This paper presents, implements, and evaluates a power-regulation technique for multicore processors, based on an integral controller with adjustable gain. The gain is designed for wide stability margins, and computed in real time as part of the control law. The tracking performance of the control system is robust with respect to modeling uncertainties and computational errors in the loop. The main challenge of designing such a controller is that the power dissipation of program-workloads varies widely and often cannot be measured accurately; hence extant controllers are either ad hoc or based on a-priori modeling characterizations of the processor and workloads. Our approach is different. Leveraging the aforementioned robustness it uses a simple textbook modeling framework, and adjusts its parameters in real time by a system-identification module. In this it trades modeling precision for fast computations in the loop making it suitable for on-line implementation in commodity data-center processors. Consequently, the proposed controller is agnostic in the sense that it does not require any a-priori system characterizations. We present an implementation of the controller on Intel's fourth-generation microarchitecture, Haswell, and test it on a number of industry benchmark programs which are used in scientific computing and datacenter applications. Results of these experiments are presented in detail exposing the practical challenges of implementing provably-convergent power regulation solutions in commodity multicore processors.