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1. Proportional–integral projected gradient method for conic optimization

   https://doi.org/10.1016/j.automatica.2022.110359  

   Yu, Yue; Elango, Purnanand; Topcu, Ufuk; Açıkmeşe, Behçet (August 2022, Automatica)
2. Proportional Integral Derivative Control in Spark Plasma Sintering Simulations

   https://doi.org/10.3390/ma14071779  

   Jiang, Runjian; Torresani, Elisa; Cui, Guodong; Olevsky, Eugene A. (April 2021, Materials)

   null (Ed.)

   The prediction of microstructure evolution and densification behavior during the spark plasma sintering (SPS) process largely depends on accurate temperature regulation. A loop feedback control algorithm called proportional integral derivative (PID) control is a practical simulation tool, but its coefficients are often determined by an inefficient “trial and error” method. This paper is devoted to proposing a numerical method based on the principles of variable coefficients to construct an optimal linear PID controller in SPS electro-thermal simulations. Different types of temperature profiles were applied to evaluate the feasibility of the proposed method. Simulation results showed that, for temperature profiles conventionally used in SPS cycles, the PID output keeps pace with the desired profile. Characterized by an imperfect time delay and overshoot/undershoot, the constructed PID controller needs further advancement to provide a more satisfactory temperature regulation for non-continuous temperature profiles. The first step towards a numerical rule for the optimal PID controller design was undertaken in this work. It is expected to provide a valuable reference for the advanced electro-thermal modeling of SPS. 

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3. Extrapolated Proportional-Integral Projected Gradient Method for Conic Optimization

   https://doi.org/10.1109/LCSYS.2022.3186647  

   Yu, Yue; Elango, Purnanand; Acikmese, Behcet; Topcu, Ufuk (January 2023, IEEE Control Systems Letters)
4. Robust Generalized Proportional Integral Control for Trajectory Tracking of Soft Actuators in a Pediatric Wearable Assistive Device

   https://doi.org/10.1109/IROS55552.2023.10342528  

   Mucchiani, Caio; Liu, Zhichao; Sahin, Ipsita; Kokkoni, Elena; Karydis, Konstantinos (October 2023, IEEE)
5. Exploration of the use of a proportional-integral-derivative controller for mitigation of seismic base excitation in civil structures

   https://doi.org/10.1117/12.2612604  

   Ngoma, Mary; Peckens, Courtney A. (April 2022, SPIE Smart Structures + Nondestructive Evaluation)

   Zonta, Daniele; Su, Zhongqing; Glisic, Branko (Ed.)

   Civil infrastructures are susceptible to damage due to external forces such as winds and earthquakes. These external forces cause damage to buildings and different civil structures. To prevent this, active control systems are executed. These systems use sensors to measure the displacement of the infrastructure, then actuators are utilized to provide a force that counteracts that displacement. In this study, a Proportional Integral Derivative (PID) controller was used to minimize the impact of an earthquake disturbance on multi-story structures. The proportional, integral, and derivative gains of the controller were obtained using Particle Swarm Optimization (PSO). This PID controller was validated on a simulated five-story structure based on the Kajima Shizuoka building with five ideal actuators. The effectiveness of the PID controller in reducing the seismic response of the structure with regards to inter-story displacement and acceleration was compared to the uncontrolled response of the structure. It is found that the PID controller with PID parameters obtained from the PSO algorithm offers effective control for the simulated five story structure. 

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