## 1 Introduction  
With the intensification of global warming, summer heat stress has emerged as a critical limiting factor in greenhouse vegetable cultivation [1]. Lettuce (_Lactuca sativa_ L.), a widely cultivated semi-cold-resistant vegetable, thrives in cool and humid climates and exhibits poor heat tolerance [2]. Its summer cultivation frequently encounters heat stress challenges [3, 4], necessitating production in specific cool-climate regions or facilitiesequipped with cooling capabilities. Excessive growth temperatures can lead to developmental abnormalities, yield reduction, and premature bolting in lettuce. To ensure successful summer cultivation of lettuce in high-temperature environments, traditional cooling methods typically focus on air temperature regulation within greenhouses [5]. However, during summer, indoor temperatures in greenhouses are often extreme and susceptible to fluctuations influenced by solar radiation [6], resulting in significant temperature variability, high energy consumption for regulation [7], and limited effectiveness in controlling the root-zone microenvironment. In contrast, localized cooling strategies, particularly root-zone temperature control, have demonstrated superior energy efficiency, rapid response, and effectiveness for summer lettuce production [8], emerging as a viable alternative that has attracted extensive research attention. Studies have demonstrated that root-zone cooling can significantly enhance lettuce yield and quality [9; 10], potentially enabling commercial-scale summer production [11]. This approach not only mitigates direct damage from elevated root-zone temperatures but also alleviates heat stress effects on aboveground plant parts. Consequently, developing advanced and intelligent root-zone cooling technologies represents a crucial pathway for achieving high-quality and high-yield summer lettuce production. Soilless cultivation techniques, including hydroponics and substrate culture, have enhanced the feasibility of regulating root-zone environments by replacing soil with nutrient solutions or growth media [12; 13], offering innovative approaches to mitigate heat stress. In hydroponic systems, the majority of plant roots grow directly within the nutrient solution, absorbing essential water and nutrients [14]. The temperature of the nutrient solution directly influences root-zone temperature, enabling precise regulation through heating or cooling. Although nutrient solutions exhibit greater thermal buffering capacity compared to air, they still rapidly absorb heat under intense light and high-temperature conditions, often exceeding 30 \({}^{\circ}\)C [15]. Elevated temperatures reduce dissolved oxygen concentration in the nutrient solution [16], accelerate root respiration, promote root senescence, and inhibit water and nutrient uptake [17]. [PERSON] et al. developed a root-zone temperature control system utilizing an air-source heat pump [18], which achieved enhanced pepper growth and yield through nutrient solution cooling and chilled water circulation. While this system effectively reduced average root-zone temperatures during cultivation, it faced challenges in maintaining nutrient solution temperature stability during peak daytime heat, with deviations up to 6 \({}^{\circ}\)C from set values. Furthermore, research indicates that plants exhibit greater sensitivity to root-zone temperature variations than air temperature fluctuations, with even 1 \({}^{\circ}\)C changes potentially causing significant growth alterations [19; 20]. Given the rapid advancement of hydroponic technologies, developing more precise and stable nutrient solution temperature control systems in high-temperature environments may represent a promising research direction. In the field of temperature control, Proportional-Integral-Derivative (PID) controllers have been extensively utilized due to their structural simplicity and implementation convenience [21]. [PERSON] et al.