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Proportional-Integral-Derivative (PID) controllers are widely used in various control systems to enhance stability and performance. In a thermostat, it adjusts heating or cooling based on the temperature difference between the actual and desired levels. They are often used in automotive speed systems, effectively managing sudden speed changes while maintaining a constant speed under varying conditions. On the other hand, PI controllers, commonly employed in voltage regulation, enhance stability...
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In automotive engineering, car suspension systems often employ Proportional Derivative (PD) controllers to enhance performance. PD controllers are utilized to adjust the damping force in response to road conditions. A controller, acting as an amplifier with a constant gain, demonstrates proportional control, with output directly mirroring input.
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Nonlinear 2-DOF PID controller optimized by artificial lemming algorithm for robust engine speed regulation in

Serdar Ekinci1, Davut Izci2,3, Mostafa Jabari4

  • 1Department of Computer Engineering, Bitlis Eren University, Bitlis, 13100, Turkey.

Scientific Reports
|November 26, 2025
PubMed
Summary

A new nonlinear two-degree-of-freedom (2-DOF) PID controller optimized by the artificial lemming algorithm (ALA) significantly improves engine speed regulation in spark-ignition (SI) systems. This ALA-based controller offers superior accuracy and robustness against disturbances compared to other metaheuristic methods.

Keywords:
Artificial lemming algorithmAutomotive controlDisturbance rejectionEngine speed regulationMetaheuristic optimizationNonlinear systemsPID tuningTwo-degree-of-freedom PID

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Area of Science:

  • Control Systems Engineering
  • Automotive Engineering
  • Artificial Intelligence in Engineering

Background:

  • Precise engine speed regulation in spark-ignition (SI) internal combustion engines (ICEs) is challenging due to nonlinearities and disturbances.
  • Conventional proportional-integral-derivative (PID) controllers struggle with fast tracking and robust disturbance rejection in dynamic conditions.

Purpose of the Study:

  • To develop and optimize a nonlinear two-degree-of-freedom (2-DOF) PID controller for enhanced SI engine speed regulation.
  • To evaluate the performance of the artificial lemming algorithm (ALA) in optimizing controller gains for improved accuracy and robustness.

Main Methods:

  • A detailed mathematical model of an SI engine was used, including throttle, manifold pressure, combustion, and crankshaft dynamics.
  • The artificial lemming algorithm (ALA), a bio-inspired metaheuristic, was employed to optimize the 2-DOF PID controller gains.
  • A multi-term cost function minimizing overshoot, steady-state error, and stability coefficients was used for optimization.

Main Results:

  • The ALA demonstrated superior convergence stability compared to other tested metaheuristic algorithms.
  • The ALA-optimized controller achieved significantly reduced rise time (0.3114 s), settling time (2.4313 s), and negligible overshoot (0.0027%).
  • Exceptional steady-state error (2.62 × 10⁻¹¹%) and disturbance rejection capability (speed deviation < 0.5%) were achieved.

Conclusions:

  • The ALA-based nonlinear 2-DOF PID controller provides a robust, accurate, and energy-efficient solution for SI engine speed regulation.
  • The proposed controller outperforms existing metaheuristic-based approaches in accuracy and reliability.
  • The adaptive and scalable design is suitable for real-time embedded systems, hybrid powertrains, and other nonlinear control applications.