This study proposes an enhanced derivative control strategy, named $PI$-$D^{\AE }$, designed to overcome key limitations of the derivative ($D$) term, such as noise amplification, derivative kick $(D$-$k)$, and tuning difficulties. These issues often arise in high-frequency or rapidly changing systems, in which traditional PID controllers struggle. The proposed solution introduces a novel adaptive exponent algorithm (Æ) that dynamically modulates the $D$ term based on the evolving relationship between system output and setpoint. This yields the $PI$-$D^{\AE }$ controller, which adapts in real time to changing conditions. The results show significant performance improvements. Simulation results on two systems demonstrate that $PI$-$D^{\AE }$ achieves a 90% faster response time, a 35% reduction in peak time, and a 100% improvement in settling time compared with conventional PID controllers, all while maintaining a near-zero steady-state error even under external disturbances. Unlike more-complex alternatives such as fuzzy logic, neural networks, or sliding mode control, $PI$-$D^{\AE }$ retains the simplicity and robustness of PID, avoiding high computational costs or intricate setups. This adaptive exponent strategy offers a practical and scalable enhancement to classical PID, improving performance and robustness without added complexity, and thus provides a promising control solution for real-world applications in which simplicity, adaptability, and reliability are essential.

Artificial vision system applications have generated significant interest as they allow information to be obtained through one or several of the cameras that can be found in daily life in many places, such as parks, avenues, squares, houses, etc. When the aim is to obtain information from large areas, it can become complicated if it is necessary to track an object of interest, such as people or vehicles, due to the vision space that a single camera can cover; this opens the way to distributed zone monitoring systems made up of a set of cameras that aim to cover a larger area. Distributed zone monitoring systems add great versatility, becoming more complex in terms of the complexity of information analysis, communication, interoperability, and heterogeneity in the interpretation of information. In the literature, the development of distributed schemes has focused on representing data communication and sharing challenges. Currently, there are no specific criteria for information exchange and analysis in a distributed system; hence, different models and architectures have been proposed. In this work, the authors present a framework to provide homogeneity in a distributed monitoring system. The information is obtained from different cameras, where a global reference system is defined for generated trajectories, which are mapped independently of the model used to obtain the dynamics of the movement of people within the vision area of a distributed system, thus allowing for its use in works where there is a large amount of information from heterogeneous sources. Furthermore, we propose a novel similarity metric that allows for information queries from heterogeneous sources. Finally, to evaluate the proposed performance, the authors developed several distributed query applications in an augmented reality system based on realistic environments and historical data retrieval using a client–server model.