A Control Co-Design Framework to Optimize Sustainability with Application to Microgrid-Driven Data Centers

arXiv:2609.01912 · eess.SY, cs.SY · Submitted 2026-09-01 · Read on arXiv

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Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: I'm Rosa.

Dev: And I'm Dev, here with Taro.

Rosa: We're looking at the paper: "A Control Co-Design Framework to Optimize Sustainability with Application to Microgrid-Driven Data Centers".

Dev: The gist The work studies the optimization of physical plant characteristics and controller parameters for sustainability in microgrid-driven data centers.

Rosa: First, who's behind it and why it matters.

Title and authors: Rosa: So we've covered the title and authors of this paper and what they are trying to achieve with this Control Co-Design Framework for data centers and microgrids. We talked about how they structure their objectives across manufacturing, operation, and disposal stages.

Dev: And we touched on how they use both plant design variables, like sizing components, and controller design variables to expand the search space for optimization.

Taro: It makes sense that they'd want to look at both because the hardware choices have a huge upfront impact on manufacturing waste, and the control strategy affects how much energy you use over time.

Rosa: The paper outlines this framework by first defining those three lifecycle stages and then formulating the total objective function as a weighted sum of J m, J o, and J d.

Dev: They lay out the specifics of what manufacturing looks like, which includes impacts from raw material extraction and assembly, while operation covers electricity use, heat generation, and noise production.

Taro: And disposal is about things like improper waste handling or the need for new resources later on. It's a comprehensive way to look at it.

Rosa: The real strength here is that they are not just looking at one thing; they are explicitly trying to find the trade-offs between these three objectives using Pareto optimal designs.

Dev: And when you look at the results, they found specific insights into how those objective functions relate to each other, which helps guide future design choices.

Taro: So what does this mean for someone just looking at how a system runs? It means that the decision on whether to use a bigger battery or a different control algorithm directly impacts your environmental score across the whole life of the data center.

The paper's summary: Rosa: To summarize, this paper proposes this sustainability-centric control co-design framework as a way to solve problems where people usually optimize either the hardware or the software in isolation.

Dev: They introduce a specific model that couples microgrid and data center dynamics, which has thirty-seven states, including everything from voltage buses to server rack temperatures. This is the physical system they are optimizing.

Taro: That detailed model is key because it shows all these components interacting—the power flow, the heat transfer between the racks, and how the battery manages things during a blackout scenario.

Rosa: The paper then presents Section two of this framework, which describes exactly how they define those sustainability metrics for each lifecycle stage <ref:2609.01912#pg2>. J m captures things like pollutants from manufacturing materials.

Dev: Then they outline Section three which details the candidate model of the microgrid and data center that they're plugging into their optimization framework <ref:2609.01912#pg3,candidate model of the microgrid and data center>. This is the physical system setup itself.

Taro: And Section four presents the controller used to manage this system, validating its performance for a small set of designs before applying it to a blackout scenario in Section five <ref:2609.01912#pg3,Section 4 presents the controller used to manage>.

Rosa: So it’s a complete loop: defining the variables, building the model, designing the controller, and then applying that whole thing to test sustainability goals over twenty-four hours <ref:2609.01912#pg3>.

Dev: The key contribution is integrating this optimization with these sustainability metrics so that you are not just minimizing power tracking error but also minimizing environmental harm.

Taro: It shifts the focus from just making the system run well to making it run well *and* sustainably, which is a necessary shift for modern infrastructure.

The paper's improvements: Rosa: The authors suggest several ways this work can be improved, mainly by focusing on how they use those design variables and what they find when comparing them to the baseline.

Dev: One key improvement is realizing that the manufacturing objective function relies solely on plant design variables when you adjust theta sh, which means the physical component choices have a direct impact there.

Taro: That makes sense because if you change the battery pack size, that directly affects e-waste, as they pointed out. It confirms that hardware sizing is a critical lever for manufacturing impacts.

Rosa: They also highlight that for the degradation objective related to battery packs, it's the plant design variable theta sh and not the controller design variable phi one that has a higher impact on e-waste <ref:2609.01912#pg1>.

Dev: That tells us where to focus our attention: when trying to reduce waste heat or GHG emissions, we should prioritize optimizing the physical plant parameters rather than just tweaking the control algorithm settings.

Taro: So, if I'm looking at the operational objective, that suggests that adjusting those controller design variables phi one will be more effective for reducing heat generation <ref:2609.01912#pg1>.

Rosa: Exactly. They also point out that by constructing 2D Pareto fronts comparing manufacturing emissions and operation costs, you can determine which design variable should be the focus to improve sustainability based on sensitivity terms <ref:2609.01912#pg2>.

Dev: That analysis is powerful because it lets engineers see clearly which design variable—plant versus controller—is more sensitive for a given objective.

Conclusion: Rosa: So wrapping up, this paper with the title "A Control Co-Design Framework to Optimize Sustainability with Application to Microgrid-Driven Data Centers" shows that by prioritizing sustainability attributes, designers can achieve significant reductions in environmental impacts compared to baseline approaches.

Dev: They found that compared to baseline designs that just minimize power tracking error, the CCD framework yields a fifty percent reduction in emissions and e-waste.

Taro: It really proves that you don't have to sacrifice system performance for sustainability; you can actually get both things done better together.

Rosa: The paper concludes that by prioritizing J 1v, the baseline design gets the design furthest to the left on the J m versus J 1v Pareto front <ref:2609.01912#pg1>.

Dev: This framework is a valuable tool for optimizing energy systems because it integrates sustainability criteria across all lifecycle stages, from building to disposal.

Taro: So for my final thought, this CCD-oriented model provides a way to optimize energy systems by linking sustainability criteria across all those stages, which is what we need when designing real infrastructure.

Rosa: That's the gist of it. We'll keep an eye on this work as we keep looking at how AI and control strategies can drive more sustainable hardware choices.

Dev: Indeed. Next time, we'll look at some other interesting papers that tackle different aspects of autonomous systems and control loops.

Texas Tech University

eess.SY, cs.SY

Submitted: 2026-09-01

Updated: 2026-10-16

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 76/100

The gist: The gist The work studies the optimization of physical plant characteristics and controller parameters for sustainability in microgrid-driven data centers.

Key concepts

Control Co-Design (CCD) Framework
This is a generalized method that combines optimizing physical system characteristics (plant design variables, like battery size) with optimizing controller settings (controller design variables, like gains). The framework aims to minimize a total sustainability objective function across all lifecycle stages.
Sustainability Metrics ($J_{total}$)
Sustainability is measured across three stages: manufacturing impacts (raw material use), operational impacts (energy and heat), and disposal impacts (e-waste). The total objective function weights these three metrics to find the most sustainable system design.
Design Variables ($ heta$ and $oldsymbol{ ext{f}}$)
The optimization involves two types of variables: plant design variables ($ heta$), which relate to physical hardware like PV array configuration or battery cell count, and controller design variables ($oldsymbol{ ext{f}}$), which relate to control settings such as predictive horizons or gains.

Summary

The gist The work studies the optimization of physical plant characteristics and controller parameters for sustainability in microgrid-driven data centers.

Control Co-Design Framework

The authors established a generalized, sustainability-centric control co-design (CCD) framework for energy systems to address gaps in prior research. This framework defines and categorizes sustainability metrics into three lifecycle stages: manufacturing, operation, and disposal. The total objective function is formulated as a weighted sum of these three metrics: J total = w m J m + w o J o + w d J d where the individual objectives are defined as Manufacturing (Jm), Operation (Jo), and Disposal (Jd).

Design Variables and Constraints

The CCD framework incorporates both plant design variables (θ) and controller design variables (φ) to expand the design space. Plant design variables include sizing- and topology-related parameters of the system such as PV array configuration, number of battery cells, and converter size and material selection <ref:2609.01912#pg3> while controller design variables can include control architecture settings, timesteps, predictive horizons, and gains within a control algorithm <ref:2609.01912#pg3>. The optimization problem is structured into five steps to solve the CCD problem. The constraints ensure physical and practical limitations are obeyed <ref:2609.01912#pg6> including equality constraints representing plant dynamics described by Equation (2) and inequality constraints limiting the metrics to upper bounds M max and design variable ranges.

Model Dynamics

The system model couples microgrid and data center components through algebraic relationships and thermal matching. The combined model involves several dynamic systems, including voltage bus dynamics (Equation 8), converter dynamics (Equations 9-10), PV subsystem dynamics (Equation 11), battery pack dynamics (Equations 12-14), server rack temperature dynamics (Equation 15), and various air flow CVs in the data center. The full system state vector has N=37 states, and there are N=6 control inputs representing converter duty cycles <ref:3pg13,There are Ns = 37 states of the system: Vbus1, Vbus2, T pv, SOC, Vbat volt2 to Vbat volt4, Track1 and TRack2 and TRackair1 to TRackair8 and Trackair9 to Trackair3, Xpbpk and the twelve Vin and Vout states of the converters <ref:2609.01912#pg14>.

Optimization Results

The optimization procedure uses a grid search on design variables, resulting in 166 designs tested. Sensitivity analyses reveal that the manufacturing objective function relies solely on the plant design variable when adjusting theta sh. Furthermore, battery pack size has higher impact on the production of e-waste rather than the controller design variable for the degradation objective. The comparison with a baseline design shows that the proposed has a 50% reduction over the baseline in the manufacturing objective value.

Conclusion

The CCD framework demonstrates that by prioritizing sustainability attributes, designers can achieve significant reductions in environmental impacts compared to baseline approaches. The results indicate that GHG emissions during manufacturing are the highest for the system analyzed. Compared to baseline designs that minimize power tracking error, the CCD framework can yield a 50% reduction in emissions and e-waste. The work concludes by showing that by prioritizing J1v, the baseline gets the design the furthest to the left on the Jm vs. J1v Pareto front. The CCD framework is a valuable tool for optimizing energy systems by integrating sustainability criteria across all lifecycle stages. The developed CCD-oriented model is connected to a perturb-and-observe algorithm to control the system dynamics.

How it works

The optimization problem is formulated as minimizing J total = w m J m + w o J o + w d J d. The plant dynamics are augmented by design variables using diagonal design matrices κc(θ) and κ(θ). The control algorithm uses a model-free approach, specifically Perturb and observe methods [52] to compute duty cycle values. The controller's performance is validated by testing the model under small variations in certain parameters <ref:2609.01912#pg16> and includes nine discrete modes for the controller as presented in Table 8.

Sustainability Metrics

The sustainability metrics are categorized into three distinct stages to support comparative analysis. The manufacturing objective function Jm captures impacts from net energy consumption, waste generation, and pollutants emitted during the extraction, transportation, and assembly of raw materials <ref:2609.01912#pg5> while the operation objective function Jo accounts for electricity consumption, resource use, control strategies, heat generation, and noise production <ref:2609.01912#pg6>. The disposal objective function Jd agglomerates metrics related to improper waste disposal, inadequate recycling, and increased demand for new resources <ref:2609.01912#pg6>.

Pareto Front Analysis

The analysis involves constructing 2D Pareto fronts from the Pareto-optimal solutions to compare competing sustainability objective functions. The comparison between Jm and Jo shows that the operation objective is more sensitive to changes in the plant design variable over the controller design variable. The analysis of Jd versus design variables shows that generated e-waste is more heavily influenced by theta sh as compared to phi1 for this subset of designs. The threshold value c dEphi = 5.33 provides guidance for engineers on how to balance waste heat or GHG emissions against e-waste <ref:6pg22,With w m = 0, w o = 1, w d = c dEphi/365.25 to convert into kg per day, Equation (1) is calculated twice: for the leftmost design (Jd = 7.424 × 10 cubed and Jo = 42.

Improvements for AI systems

  1. Bold plant design variables to optimize manufacturing emissions: The framework allows optimization of plant design variables, including battery pack size (scaling factor thetaଵ) and rack height (scaling factor thetaଶ), which directly correlate with sustainability metrics such as the manufacturing objective function, The functionJ௠ captures all sustainability metrics relating to the manufacturing of components for, and the construction of, the energy system.

  2. Bold controller design variables to optimize operational waste heat: The control co-design (CCD) framework optimizes controller design variables (scaling factor phiଵ), which influence the operation objective functionJ௢ accounts for environmental impacts relating to the operation of the energy system, thereby minimizing waste heat generation.

  3. Bold disposal metrics to inform end-of-life decisions: The framework categorizes sustainability into three lifecycle stages, including Disposal: The objective functionJௗ agglomerates sustainability metrics categorized by the ending lifecycle stage for plant components, electronic devices, and other pieces of the system, enabling optimization based on e-waste generation.

  4. Implement a multi-objective trade-off analysis: By constructing 2D Pareto fronts comparing objectives like manufacturing emissions and operation costs, designers can determine which design variable should be the focus to improve sustainability by analyzing sensitivity terms, such as the comparison of terms related to plant versus controller design variables.

  5. Integrate model-free control for real-time adaptation: The system uses a model-free approach with Perturb and observe methods [52] especially appropriate to compute duty cycle values, allowing the AI system to dynamically adjust converter duty cycles based on real-time measurements, such as SOCI, T௦,ଵ and T௦,ଶ.

  6. Develop predictive load tracking capability: The controller is validated by demonstrating that it can track the reference power to the servers for at least 20 hours, which is crucial for maintaining system functionality under dynamic conditions.

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