PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION

Süleyman Mert Özer

doi:10.18038/estubtda.1935904

EN

PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION

Abstract

Servo-based DC motor systems are widely employed in industrial automation and robotics due to their high precision in position control. However, the presence of time delay in feedback loops, arising from sensing, computation, and signal transmission, can significantly degrade system performance and may even lead to instability. This study proposes a delay-aware control design framework for a rotary servo-based DC motor system using a proportional-integral-velocity (PIV) controller. The proposed approach extends conventional proportional-velocity (PV) control by incorporating an integral action to eliminate steady-state errors in position tracking while preserving the favorable damping characteristics of velocity feedback. The controller design is formulated as a spectral abscissa minimization problem, where the real part of the rightmost closed-loop mode is minimized with respect to the controller parameters. Due to the nonconvex and nonsmooth nature of the problem, a derivative-free optimization strategy based on the Nelder–Mead algorithm is employed, and multiple initializations are considered to improve robustness of the solution. The closed-loop system is modeled as a delay-differential equation, and its stability properties are analyzed through spectral methods. In addition, the delay robustness of the designed controllers is systematically investigated by evaluating their performance under representative delay values. The effectiveness of the proposed approach is demonstrated through both spectral analysis and real-time experiments conducted on the Quanser SRV02 platform. The results show that the proposed PIV controller achieves stable closed-loop behavior with improved transient performance and eliminates steady-state error in position control, outperforming previously reported PV-based designs in the presence of time delay.

Keywords

DC-motor, PIV control, Time-Delay systems, Optimal control, Delay margin

References

[1] Younkin GW. Industrial Servo Control Systems: Fundamentals and Applications. Boca Raton, FL, USA: CRC Press, 2002.
[2] Dote Y. Brushless Servomotors: Fundamentals and Applications. Oxford, England: Clarendon Press, 1990.
[3] Sipahi R, Niculescu S-I, Abdallah CT, Michiels W, Gu K. Stability and stabilization of systems with time delay. IEEE Control Syst Mag 2011; 31: 38-65.
[4] Ayasun S. Stability analysis of time-delayed DC motor speed control system. Turk J Elec Eng & Comp Sci 2013; 21: 381-393.
[5] Richard J-P. Time-delay systems: an overview of some recent advances and open problems. Automatica 2003; 39: 1667-1694.
[6] Garpinger O, Hagglund T, Astrom KJ. Performance and robustness trade-offs in PID control. J Process Control 2014; 24: 568-577.
[7] Vilanova R, Visioli A. PID Control in the Third Millennium. London, England: Springer London, 2012.
[8] Astrom KJ, Hagglund T. Advanced PID Control. North Carolina, USA: ISA - The Instrumentation, Systems and Automation Society, 2006.
[9] Wang L. Implementation of PID Controllers. In: PID Control System Design and Automatic Tuning using MATLAB/Simulink. Hoboken, NJ, USA: Wiley-IEEE Press, 2020, pp. 113-138.
[10] Alla RK, Choudhary N, Lather JS, Pahuja GL. PIV and lead compensator design using Lambert W function for rotary motions of SRV02 plant. In: 2014 IEEE 10th International Colloquium on Signal Processing & its Applications (CSPA); 7–9 March 2014; Kuala Lumpur, Malaysia. pp. 266-270.

[11] Quanser. SRV-02 Rotary Servo Based Unit User Manual. Canada: QUANSER, 2015.
[12] Abdullahi ZH, Danzomo BA, Abdullahi ZS. Design and simulation of a PID controller for motion control systems. IOP Conf Ser Mater Sci Eng 2018; 344: p. 012016.
[13] Aydogdu O, Levent ML. Kalman state estimation and LQR assisted adaptive control of a variable loaded servo system. Eng Technol Appl Sci Res 2019; 9: pp. 4125-4130.
[14] Bhimte R, Shah P, Bhole-Ingale K, Sekhar R. Precise position control of Quanser servomotor using fractional order fuzzy PID controller. In: 2020 IEEE Bombay Section Signature Conference (IBSSC); 4–6 Dec 2020; Mumbai, India. pp. 58-63.
[15] Dursun EH, Durdu A. Position control by using PD type fuzzy logic: Experimental study on rotary servo system. In: ECAI 2016 - 8th International Conference on Electronics, Computers and Artificial Intelligence; 30 June–2 July 2016; Ploiesti, Romania. pp. 1-6.
[16] Khadraoui S, Nounou H, Nounou M, Datta A, Bhattacharyya SP. A model-free design of reduced-order controllers and application to a DC servomotor. Automatica 2014; 50: 2142-2149.
[17] Nerkar SS, Patre BM. Design of disturbance observer-based dynamic sliding mode control. In: Soft Computing: Theories and Applications. Singapore: Springer, 2023. pp. 623-635.
[18] Sun R, Yang T, Zhang L, Wang L, Fu Y, Tavakoli M. Haptic virtual surgery simulation system under field programmable analogue array-based hybrid control. Sci Rep 2022; 12: p. 12371.
[19] Ren B, Zhong QC, Dai J. Asymptotic reference tracking and disturbance rejection of UDE-based robust control. IEEE Trans Ind Electron 2016; 64: pp. 3166-3176.
[20] Simion MB, Selișteanu D, Șendrescu D. DC motor control using hand gestures. In: 2020 24th International Conference on System Theory, Control and Computing (ICSTCC); 8–10 Oct 2020; Sinaia, Romania. pp. 149-153.
[21] Sun J, Wang C, Xin R. Anti-disturbance study of position servo system based on disturbance observer. IFAC PapersOnLine 2018; 51 (4): 202-207.
[22] Hale JK, Verduyn-Lunel SM. Introduction to Functional Differential Equations. New York, NY, USA: Springer, 1993.
[23] Normey-Ricoa JE, Camacho EF. Dead-time compensators: A survey. Control Eng Pract 2008; 16 (4): 407-428.
[24] Smith OJM. A controller to overcome dead time. ISA J 1959; 6: pp. 28-33.
[25] Michiels W, Niculescu S-I. On the delay sensitivity of Smith predictors. Int J Syst Sci 2003; 34: pp. 543-551.
[26] Majhi S, Atherton DP. Modified Smith predictor and controller for processes with time delay. IEE Proc Control Theory Appl 1999; 146 (5): pp. 359-366.
[27] Toker O, Özbay H. On the rational H∞ controller design for infinite dimensional plants. Int J Robust Nonlinear Control 1996; 6: pp. 383-397.
[28] Kolmanovskii V, Niculescu S-I, Richard JP. On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems. Int J Control 1999; 72: pp. 374-384.
[29] Yi S, Nelson PW, Ulsoy AG. DC motor control using the Lambert W function approach. In: 10th IFAC Workshop on Time Delay Systems; June 2012; Boston, MA, USA. pp. 49-54.
[30] Yi S, Nelson PW, Ulsoy AG. Proportional-integral control of first-order time-delay systems via eigenvalue assignment. IEEE Trans Control Syst Technol 2013; 21 (5): pp. 1586-1594.
[31] Yi S, Ulsoy AG. Time-delayed vision-based DC motor control via rightmost eigenvalue assignment. In: 2014 American Control Conference (ACC); 4–6 June 2014; Portland, OR, USA. pp. 5564-5569.
[32] Silva GJ, Datta ABSP. Controller design via Padé approximation can lead to instability. In: 40th IEEE Conference on Decision and Control; December 2001; Orlando, FL, USA. pp. 4733-4737.
[33] Silva GJ, Datta A, Bhattacharyya SP. PID Controllers for Time-Delay Systems. Boston, MA, USA: Birkhäuser, 2005.
[34] Wang S, Rajendran P, Wang J, Marimuthu S, Raja V, Wong K. Metaheuristic optimization of PID controllers: methods, applications, and trends. Archives of Computational Methods in Engineering 2026; 33: pp. 6651-6697.
[35] Güven AF, Mengi OÖ. Nature-inspired algorithms for optimizing fractional order PID controllers in time-delayed systems. Optimal Control Applications and Methods 2024; 45: pp. 1251–1279.
[36] Özer SM, Yıldız S, İftar A. Optimization-based PV/PI design for a DC-motor system with delayed feedback. In: 26th Mediterranean Conference on Control and Automation; June 2018; Zadar, Croatia. pp. 39-45.
[37] Özer SM, Yıldız S, İftar A. Performance analysis of a DC-motor control system with time-delay: Smith Predictor vs Optimization-based Controller Design. In: 6th International Conference on Control Engineering & Information Technology (CEIT); 25–27 October 2018; Istanbul, Turkey. pp. 1-6.
[38] Burke JV, Henrion D, Lewis AS, Overton ML. Stabilization via nonsmooth, nonconvex optimization. IEEE Trans Autom Control 2006; 51 (11): pp. 1760-1769.
[39] Gumussoy S, Henrion D, Millstone M, Overton ML. Multiobjective robust control with HIFOO 2.0. In: 6th IFAC Symposium on Robust Control Design (ROCOND); 16–18 June 2009; Haifa, Israel. pp. 144-149.
[40] Vanbiervliet J, Verheyden K, Michiels W, Vandewalle S. A nonsmooth optimization approach for the stabilization of time-delay systems. ESAIM Control Optim Calc Var 2008; 14: pp. 478-493.
[41] Michiels W. Spectrum-based stability analysis and stabilisation of systems described by delay differential algebraic equations. IET Control Theory Appl 2011; 5 (16): pp. 1829-1842.
[42] Gümüşsoy S, Michiels W. Fixed-order H-infinity control for interconnected systems using delay differential algebraic equations. SIAM J Control Optim 2011; 49(5): pp. 2212-2238.
[43] Michiels W, Vyhlidal T, Zitek P. Control design for time-delay systems based on quasi-direct pole placement. J Process Control 2010; 20(3): pp. 337-343.
[44] Özer SM, İftar A. Observer-based stabilization of time-delay systems: An application to diesel engine. In: 12th Asian Control Conference (ASCC); 17–20 Dec 2017; Gold Coast, Australia. pp. 505-510
[45] Özer SM, İftar A. Eigenvalue optimisation-based centralised and decentralised stabilisation of time-delay systems. Int J Control 2021; 95(8): pp. 2245-2266.
[46] Wu Z, Michiels W. Reliably computing all characteristic roots of delay differential equations in a given right half-plane using a spectral method. J Comput Appl Math 2012; 236(9): pp. 2499-2514.
[47] Michiels W, Niculescu S-I. Stability, Control, and Computation for Time-Delay Systems: An Eigenvalue-Based Approach. Philadelphia, PA, USA: SIAM, 2014.
[48] Appeltans P, Silm H, Michiels W. TDS-CONTROL: a MATLAB package for the analysis and controller-design of time-delay systems. In: 18th IFAC Workshop on Control Applications of Optimization; 2022; Gif-sur-Yvette, France. pp. 272-277.

Details

Primary Language

English

Subjects

Control Theoryand Applications, Control Engineering

Journal Section

Research Article

Authors

Süleyman Mert Özer ^*
0000-0001-5019-629X
Türkiye

Publication Date

September 25, 2026

Submission Date

April 22, 2026

Acceptance Date

July 17, 2026

Published in Issue

Year 2026 Volume: 27 Number: 3

DOI

https://doi.org/10.18038/estubtda.1935904

IZ

https://izlik.org/JA97RE62GB

APA

Özer, S. M. (2026). PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, 27(3), 403-422. https://doi.org/10.18038/estubtda.1935904

AMA

1.Özer SM. PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION. Estuscience - Se. 2026;27(3):403-422. doi:10.18038/estubtda.1935904

Chicago

Özer, Süleyman Mert. 2026. “PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 27 (3): 403-22. https://doi.org/10.18038/estubtda.1935904.

EndNote

Özer SM (September 1, 2026) PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 27 3 403–422.

IEEE

[1]S. M. Özer, “PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION”, Estuscience - Se, vol. 27, no. 3, pp. 403–422, Sept. 2026, doi: 10.18038/estubtda.1935904.

ISNAD

Özer, Süleyman Mert. “PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 27/3 (September 1, 2026): 403-422. https://doi.org/10.18038/estubtda.1935904.

JAMA

1.Özer SM. PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION. Estuscience - Se. 2026;27:403–422.

MLA

Özer, Süleyman Mert. “PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 27, no. 3, Sept. 2026, pp. 403-22, doi:10.18038/estubtda.1935904.

Vancouver

1.Süleyman Mert Özer. PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION. Estuscience - Se. 2026 Sep. 1;27(3):403-22. doi:10.18038/estubtda.1935904

Abstract

PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite