The robust controllability (RC) of a complex system tries to select a set of dominating entities for the functional control of this entire system without uncertain disturbances, and the research on RC will help to understand the system's underlying functions. In this article, we introduce the control cost in signed networks and present a cost-aware robust control (CRC) problem in this scenario. The aim of CRC is to minimize the cost to control a set of dominating nodes and transform a set of unbalanced links into balanced ones, such that the signed network can be robustly controlled without uncertain unbalanced factors (like nodes and links). To solve this problem, we first model CRC as a constrained combination optimization problem, and then present a memetic algorithm with some problem-specific knowledge (like the neighbors of nodes, the constraints of CRC, and the fast computation of the cost under each optimization) to solve this problem on signed networks. The extensive experiments on both real social and biological networks assess that our algorithm outperforms several state-of-the-art RC algorithms.