Adaptive Intelligent Control of a Lumped Evaporator Model Using Wavelet-Based Neural PID with IIR Filtering

This article presents an adaptive intelligent control strategy applied to a lumped-parameter evaporator model, i.e., a simplified dynamic representation treating the evaporator as a single thermal node with uniform temperature distribution, suitable for control design due to its balance between physical fidelity and computational simplicity. The controller uses a wavelet-based neural proportional, integral, derivative (PID) controller with IIR filtering (infinite impulse response). The dynamic model captures the essential heat and mass transfer phenomena through a nonlinear energy balance, where the cooling capacity “ $Q_{evap}$” is expressed as a non-linear function of the compressor frequency and the temperature difference, specifically, $Q_{evap}=k_{1}u(T_{in}-T_e)$ with $u$ as compressor frequency, $T_e$ evaporator temperature, and $T_{in}$ inlet fluid temperature. The operating conditions of the system, in general terms, focus on the following variables, the overall thermal capacity is 1000 J/K, typical for small-capacity heat exchangers, The mass flow is 0.05 kg/s, typical for secondary liquid cooling circuits, the overall loss coefficient of 50 W/K that corresponds to small evaporators with partial insulation, the temperatures (inlet) of ${10}^{\circ }$C and the temperature of environment of ${25}^{\circ }$C, thermal load of 200 W that corresponds to a small-scaled air conditioning applications. To handle system nonlinearities and improve control performance, a Morlet wavelet-based neural network (Wavenet) is used to dynamically adjust the PID gains online. An IIR filter is incorporated to smooth the adaptive gains, improving stability and reducing oscillations. In contrast to prior wavelet- or neural-adaptive PID controllers in HVAC applications, which typically adjust gains without explicit filtering or not tailored to evaporator dynamics, this work introduces the first PID–Wavenet scheme augmented with an IIR-based stabilization layer, specifically designed to address the combined challenges of nonlinear evaporator behavior, gain oscillation, and real-time implementability. The proposed controller (PID-Wavenet+IIR) is implemented and validated in MATLAB/Simulink, demonstrating superior performance compared to a conventional PID tuned using Simulink’s auto-tuning function. Key results include a reduction in settling time from 13.3 to 8.2 s, a reduction in overshoot from 3.5% to 0.8%, a reduction in steady-state error from ${0.12}^{\circ }$C to ${0.02}^{\circ }$C and a 13% reduction in energy overall consumption. The controller also exhibits greater robustness and adaptability under varying thermal loads. This explicit integration of wavelet-driven adaptation with IIR-filtered gain shaping constitutes the main methodological contribution and novelty of the work. These findings validate the effectiveness of the wavelet-based adaptive approach for advanced thermal management in refrigeration and HVAC systems, with potential applications in controlling variable-speed compressors, liquid chillers, and compact cooling units.