The next generation of giant ground and space telescopes will have the light-collecting power to detect and characterize potentially habitable terrestrial exoplanets using high-contrast imaging for the first time. This will only be achievable if the performance of the Giant Segment Mirror Telescopes (GSMTs) extreme adaptive optics (ExAO) systems are optimized to their full potential. A key component of an ExAO system is the wavefront sensor (WFS), which measures aberrations from atmospheric turbulence. A common choice in current and next-generation instruments is the pyramid wavefront sensor (PWFS). ExAO systems require high spatial and temporal sampling of wavefronts to optimize performance and, as a result, require large detectors for the WFS. We present a closed-loop testbed demonstration of a three-sided pyramid wavefront sensor (3PWFS) as an alternative to the conventional four-sided pyramid wavefront (4PWFS) sensor for GSMT-ExAO applications on the innovative comprehensive adaptive optics and coronagraph test instrument (CACTI). The 3PWFS is less sensitive to read noise than the 4PWFS because it uses fewer detector pixels. The 3PWFS has further benefits: a high-quality three-sided pyramid optic is easier to manufacture than a four-sided pyramid. We describe the design of the two components of the CACTI system, the adaptive optics simulator and the PWFS testbed that includes both a 3PWFS and 4PWFS. We detail the error budget of the CACTI system, review its operation and calibration procedures, and discuss its current status. A preliminary experiment was performed on CACTI to study the performance of the 3PWFS to the 4PWFS in varying strengths of turbulence using both the raw intensity and slopes map signal processing methods. This experiment was repeated for a modulation radius of 1.6 and 3.25 λ / D. We found that the performance of the two wavefront sensors is comparable if modal loop gains are tuned.