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PID Controller01:19

PID Controller

641
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...
641
PD Controller: Design01:26

PD Controller: Design

611
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.
Designing a continuous-data controller requires selecting and linking components like adders and integrators, which are fundamental in Proportional,...
611
Time and frequency -Domain Interpretation of PI Control01:27

Time and frequency -Domain Interpretation of PI Control

392
Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires...
392
PI Controller: Design01:24

PI Controller: Design

1.2K
Proportional Integral (PI) controllers are a fundamental component in modern control systems, widely used to enhance performance and mitigate steady-state errors. They are particularly effective in applications such as automatic brightness adjustment on smartphones, where they excel at mitigating steady-state errors for step-function inputs. Unlike PD controllers, which require time-varying errors to function optimally, PI controllers leverage their integral component to address residual...
1.2K
Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

364
Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
364
Frequency-Domain Interpretation of PD Control01:24

Frequency-Domain Interpretation of PD Control

346
Proportional-Derivative (PD) controllers are widely used in fan control systems to improve stability and performance. A fan control system can be effectively represented using a Bode plot to illustrate the impact of a PD controller through its transfer function. The Bode plot visually conveys how PD control modifies the fan's response across various frequencies, providing a frequency domain interpretation of the controller's behavior.
The proportional control gain, combined with the...
346

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Related Experiment Video

Updated: Jan 13, 2026

Temperature-Controlled Assembly and Characterization of a Droplet Interface Bilayer
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A novel hyperbolic tangent-based PID controller tuned by the artificial lemming algorithm for nonlinear steam

Serdar Ekinci1, Davut Izci2,3, Mostafa Jabari4

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

Scientific Reports
|January 9, 2026
PubMed
Summary

A new hyperbolic tangent-based PID controller, tuned with the artificial lemming algorithm, significantly improves pressure regulation in steam condensers. This advanced control strategy enhances efficiency and safety in power generation systems.

Keywords:
Artificial lemming algorithmHyperbolic tangent PIDNonlinear dynamicsRobustness analysisSteam condenser controlTime-domain performance

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Area of Science:

  • * Control Systems Engineering
  • * Thermodynamics and Heat Transfer
  • * Artificial Intelligence in Engineering

Background:

  • * Precise pressure control in shell-and-tube steam condensers is critical for thermal efficiency and safety in power plants.
  • * Conventional proportional-integral-derivative (PID) controllers exhibit limitations in handling the nonlinear dynamics of these systems, resulting in poor performance.
  • * Existing controllers often suffer from overshoot, slow settling times, and reduced robustness in complex operational environments.

Purpose of the Study:

  • * To develop and evaluate a novel hyperbolic tangent-based PID (tanh-PID) controller for enhanced pressure regulation in nonlinear steam condensers.
  • * To introduce smooth nonlinear gain modulation for improved damping and transient response characteristics.
  • * To optimize the tanh-PID controller using the artificial lemming algorithm (ALA) for minimizing performance errors.

Main Methods:

  • * Development of a hyperbolic tangent-based PID (tanh-PID) controller with nonlinear gain modulation.
  • * Optimal tuning of the tanh-PID controller using the artificial lemming algorithm (ALA) to minimize integral of time-weighted absolute error (ITAE).
  • * Simulation studies using a nonlinear condenser model including steam-air interactions and hot-well dynamics, benchmarked against other algorithms and controllers.

Main Results:

  • * The ALA-tuned tanh-PID controller achieved the lowest ITAE (2.1189), fastest rise time (0.5960 s), and minimal settling time (12.4799 s).
  • * The proposed controller demonstrated minimal overshoot (5.8056%) and near-zero steady-state error (4.0776 × 10⁻⁴%), outperforming PI, FOPID, and other optimization algorithms.
  • * Robustness analyses confirmed superior disturbance rejection and reliable reference tracking under dynamic uncertainties.

Conclusions:

  • * The proposed ALA-tuned tanh-PID controller offers a high-performance, low-complexity solution for precise pressure regulation in industrial steam condensers.
  • * The nonlinear gain modulation effectively enhances damping behavior and transient shaping, addressing limitations of conventional controllers.
  • * The methodology shows significant potential for real-time deployment, improving operational efficiency and safety in power generation systems.