High-Performance Computing (HPC) processors are nowadays integrated Cyber-Physical Systems demanding complex and high-bandwidth closed-loop power and thermal control strategies. To efficiently satisfy real-time multi-input multi-output (MIMO) optimal power requirements, high-end processors integrate an on-die power controller system (PCS). While traditional PCSs are based on a simple microcontroller (MCU)-class core, more scalable and flexible PCS architectures are required to support advanced MIMO control algorithms for managing the ever-increasing number of cores, power states, and process, voltage, and temperature variability. This paper presents ControlPULP, an open-source, HW/SW RISC-V parallel PCS platform consisting of a single-core MCU with fast interrupt handling coupled with a scalable multi-core programmable cluster accelerator and a specialized DMA engine for the parallel acceleration of real-time power management policies. ControlPULP relies on FreeRTOS to schedule a reactive power control firmware (PCF) application layer. We demonstrate ControlPULP in a power management use-case targeting a next-generation 72-core HPC processor.We first show that the multi-core cluster accelerates the PCF, achieving 4.9x speedup compared to single-core execution, enabling more advanced power management algorithms within the control hyper-period at a shallow area overhead, about 0.1% the area of a modern HPC CPU die. We then assess the PCS and PCF by designing an FPGA-based, closed-loop emulation framework that leverages the heterogeneous SoCs paradigm, achieving DVFS tracking with a mean deviation within 3% the plant's thermal design power (TDP) against a software-equivalent model-in-the-loop approach. Finally, we show that the proposed PCF compares favorably with an industry-grade control algorithm under computational-intensive workloads.