High-precision temperature control algorithm based on equivalent circuit model of thermoelectric cooling

<sec>High-precision temperature control systems based on thermoelectric cooling (TEC) have important applications in maintaining the stability and operational precision of advanced semiconductor optoelectronic devices, including single-frequency semiconductor lasers, optical frequency combs, and photometric measurement systems. However, the intrinsic high thermal inertia and nonlinear electro-thermal coupling characteristics of TEC systems make it challenging for traditional proportional-integral-derivative (PID) control algorithms to achieve the required millikelvin-level (mK) precision due to their tendency toward overshoot and oscillation.</sec><sec>In response to these issues, the internal electro-thermal conversion mechanisms, heat conduction, and dissipation dynamics of TEC systems are investigated in this work, and a high-precision temperature control approach is proposed based on an equivalent circuit model. By accurately constructing and verifying this equivalent circuit model, the oscillation characteristics and limitations inherent in traditional PID control are studied. Subsequently, an adaptive PID algorithm incorporating dynamic DC bias for enhanced precision is introduced. Specifically, the algorithm utilizes a traditional PID strategy to rapidly approximate the target temperature in the initial control stage. As the system approaches the target temperature and the temperature fluctuation decreases, it will automatically switch to an adaptive high-precision PID mode with dynamic DC bias. In this adaptive mode, the system continuously calculates the average output current and integrates temperature control errors over nearest time intervals. The overall control output is dynamically adjusted through adaptive weighting and deviation calculation to effectively counteract asymptotic and transient environmental disturbances. Additionally, the algorithm adopts an enhanced control strategy that combines dual-temperature sensing, primarily leveraging dynamic analysis of the hot-side temperature measurement to anticipate and counteract thermal disturbances. This predictive feedforward compensation, based on analyzing the rapid dynamic trends of the hot-side temperature, enables the controller to react preemptively to fast-changing disturbances before they significantly affect the controlled object, thereby substantially improving overall system stability and precision.</sec><sec>Simulation results demonstrate that the proposed adaptive PID algorithm with dynamic DC bias can consistently maintain temperature control accuracy at a millikelvin level. It effectively mitigates transient and gradual environmental temperature disturbances, exhibiting excellent robustness against varying PID parameter settings. Furthermore, the core logic of the algorithm remains straightforward, computationally efficient, and hardware-friendly, making it particularly suitable for embedded system implementation and practical engineering deployment.</sec><sec>In conclusion, the high-precision adaptive PID temperature control strategy presented herein possesses significant theoretical and practical value by addressing inherent TEC system challenges through detailed internal modeling and adaptive control strategies, contributing both theoretically and practically to high-precision temperature control engineering.</sec>