Balancing energy consumption and performance remains a critical challenge in High Performance Computing (HPC) systems. While static power capping mechanisms such as Intel's Running Average Power Limit (RAPL) offer basic control capabilities, they lack the flexibility to adapt to dynamically varying workloads. This work studies dynamic power regulation for mixed workload scenarios. We investigate two feedback strategies: a gain scheduled proportional-integral (PI) controller and a polytopic linear parameter-varying (LPV) controller synthesized via H$\infty$ control, both scheduled by a workload indicator that changes between memory and compute phase. We evaluate tracking performance, phase switching, and robustness under practical power cap constraints. While both controllers respect power limits, the LPV design achieves lower tracking error, lower control variance, and smoother transients during phase changes than gain scheduled PI.

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