Autonomous driving simulators still lack high-fidelity radar, even though radar is critical for robust perception in adverse weather. A key obstacle is that raw radar point clouds are extremely sparse and stochastic, making it difficult to model; we argue that simulating the full range-azimuth-Doppler cube is a more principled target. Existing radar cube simulators either rely purely on neural generators, which are opaque and offer little control over sensor attributes, or on detailed electromagnetic pipelines, which are slow, require proprietary hardware specifications, and still struggle to capture real-world complexity. We introduce Ctrl-RS, a controllable radar cube simulation framework that combines the strengths of both worlds. First, we build an environment reflection tensor from diverse sensor sources (including LiDAR, monocular cameras, and existing radar). Second, we abstract radar physics into a compact set of waveform parameters that characterize the 3D point spread function, yielding an intuitive embedding of radar attributes such as range resolution, Doppler broadening, and azimuth beam shape. Third, we train a WARP-Net on a large mixed dataset that fuses real, analytically synthesized, and simulator-generated radar cubes to cover a wide distribution of radar attributes. Ctrl-RS supports viewpoint changes, actor removal, and attribute editing. Experiments on RADDet, Carrada, and nuScenes show that our simulated data can match or surpass real radar in 2D detection and semantic segmentation, and consistently boosts performance in 3D detection when combined with real data. The Project is available at https://github.com/zhuxing0/Ctrl-RS.