We formulate a modeling and control framework aimed at direct liquid cooling of data servers. In our application scenario, the server's heat load is rejected into a liquid cooling circuit that extends to individual chips. We start with a comprehensive discussion of our modeling derivations. We then show how to dynamically provision the coolant, while 1) regulating the temperatures of any self-heating components within the safe operational envelope; 2) minimizing the coolant supply cost; and 3) increasing the server outflow temperature (a key performance objective toward heat recovery systems). We confirm experimentally the benefits of the proposed controlled cooling strategy over several realistic scenarios corresponding to different inlet coolant temperatures and computational loads.

This paper considers the problem of optimizing the operation of Indirect Adiabatic Cooling (IAC) systems with application to data centers. Optimal operation is achieved when the required cooling demand is satisfied at the minimum energy cost. For this purpose, we design a supervisory control system, where the higher layer determines the optimal set‐points for the local controllers by employing an Extremum Seeking Control (ESC) scheme. In particular, we consider a Newton‐like phasor ESC, which augments the derivative estimator underlying the phasor approach to capture also the Hessian of the plant index and then it uses these estimates to steer the system along a Newton‐like direction. The effectiveness of the considered approach is tested in simulation by exploiting a Matlab‐based simulation environment including an IAC system and a computer room.

We consider an adaptive control problem for a homogeneous population of systems that operate in close conditions. Drawing a connection to Design of Experiments (DoE), we study an extremum seeking controller that operates the population economically by either minimizing a group cost or maximizing a group utility. The controller is formalized in full detail within a dynamic setting that extends the previous treatment. The applicability and effectiveness of the strategy is commented upon and supported through different examples. We argue that this class of control systems should be addressed as a design pattern where possible in view of its capacity to enable both simple and effective online optimizing control strategies.

Given a generic Control Configuration Selection (CCS) protocol and a plant uncertainty description isomorph to a unit ball in a finite-dimensional Lp space, we search for the largest perturbation radius for which the nominal configuration remains the preferred one. To this aim, we develop a randomized search algorithm based on sampling the uncertain plants and characterize its statistical performance. By adopting an intuitive accuracy measure that relates to the volume of points in which the preferred configuration differs from the nominal one, we devise a generally applicable strategy that allows for arbitrarily accurate estimates, in a specific probabilistic sense, depending on the number of uncertain plants that are sampled. We benchmark the proposed algorithm using examples from the literature and in a data center flow provisioning problem. In the latter setting, we identify the uncertainty description with the space of controls and sample the “uncertain” plants from an underlying nonlinear model.

We study the economic operation of a free-cooling setup in which an Indirect Adiabatic Air Handler (IAAH) recovers heat from an array of server racks placed in a contained aisle. For this setting we propose two different control policies: in the first approach, the airflow supply rate to the racks is maintained constant while only the process- side operations of the IAAH are optimized. In the second approach, also the room-side rate is updated adaptively. Building on calibrated models of the IAAH and the servers, we design experimental trials considering different outdoor temperatures and humidity conditions as well as varying computational workloads. The in silico analysis contributes actionable insights on the optimal thermal and cost operations of the system.

In this paper, we propose an extension for the phasor extremum seeking control approach to solve constrained optimization problems. The proposed technique uses phasor estimates of the objective function and the constraints to compute a geometric constraint satisfaction approach that avoids the violation of the constraints. The proposed method is illustrated to solve several nonlinear optimization problems subject to equality and inequality constraints. Finally, the effectiveness of the proposed approach is illustrated for the optimal operation of a parallel isothermal stirred-tank reactor system.

This work considers how to provision efficiently the cooling airflow in server rooms. We focus on raised plenum and perforated tiles setups and devise ColdSpot: an optimizing thermal supervisor that adaptively regulates the cooling airflow across the floor plane. ColdSpot operates by pairing 1) model-free estimators of the supply flow requirements at each perforated tile and 2) a model-based cost optimizer that actuates the room's Air Conditioning Units (ACUs) to satisfy the above rate requirements. We propose to use an array of Gaussian Processes (GPs) to capture the nonlinear flow model of each tile and present a hierarchical control structure on top of this modeling. We validate in silico the prediction accuracy of GPs in this context and demonstrate the performance of ColdSpot in regulating the cold-isles temperatures in spite of varying heat and airflow transport disturbances within the room.

Data centers are facilities dedicated to the processing, storage, and relay of large amounts of digital information. As a whole, it is an energy intensive industry, characterized by a sizable carbon footprint and a short-term exponential growth rate. At a macroscopic level, their operation requires balancing the offer and demand of computational, cooling, and electrical power resources. The computational workload is influenced by external factors such as the end-users’ activity, while the overall run-time costs depend on the weather conditions and the fluctuating pricing of electricity. In this context, the adoption of optimizing control strategies and co-design methodologies that address simultaneously both the mechanical and control aspects, has the potential to unlock more sustainable designs. Improvements in the overall energetic efficiency open to larger-scale deployments in less favorable geographical locations. Recovery systems addressing the vast amounts of by-product heat can support other heat intensive processes such as district networks, wood drying, greenhouses, and food processing. This work focuses on how to adapt the provisioning of the cooling resources to the cooling demand, without negotiating the computational throughput. We devise top-down designs, that address unexplored control possibilities in existing deployments. We moreover apply a bottomup perspective, by modeling and studying co-designed cooling setups which bring significant simplifications to data center level optimal provisioning problems. The analysis aims at the different levels of the data center infrastructure hierarchy, and provides answers to centerpiece questions such as i) what are the optimal flow provisioning policies at different levels of the data centers?; ii) how to design simple but effective control strategies that address the complexity induced by the large scales?; iii) what are the exhaust heat properties that can be expected in air-cooled and liquid-cooled data centers?. Exploiting a model-centric approach we demonstrate the effectiveness of tailored control strategies in both achieving better cooling efficiency and a higher quality of the heat harvest. This thesis presents opportunities to simplify data center control structures while retaining or improving their performance. Furthermore, it lays modeling and control methodologies toward the holistic control-oriented treatment of the computing, cooling, and power distribution infrastructures. The results have a practical character and the model-based analysis establishes important development directions, confirming existing trends. Enabling intelligent data center management systems might not need to imply more complex tools; rather, a co-design effort might yield both simpler and effective control systems.

We consider the thermal management problem of provisioning the cooling airflow to data center rooms. Building on a virtual plant capturing the thermal behaviour of both the cooling equipment and the room-side heat load, we evaluate a 2D phasor-based Extremum Seeking Control (ESC) strategy that strives to satisfy the cooling demand while minimizing the cooling provisioning cost.