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1. INTRODUCTION
Ultraviolet-C (UV-C) radiation generated by discharge lamps is a widely adopted and effective method for water sterilization, operating in pseudo-continuous mode to ensure both safety and efficacy (Aissa-Bokhtache et al., 2021). The germicidal effect at the 253.7 nm wavelength is critical for destroying microorganisms, including viruses, bacteria, and algae. However, maintaining stable lamp operation is challenging due to the complex interplay of electrical, thermal, and chemical processes inherent to discharge lamps.
A key requirement for optimal UV-C lamp performance is a high-frequency (50 kHz) current source with a stable arc current of 0.65 A to maximize UV output and lamp longevity (Minzu et al., 2021; Mrabet et al., 2006). Yet achieving this stability is complicated by current fluctuations caused by water basin temperature variations, power supply inconsistencies, and electrode degradation; harmonic distortion, which reduces efficiency and compromises sterilization performance; and slow disturbance rejection in traditional control methods, which struggle with these nonlinear dynamics (Chia, 2017).
The literature reveals a limited number of studies focused on current regulation within the specific context of electronic ballasts supplying UV-C discharge lamps. While prior studies have explored solutions using advanced controllers such as robust designs in Mrabet et al. (2006) and fuzzy logic optimization in Aissa-Bokhtache et al. (2016), a significant gap remains in achieving real-time disturbance rejection and low harmonic distortion for stable arc current regulation.
This paper addresses these challenges by developing and comparing two closed-loop control strategies: a Proportional-Integral (PI) controller, widely used in industry for its simplicity; a Model Predictive Controller (MPC). The MPC was employed for its advantages, as demonstrated in various applications such as: power converters, where Medina Sánchez et al. (2021) used MPC in a buck converter to achieve better dynamic performance than conventional methods; robotics: where Gonzales et al. (2014) employed MPC in the trajectory tracking of wheeled robots, which demonstrated its robustness; industrial processes: where González et al. (2023) employed MPC to effectively regulate an agitated pond and distillation column, demonstrating its process control robustness; marine systems: where Gonzales, Rosero and Rosales (2017) developed an MPC-based path-tracking controller for ships with a focus on its predictability in dynamic conditions; and nonlinear mechanical systems: Prado et al. (2020) utilized a nonlinear version of MPC to stabilize a Furuta pendulum, demonstrating its applicability in highly unstable systems.
The key objectives of this study are: maintain a stable 0.65 A arc current under perturbations; reduce total harmonic distortion (THD) to meet the international standards (IEC 61000-3-2 (Class C) and IEEE 519-2022 are recommended THD less than 5% for industrial systems); and achieve a fast disturbance rejection.
The paper is organized as follow: section 2 will introduce the electronic ballast schematic and the overall model. Moreover, the two control methods are presented. Section 3 discusses the achieved results. Also, a comparative study is presented between the PI controller and the MPC controller to clearly the advantages of the implemented control techniques on the discharge lamp. The paper presents the conclusion in section 4.
2. METHODOLOGY
The electrical circuit model of the discharge lamp (Aissa-Bokhtache et al., 2021) is depicted in Figure 1. It consists of two main components: the filament resistors "r f " for each cathode and the arc resistor "R arc ". The electrical characteristics of the arc of the lamp, affected by its power and temperature, are represented by the "R arc " resistor. The purpose of this resistor is to mimic the discharge characteristics of the lamp.
The suggested system shown in Figure 2, primarily comprises a full-bridge inverter with MOSFET operating at a frequency of 50 kHz. It also includes a PWM control circuit, a phase rectifier with a filter for maintaining electromagnetic compatibility, and a resonant circuit L r and C r for initiating the lighting of the lamp with the support of the starter C p . Notably, the additional preheating circuit, which is used to prevent filament damage during ignition, is not included in this configuration. The ballast design aims to achieve null average current operation, fast switching times for quick discharge reboots with consistent current, adjustable duty cycle and frequency (Aissa-Bokhtache et al., 2023).
The corresponding circuit of the suggested system is shown in Figure 3, the full-bridge inverter powers the electronic ballast-discharge light.
In this study, the design incorporated a 65-watt Philips lamp, which is specially engineered for water purification processes at room temperature, producing light with a wavelength of 253.7 nanometers. The essential lamp parameters extracted from the datasheet are summarized in Table 1 (Aissa-Bokhtache et al., 2023).
To further regulate the arc current of the lamp (I arc ), the transfer function derivation enables system stability analysis relative to arc current variations. The current divider rule allows to calculate the following expression (1), the open loop transfer function of the proposed system G(s).
Where:
2.1. The classic PI control technique
PI controllers have become indispensable tools in both research and industrial applications due to their proven ability to maintain system stability and precision (Yandun et al., 2018). By intelligently combining proportional and integral actions, these controllers effectively correct deviations, keeping processes running smoothly within specified limits. Their widespread adoption across various industries highlights their fundamental importance in control engineering (Borase et al., 2021; Djari et al., 2014). In the chosen discharge lamp model, maintaining a steady Root-Mean-Square (RMS) arc current of about 0.65 A is critical for optimal lamp performance in the radiation plane. To achieve this, we have implemented a PI controller to precisely regulate the arc current. Figure 4 illustrates the complete control scheme with the PI controller configuration.
Note that the transfers function of the proportional-integral controller C(s) is given by:
Where: 
and 
are the gains of the controller.
Using equations (1) and (2), the Closed-Loop Transfer Function (TFCL) of the system can be calculated by:
Where G(s) is the open-loop transfer function of the system.
The parameters of the PI controller are calculated using the pole placement method, 
.
2.2. The model predictive control technique
The fundamental principle of predictive control is to consider, at a given time, the future behavior of a system using a numerical model of the process to predict its outputs over a defined prediction horizon. One of the advantages of predictive methods lies in their ability to leverage information about predefined future trajectories, by adjusting the system output to match a reference over this finite horizon (Ganzaroli et al., 2022).
Predictive control is the repeated resolution, at each time step, of an optimal control problem, how to move from the current state to a target optimally while satisfying constraints. To accomplish this, it is essential to determine the state of the system at every iteration by utilizing a numerical solution method. The functional diagram of predictive control is presented in Figure 5.
To effectively manage the arc current of the discharge lamp, a predictive control framework integrated with PWM will be implemented.
Optimizing the parameters of predictive control is crucial due to the absence of general analytical rules for selecting them based on the type of process and required performance. This step typically requires multiple simulation trials to achieve an optimal choice. Modifying each parameter individually reveals their effect on control performance, including speed, response time, overshoots and stability. Selecting parameters that optimize these criteria ensures the best control performance. Using predictive laws expressed by the following function (4).
With a sampling period of 
sec, the polynomials 
of the KARIMA model are:
Note that the choice of tuning parameters: 
, results in a stable and well-damped behavior. It is worth noting that there is no strict rule for adjusting these control parameters, and the choice was made after a number of attempts.
3. RESULTS AND DISCUSSIONS
The performance of the discharge lamp in water treatment is significantly influenced by the quality of its electrical power supply. Therefore, it is crucial to analyze the waveform of the ballast's output current and voltage to assess the harmonics generated. Simulations and Data extraction (curves and THD values) were performed under MATLAB environment.
Three tests are selected for comparison. The discharge lamp-electronic ballast system is first tested in an open-loop setup. Following this, the system is evaluated in a closed-loop arrangement using two control methods: a traditional PI controller and a predictive controller.
3.1. Simulation of the Ballast in Open-Loop Operation
Figure 6 presents the arc voltage and current of the discharge lamp in open-loop operation. Upon analyzing Figure 6, it is evident that the obtained arc current and voltage exhibit alternating forms at a frequency of 50 kHz, with apparent symmetry. These waveforms closely resemble sine waves, with a THD of 15.80 %.
3.2. PI Control of the Ballast
Figure 7 depicts the waveform findings acquired from the simulation of the system following the implementation of thePIcontroller.
Figure 7 clearly demonstrates the enhancements made to the waveforms in comparison to those achieved in the open-loop simulation. The current of the discharge lamp now exhibits a closer waveform to the sinusoidal waveform comparing with the open loop current waveform. This improvement is indicated by the substantial reduction in theTHDrate. TheTHDindicator shows a decreasing rate to 6.00 % for the PI controlling against 15.80 % during open-loop operation.
3.3. MPC Control of the Ballast
Figure 8 illustrates the waveform results obtained from the simulation of the system after the introduction of the predictive controller. Figure 8 demonstrates the improvements made to the waveforms compared to those obtained with classical PI control. It highlights a significant reduction in the harmonic distortion rate of the lamp arc current for predictive control, which is reduced to 2.21 % compared to 6.00 % with PI control. This results in a waveform that closely resembles a sine wave at a frequency of 50 kHz.
3.4. Comparison and robustness test of MPC and PI controls
This subsection presents a comprehensive evaluation of conventional PI control versus MPC in discharge lamp-electronic ballast applications, with emphasis on three critical performance metrics: (1) transient response characteristics, (2) power quality (THD), and (3) robustness against parametric variations. The analysis builds upon established control theory frameworks and recent advancements in power electronics control.
Figure 9 (a) compares system behavior across three operational modes: Open-loop, PI control, and MPC control, revealing significant performance differences:
Open-loop operation achieves the target RMS current (0.65 A) but suffers from excessive settling time (150 ms) and unacceptable THD (15.8 %), exceeding IEC 61000-3-2 limits. This mode exhibits known failure modes, including accelerated electrode degradation, reduced UV-C output efficiency, and decreased mean time between failures.
Closed-loop PI control improves performance substantially, reducing settling time to 29 ms (82 % faster than open-loop) and THD to 6 % (62 % lower than open-loop).
MPC Implementation outperforms both methods, achieving a 14 % faster settling time (25 ms vs. PI) and a 63 % lower THD (2.21 %). It demonstrates the predictive control advantages, including: anticipatory disturbance rejection, active constraint handling, and excellent current tracking (steady-state error less than 0.5 %). The results highlight MPC’s superior dynamic response and precision, making it the best choice for high-performance.
A temperature fluctuation is one of the major disturbances that significantly affect arc voltage, current, and ultimately the intensity of UV-C radiation. Thus, it is crucial to establish robustness test against temperature disturbances of the proposed MPC controller and compare it with the PI results.
To evaluate the system resilience, a step disturbance of 40 % from the nominal temperature will be applied. To clearly isolate the response to the disturbance from the transient behaviors and see clearly the controller effectiveness, the disturbance is introduced when the steady state is established (at time t = 0.07 s).
With such high disturbance step, the robustness of both controllers will experience an extreme parametric variation in arc current (the analysis considers arc resistance changes, following the physical relationships established in the transfer function given by equation (1)), which is inversely proportional to temperature. Figure 9 (b) demonstrates disturbance rejection. The zoomed-in view reveals that the PI controller stabilizes the system within 0.002 s after the disturbance, while the MPC recovers equilibrium in just 0.001 s, showcasing faster rejection.
Both controllers maintain the steady-state error within internationally accepted tolerance bounds (Elamri et al., 2024). However, the MPC exhibits significantly higher robustness, ensuring stable operation even under severe disturbances.
4. CONCLUSION
Predictive control is a model-driven approach that employs a real-time dynamic process model within the controller to predict and optimize future system behavior. The study employed MATLAB-SimPowerSystems software to simulate the system, iteratively adjusting the parameters to achieve good results. The goal was to ensure a stable power supply for the discharge lamp-electronic ballast setup, producing a sinusoidal current with low total harmonic distortion. This current operates at a frequency of 50 kHz and an RMS value of 0.65 A, aiming to maximize UV radiation output at a wavelength of 253.7 nm. According to the presented results, THD S of the system with MPC control is less than 5 %, which complies with the international standards. Moreover, the simulations revealed precise regulation, stability of system, and being able to follow reference signals while ensuring a rapid response time to sudden changes. Simulation results demonstrated the effectiveness of predictive control, providing satisfactory performance under both set-point changes and disturbances. In summary, predictive control offers advantages over PI control technique in terms of system stability. However, it requires careful selection of synthesis parameters to achieve the desired performance. As an extension to the work, it would be interesting to assess the effects of system experimental implementation. On the other hand, to explore new research topics, this work paves the way for studying other related systems, such as extending the system with other converter topologies and integrating renewable energy such as photovoltaic solar, wind, or hybrid systems like photovoltaic-wind, which have garnered significant attention due to their sustainability.
