In the upcoming Internet of Things era, reducing energy consumption of embedded processors is highly desired. Minimum Energy Point Tracking (MEPT) is one of the most efficient methods to reduce both dynamic and leakage energy consumption of a processor. Previous works proposed a variety of MEPT methods over the past years. However, none of them incorporate their algorithms with practical real-time operating systems, although edge computing applications often require low energy task execution with guaranteeing real-time properties. The difficulty comes from the time complexity for identifying MEP and changing voltages, which often prevents real-time task scheduling. This paper proposes an approximated MEPT algorithm, which reduces the complexity of identifying MEP down to that of Dynamic Voltage and Frequency Scaling (DVFS). We also propose a task scheduling algorithm, which adjusts processor performance to the workload, and provides a soft real-time capability to the system. With these two methods, MEPT became a general task, and the operating system stochastically adjusts the average response time of a processor to be equal to a specified deadline. The experiments using a fabricated test chip show that the proposed algorithm introduced the energy loss by only 0.5 % at most without sacrificing the fundamental real-time properties.