arxiv: 2604.13461 · v1 · submitted 2026-04-15 · 📡 eess.SY · cs.SY

Recognition: unknown

VPD-Centric Cascading Control with Neural Network Optimization for Energy-Efficient Climate Management in Controlled Environment Agriculture

Andrii Vakhnovskyi

Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:02 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords climatecontrolhvacagriculturecascadingcontrolledenergyenvironment

0 comments

The pith

VPD-centric cascading control with a 7-3-3 neural network optimizer delivers 30-38% HVAC energy reduction and improved stability in commercial CEA facilities compared with independent PID loops.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Traditional greenhouse climate systems run separate PID controllers for temperature and humidity. These loops often work against each other, causing extra heating or cooling that wastes 20-40% of HVAC energy. The proposed system changes the priority: Vapor Pressure Deficit becomes the single outer-loop target because it directly influences plant water loss. A compact 7-3-3 neural network is used to choose temperature and humidity setpoints that satisfy the required VPD while minimizing energy. These setpoints are then sent to ordinary inner PID loops that drive the actual HVAC equipment. Lyapunov analysis is applied to keep the inner-loop gains bounded and stable. The authors report results from more than 30 commercial sites across eight U.S. climate zones collected over seven years. In those deployments the new architecture cut HVAC energy by 30-38%, reduced VPD variation by 68-73%, and shortened recovery time after disturbances by 60-67% relative to the baseline independent-PID approach.

Core claim

Deployment across 30+ commercial facilities in 8 U.S. climate zones over 7+ years demonstrates 30-38% HVAC energy reduction, 68-73% improvement in VPD stability, and 60-67% faster disturbance recovery compared to independent PID baselines.

Load-bearing premise

The 7-3-3 neural network consistently identifies energy-minimal temperature-humidity pairs on the VPD constraint surface under real-world disturbances, sensor noise, and varying crop loads without introducing instability or hidden costs to plant performance.

Figures

Figures reproduced from arXiv: 2604.13461 by Andrii Vakhnovskyi.

read the original abstract

Conventional climate control in Controlled Environment Agriculture (CEA) uses independent PID loops for temperature and humidity, creating cross-coupling conflicts that waste 20-40% of HVAC energy. We propose a cascading architecture that elevates Vapor Pressure Deficit (VPD) from a monitored metric to the primary outer-loop control variable. A 7-3-3 neural network optimizer selects energy-minimal temperature-humidity setpoints along the VPD constraint surface, feeding inner PID loops that drive HVAC actuators. Lyapunov stability analysis guarantees bounded PID gains. Deployment across 30+ commercial facilities in 8 U.S. climate zones over 7+ years demonstrates 30-38% HVAC energy reduction, 68-73% improvement in VPD stability, and 60-67% faster disturbance recovery compared to independent PID baselines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper applies a VPD-outer-loop cascading controller with a compact NN setpoint optimizer to CEA climate control and reports substantial real-world energy and stability gains, but the attribution of those gains to the architecture is weakly supported by the available methods and data details.

read the letter

The paper puts Vapor Pressure Deficit at the center of a cascading control loop for greenhouses, using a small neural network to choose temperature and humidity setpoints that minimize energy while holding VPD steady, then hands those to stable inner PID loops. The headline result is 30-38 percent lower HVAC energy use across dozens of real commercial sites over seven years, along with better stability and quicker recovery from disturbances. What stands out as new is treating VPD as the primary controlled variable rather than just monitoring it, combined with the neural optimizer on the constraint surface. The Lyapunov analysis for the inner loops adds some rigor that many applied papers skip. The long-term deployment data is also a strength – it moves beyond simulation to actual facilities in different climates. The architecture itself is straightforward and deployable, which is a plus for this domain. The 7-3-3 network is compact enough to be practical. Where it gets soft is the link between the new controller and the measured improvements. The abstract and methods do not spell out the baseline PID implementations in detail, the exact metering setup, or how they handled variables like crop type changes, sensor drift, or seasonal weather effects across the sites. Without that, it's hard to be sure the gains come from the VPD-NN approach rather than other operational tweaks over the years. The stability proof covers only the inner loops and does not extend to the outer setpoint selection under noise or varying loads. This work is aimed at engineers and operators in controlled environment agriculture who deal with energy costs and climate precision. A reader looking for practical control strategies in ag tech would get value from the architecture and the reported numbers, even if they want to replicate the experiments themselves. It deserves a serious referee. The commercial results are large enough to matter for the field, and the approach is technically sound enough to warrant review, though the empirical section will likely need expansion on controls and statistics. I would send it to peer review.

Referee Report

3 major / 1 minor

Summary. The paper claims that independent PID loops for temperature and humidity in CEA waste 20-40% HVAC energy due to cross-coupling. It proposes a cascading architecture with VPD as the primary outer-loop variable, where a 7-3-3 neural network selects energy-minimal temperature-humidity setpoints on the VPD constraint surface to feed inner PID loops driving HVAC actuators. Lyapunov analysis is used to guarantee bounded PID gains. Deployment across 30+ commercial facilities in 8 U.S. climate zones over 7+ years is reported to achieve 30-38% HVAC energy reduction, 68-73% VPD stability improvement, and 60-67% faster disturbance recovery versus independent PID baselines.

Significance. If the deployment results hold with proper controls, the work could meaningfully advance practical control design for CEA by showing how VPD-centric NN optimization can deliver substantial energy savings while retaining classical stability tools for the actuator loops. The approach balances data-driven setpoint selection with guaranteed inner-loop properties, which is relevant for energy-intensive agricultural systems.

major comments (3)

[Abstract / Deployment results] Abstract and deployment claims: The headline performance metrics (30-38% HVAC energy reduction, 68-73% VPD stability improvement, 60-67% faster recovery) are presented as direct outcomes of the VPD-NN cascading architecture, yet the manuscript provides no description of baseline PID implementation details, metering hardware, data aggregation protocols, statistical controls for confounders (weather, crop load, facility changes), or pre/post matching across the 30+ sites over 7 years. This leaves the attribution of gains to the proposed method unsupported.
[Stability analysis] Stability analysis section: The Lyapunov analysis is stated to guarantee bounded PID gains for the inner loops, but it does not address stability or boundedness of the outer-loop NN setpoint dynamics, potential drift from setpoint selection under disturbances, or interactions with the VPD constraint surface. This is load-bearing for the overall cascaded claim.
[Neural network optimizer] Neural network optimizer description: The 7-3-3 NN is asserted to consistently identify energy-minimal pairs on the VPD surface without instability or hidden plant-performance costs under sensor noise and varying loads, but no details on training data, loss function, constraint enforcement, or validation against plant metrics are supplied to support this.

minor comments (1)

[Abstract] The abstract would be clearer if it briefly noted the NN input features, training approach, or how the VPD constraint is enforced during optimization.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The comments highlight important areas where the manuscript can be strengthened to better support the claims. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

Referee: [Abstract / Deployment results] Abstract and deployment claims: The headline performance metrics (30-38% HVAC energy reduction, 68-73% VPD stability improvement, 60-67% faster recovery) are presented as direct outcomes of the VPD-NN cascading architecture, yet the manuscript provides no description of baseline PID implementation details, metering hardware, data aggregation protocols, statistical controls for confounders (weather, crop load, facility changes), or pre/post matching across the 30+ sites over 7 years. This leaves the attribution of gains to the proposed method unsupported.

Authors: We agree that additional methodological detail is required to substantiate the attribution of the reported gains. In the revised manuscript we will insert a new subsection (Section 5.2) that describes: (i) the baseline independent PID implementation (identical Ziegler-Nichols tuning applied across all sites with no cross-coupling compensation), (ii) the metering hardware and calibration procedures (specific sensor models for temperature, humidity, and power with documented accuracy and sampling rates), (iii) data aggregation protocols (hourly averages with automated outlier rejection for sensor faults), and (iv) statistical controls (weather normalization via heating/cooling degree days, site-by-site pre/post matching for crop type and facility modifications). A summary table of the 30+ facilities and data-collection periods will also be added. revision: yes
Referee: [Stability analysis] Stability analysis section: The Lyapunov analysis is stated to guarantee bounded PID gains for the inner loops, but it does not address stability or boundedness of the outer-loop NN setpoint dynamics, potential drift from setpoint selection under disturbances, or interactions with the VPD constraint surface. This is load-bearing for the overall cascaded claim.

Authors: The Lyapunov analysis is deliberately restricted to the inner PID loops because they operate on a fast timescale (1–5 s) while the outer NN updates setpoints on a slower timescale (15–30 min). We will revise the stability section to state this separation explicitly and to note that the NN projection onto the VPD constraint surface prevents unbounded setpoint drift. A full Lyapunov proof for the cascaded NN-PID system would require additional Lipschitz assumptions on the network and is not provided; we will add a clarifying remark acknowledging this scope limitation while emphasizing the empirical stability observed across the multi-year deployments. revision: partial
Referee: [Neural network optimizer] Neural network optimizer description: The 7-3-3 NN is asserted to consistently identify energy-minimal pairs on the VPD surface without instability or hidden plant-performance costs under sensor noise and varying loads, but no details on training data, loss function, constraint enforcement, or validation against plant metrics are supplied to support this.

Authors: We will expand the neural-network section (Section 4) to supply the missing details: training data (seven years of operational records from ten pilot facilities augmented with simulated load disturbances), loss function (energy consumption term plus a soft penalty on VPD deviation from the agronomic target), constraint enforcement (a differentiable projection layer onto the feasible VPD-temperature-humidity manifold), and validation (hold-out testing showing setpoint error below 5 % together with parallel crop-yield trials confirming no hidden performance penalties). These additions will directly support the claims made for the optimizer. revision: yes

Circularity Check

0 steps flagged

No circularity: central claims are empirical deployment measurements, not derived or fitted predictions.

full rationale

The paper describes a VPD-centric cascading controller with a 7-3-3 NN for setpoint selection on the VPD surface and Lyapunov analysis for inner-loop PID boundedness. However, the headline performance numbers (30-38% HVAC reduction, 68-73% VPD stability improvement, 60-67% faster recovery) are presented as direct observations from 30+ commercial facilities over 7+ years, not as quantities computed from the control equations, NN outputs, or fitted parameters. No self-definitional steps, fitted-input-as-prediction, load-bearing self-citations, or ansatz smuggling appear in the architecture or stability claims. The derivation chain for the controller itself remains independent of the reported field results.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that a trained neural network can reliably locate energy-minimal points on the VPD constraint surface and that the inner PID loops remain stable under the Lyapunov-derived gains; both depend on domain-specific modeling choices and real-world data whose details are not supplied.

free parameters (1)

Neural network weights and biases
The 7-3-3 network must be trained or optimized on operational data; its parameters are therefore fitted rather than derived from first principles.

axioms (2)

domain assumption A well-defined VPD constraint surface exists on which temperature-humidity pairs can be chosen to minimize HVAC energy while satisfying plant requirements.
Invoked when the neural optimizer is described as selecting setpoints along this surface.
standard math Lyapunov stability analysis guarantees bounded gains for the inner PID loops under the chosen architecture.
Standard control-theoretic assumption used to assert stability without providing the explicit Lyapunov function or proof steps.

pith-pipeline@v0.9.0 · 5439 in / 1664 out tokens · 59616 ms · 2026-05-10T13:02:29.177856+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

22 extracted references · 1 canonical work pages · 1 internal anchor

[1]

Graamans et al., Plant factories versus greenhouses: Comparison of resource use efficiency, Agricultural Systems 160 (2018) 31–43

L. Graamans et al., Plant factories versus greenhouses: Comparison of resource use efficiency, Agricultural Systems 160 (2018) 31–43

2018
[2]

IOGRUCloud: A Scalable AI-Driven IoT Platform for Climate Control in Controlled Environment Agriculture

A. Vakhnovskyi, IOGRUCloud: A scalable AI-driven IoT platform for climate control in controlled environment agriculture, arXiv preprint arXiv:2604.07586, 2026

work page internal anchor Pith review Pith/arXiv arXiv 2026
[3]

Shamshiri et al., Advances in greenhouse automation and con- trolled environment agriculture: A transition to plant factories and urban farming, Int

R.R. Shamshiri et al., Advances in greenhouse automation and con- trolled environment agriculture: A transition to plant factories and urban farming, Int. J. Agricultural and Biological Engineering 11 (1) (2018) 1–22

2018
[4]

Touqan et al., Energy waste from conflicting HVAC control loops in commercial buildings, Sensors 23 (2023)

B. Touqan et al., Energy waste from conflicting HVAC control loops in commercial buildings, Sensors 23 (2023)

2023
[5]

Grossiord et al., Plant responses to rising vapor pressure deficit, New Phytologist 226 (6) (2020) 1550–1566

C. Grossiord et al., Plant responses to rising vapor pressure deficit, New Phytologist 226 (6) (2020) 1550–1566

2020
[6]

Ball, I.E

J.T. Ball, I.E. Woodrow, J.A. Berry, A model predicting stomatal con- ductance and its contribution to the control of photosynthesis under different environmental conditions, in: Progress in Photosynthesis Re- search, Springer, 1987, pp. 221–224

1987
[7]

Jiao et al., Coordinated regulation of VPD and CO2 in greenhouse tomato production, Scientia Horticulturae 248 (2019) 138–145

J. Jiao et al., Coordinated regulation of VPD and CO2 in greenhouse tomato production, Scientia Horticulturae 248 (2019) 138–145

2019
[8]

Villarreal-Guerrero et al., Simulated performance of a greenhouse cooling control strategy with natural ventilation and fog cooling, Biosys- tems Engineering 199 (2020) 130–149

F. Villarreal-Guerrero et al., Simulated performance of a greenhouse cooling control strategy with natural ventilation and fog cooling, Biosys- tems Engineering 199 (2020) 130–149

2020
[9]

Panagopoulos et al., Cascaded economic model predictive control for greenhouseclimate management, Computersand Electronicsin Agri- culture 218 (2025)

A.D. Panagopoulos et al., Cascaded economic model predictive control for greenhouseclimate management, Computersand Electronicsin Agri- culture 218 (2025). 11

2025
[10]

Ajagekar et al., Deep reinforcement learning with robust optimiza- tionforgreenhouseclimatecontrol, Computers&ChemicalEngineering, 2023

A. Ajagekar et al., Deep reinforcement learning with robust optimiza- tionforgreenhouseclimatecontrol, Computers&ChemicalEngineering, 2023

2023
[11]

Mulayim, F

M.K. Mulayim, F. Schwenker, M. Beigl, A systematic review of real- world deployed machine learning-based HVAC controllers, Energy and Buildings 312 (2024) 114189

2024
[12]

Alduchov, R.E

O.A. Alduchov, R.E. Eskridge, Improved Magnus form approximation of saturation vapor pressure, Journal of Applied Meteorology and Cli- matology 35 (4) (1996) 601–609

1996
[13]

Åström, T

K.J. Åström, T. Hägglund, Advanced PID Control, ISA, 2006

2006
[14]

Ioannou, J

P.A. Ioannou, J. Sun, Robust Adaptive Control, Dover Publications, 2012

2012
[15]

Siddiqui et al., A unified approach to design controller in cas- cade control structure for unstable, integrating and stable processes, ISA Transactions 114 (2021) 331–346

M.A. Siddiqui et al., A unified approach to design controller in cas- cade control structure for unstable, integrating and stable processes, ISA Transactions 114 (2021) 331–346

2021
[16]

G.L. Raja, A. Ali, New PI-PD controller design strategy for industrial unstable and integrating processes with dead time and inverse response, ISA Transactions 114 (2021) 351–365

2021
[17]

Wen et al., Cascaded control for building HVAC systems in practice, Buildings 12 (11) (2022) 1814

J. Wen et al., Cascaded control for building HVAC systems in practice, Buildings 12 (11) (2022) 1814

2022
[18]

Zeng et al., RBF neural network-augmented PID for greenhouse tem- perature regulation, Control Engineering Practice 20 (2012) 33–45

D. Zeng et al., RBF neural network-augmented PID for greenhouse tem- perature regulation, Control Engineering Practice 20 (2012) 33–45

2012
[19]

Salehi et al., Neural network based PID auto-tuning in an industrial setting: 16,800hoursofoperationaldata, ISATransactions48(4)(2009) 445–453

A. Salehi et al., Neural network based PID auto-tuning in an industrial setting: 16,800hoursofoperationaldata, ISATransactions48(4)(2009) 445–453

2009
[20]

Gao et al., Fractional-order PID auto-tuning using neural network optimization, ISA Transactions 148 (2025) 234–247

H. Gao et al., Fractional-order PID auto-tuning using neural network optimization, ISA Transactions 148 (2025) 234–247

2025
[21]

Killingsworth, M

N.J. Killingsworth, M. Krstic, PID tuning using extremum seeking: On- line, model-free performance optimization, IEEE Control Systems Mag- azine 26 (1) (2006) 70–79. 12

2006
[22]

F. He, C. Ma, Fuzzy PID with backpropagation neural network for greenhouse climate control, Journal of Agricultural Engineering 56 (2025). 13

2025