This paper deals with a shared server environment where the server is divided into a number of resource partitions and used to host multiple applications at the same time. In a case study where the HP-UX Process Resource Manager is taken as the server partitioning technology, we investigate the technical challenges in performing automated sizing of a resource partition using a feedback control approach, where the CPU entitlement for the partition is dynamically tuned to regulate output metrics such as the CPU utilization or SLO-based application performance metric. We identify the nonlinear and bimodal properties of the models across different operating regions, and discuss their implications for the design of the control loops. To deal with these challenges, we then propose two adaptive controllers for tracking the target utilization and target response time respectively. We evaluate the performance of the closed-loop systems while varying certain operating conditions. We demonstrate ...