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We present a technique that controls the peak power consumption of a high-density server by implementing a feedback controller that uses precise, system-level power measurement to periodically select the highest performance state while keeping the system within a fixed power constraint. A control theoretic methodology is applied to systematically design this control loop with analytic assurances of system stability and controller performance, despite unpredictable workloads and running environments. In a real server we are able to control power over a 1 second period to within 1 W. Additionally, we have observed that power over an 8 second period can be controlled to within 0.1 W. We believe that we are the first to demonstrate such precise control of power in a real server. Conventional servers respond to power supply constraint situations by using simple open-loop policies to set a safe performance level in order to limit peak power consumption. We show that closed-loop control can provide higher performance under these conditions and test this technique on an IBM BladeCenter HS20 server. Experimental results demonstrate that closed-loop control provides up to 82% higher application performance compared to open-loop control and up to 17% higher performance compared to a widely used ad-hoc technique.