Adaptive P&O MPPT Based PID Controller and PSO Algorithm,” IEEE International Conference on Renewable Energy Research and Applications, pp. 385-390, 2021, doi: 10.1109/icrera52334.2021.9598489.

A. A. Ponomarev, Y. I. Kudinov, F. F. Pashchenko, and E. S. Duvanov, “Analysis and Synthesis of Adaptive PID Controller with MRAC-MIT System,” Proceedings - 2020 2nd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency, SUMMA 2020, pp. 527–532, 2020, doi: 10.1109/SUMMA50634.2020.9280651.

S. J. Hammoodi, K. S. Flayyih, and A. R. Hamad, “Design and implementation speed control system of DC motor based on PID control and matlab simulink,” International Journal of Power Electronics and Drive Systems, vol. 11, no. 1, pp. 127–134, 2020, doi: 10.11591/ijpeds.v11.i1.pp127-134.

B. Lai and D. S. Bernstein, “Generalized Forgetting Recursive Least Squares: Stability and Robustness Guarantees,” IEEE Trans Automat Contr, pp. 1–16, 2024, doi: 10.1109/TAC.2024.3394351.

A. L. Bruce, A. Goel, and D. S. Bernstein, “Recursive Least Squares with Matrix Forgetting,” Proceedings of the American Control Conference, pp. 1406–1410, 2020, doi: 10.23919/ACC45564.2020.9148005.

S. A. U. Islam and D. S. Bernstein, “Recursive Least Squares for Real-Time Implementation,” IEEE Control Syst, vol. 39, no. 3, pp. 82–85, 2019, doi: 10.1109/MCS.2019.2900788.

R. Ortega, V. Nikiforov, and D. Gerasimov, “On modified parameter estimators for identification and adaptive control. A unified framework and some new schemes,” Annu Rev Control, vol. 50, no. 2019, pp. 278–293, 2020, doi: 10.1016/j.arcontrol.2020.06.002.

A. L. Bruce, A. Goel, and D. S. Bernstein, “Convergence and consistency of recursive least squares with variable-rate forgetting,” Automatica, vol. 119, p. 109052, 2020, doi: 10.1016/j.automatica.2020.109052.

H.-S. Shin and H.-I. Lee, “A New Exponential Forgetting Algorithm for Recursive Least-Squares Parameter Estimation,” arXiv preprint arXiv:2004.03910, 2020.

V. Shaferman, M. Schwegel, T. Glück, and A. Kugi, “Continuous-time least-squares forgetting algorithms for indirect adaptive control,” Eur J Control, vol. 62, pp. 105–112, 2021, doi: 10.1016/j.ejcon.2021.06.015.

M. Bin, “Generalized recursive least squares: Stability, robustness, and excitation,” Syst Control Lett, vol. 161, p. 105144, 2022, doi: 10.1016/j.sysconle.2022.105144.

A. L. Bruce, A. Goel, and D. S. Bernstein, “Necessary and sufficient regressor conditions for the global asymptotic stability of recursive least squares,” Syst Control Lett, vol. 157, p. 105005, 2021, doi: 10.1016/j.sysconle.2021.105005.




DOI: https://doi.org/10.18196/jrc.v6i1.24257

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