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In the seminal paper by Foschini and Miljanic in 1993, a distributed power control algorithm was developed to meet SIR targets with minimal powers in cellular network uplinks. Since the SIR on an active link may dip below the SIR target during the transient after a new user enters the cell, Bambos proposed an active link protection algorithm to provide robustness, at the expense of higher energy consumption. This paper examines the tradeoff between energy and robustness. An optimization problem is formulated where robustness is captured in the constraint and the price of robustness penalized in the objective function. A distributed algorithm is developed to solve this problem. Local convergence and optimality of equilibrium are proved for the algorithm. The objective function modulates the tradeoff between energy and robustness, and between energy and speed of admission, as illustrated through a series of numerical experiments. A parameterized family of objective functions is constructed to control the transient and equilibrium properties of robust distributed power control.