Computational Assessment of the Effect of PWM Resolution in LED Supplementary Lighting on Plant Photosynthetic Response

Abstract

Controlled-environment agriculture (CEA) is emerging as a key platform for Agriculture 4.0, where sensors, cyber-physical systems, and artificial intelligence enable precise control over light regimes and resources. In modern greenhouses, programmable supplementary lighting using radio-controlled LED creates adaptive light scenarios, yet simultaneously renders the light system sensitive to digital control effects. Quantization error in the digital setting of the pulse-width modulation (PWM) duty cycle serves as an example of this. Photobiological studies typically focus on plant responses to photosynthetic photon flux density (PPFD), spectral composition, and pulsed light regimes, whereas analyses of LED drivers treat PWM bit depth primarily in terms of dimming accuracy, energy efficiency, and electromagnetic compatibility. Consequently, it remains unclear at which combinations of PPFD and PWM bit depth the discreteness of digital control might lead to biologically significant instability in the photosynthetic response. The objective of this study is to develop a computational criterion for evaluating the permissible bit depth of PWM control for LED supplementary lighting, limiting the relative variation in the net photosynthetic rate of plants. Materials and Methods. The authors reviewed publications on PWM-based control of LED supplementary lighting and pulsed plant lighting using targeted queries. Based on current concepts in controlled environment lighting, PPFD — the amount of useful light incident on the leaf surface per unit time — was adopted as the primary metric of the light environment. Photosynthetic activity was simulated using an empirical relationship between the net photosynthesis rate and PPFD. To assess the impact of quantization noise in the PWM control channel of the LED supplementary light system, a two-stage mathematical model has been developed. It describes how quantization parameters are converted into PPFD fluctuations, and how these, in turn, affect variations in the photosynthetic response. It also introduces a criterion for the acceptable level of photosynthesis instability along with computed requirements for bit depth, modulation frequency, and light flux pulsation depth. Results. It has been shown that the sensitivity of the net photosynthetic rate of tomato plants to PPFD fluctuations is maximal in the intermediate range of 200–600 µmol•m–2 s–1, corresponding to the steep section of the light-response curve, and decreases sharply in the light-saturation region at PPFD levels above ~1500 µmol•m–2 s–1. Numerical modeling indicates that 8-bit PWM control results in a relative variation in photosynthesis of a few percent within this range, whereas using 12-to 16-bit resolution reduces the temporal instability of the photosynthetic response to levels below 1–3%.The derived relationships made it possible to formulate engineering recommendations regarding the minimum permissible PWM bit depth and frequency for various PPFD operating ranges — providing the absence of biologically significant instability in photosynthesis — and to link the parameters of the digital LED supplementary light control system with requirements for crop yield stability in greenhouses. Discussion. The obtained light curves and their approximation using hyperbolic models confirm the classic pattern of photosynthetic light saturation: a nearly linear increase at low PPFD and a plateau at high light levels, consistent with general approaches to assessing productivity based on integrated resources. Using the derivative of the light curve as a measure of photosynthetic sensitivity to PPFD fluctuations have revealed that, within the moderate PPFD range, high-frequency pulsations caused by quantization noise can induce additional variability in the photosynthetic response of a few percent. Simulation has shown that transitioning from 8-bit to 12–16-bit PWM at kilohertz frequencies reduces this instability to levels comparable to natural microclimate fluctuations and spatial light non-uniformity, thereby transforming digital light control into a significant photobiological factor. The proposed criterion for permissible photosynthetic instability complements existing PPFD recommendations with formalized constraints on light pulsation and can be used in the design of digital control systems for LED supplementary lighting within the frameworks of Agriculture 4.0 and CEA. Conclusion. A calculation criterion has been developed for selecting the bit depth of PWM control for LED supplementary lighting. This criterion links the granularity of the PPFD setpoint to the permissible relative variation in the net photosynthetic rate of plants. Calculations based on a model light-response curve for tomato plants revealed the highest sensitivity to quantization error within the PPFD range of 200–600 µmol•m–2 s–1, whereas the impact of this error diminishes under light saturation conditions. For the selected set of parameters, a PWM resolution of 12 bits or higher ensured a calculated variation in Pn of no more than 1–2%. The results are applicable to steady-state conditions and require experimental validation using cultures with different light-response curves, as well as extension to dynamic supplementary light regimes.