For the PIP-II Injector Test (PI-Test) at Fermilab, a four-vane radio frequency quadrupole (RFQ) is designed to accelerate a 30-keV, 1-mA to 10-mA, H- beam to 2.1 MeV under both pulsed and continuous wave (CW) RF operation. The available headroom of the RF amplifiers limits the maximum allowable detuning to 3 kHz, and the detuning is controlled entirely via thermal regulation. Fine control over the detuning, minimal manual intervention, and fast trip recovery is desired. In addition, having active control over both the walls and vanes provides a wider tuning range. For this, we intend to use model predictive control (MPC). To facilitate these objectives, we developed a dedicated control framework that handles higher-level system decisions as well as executes control calculations. It is written in Python in a modular fashion for easy adjustments, readability, and portability. Here we describe the framework and present the first control results for the PI-Test RFQ under pulsed and CW operation.