A field programmable gate array (FPGA) based timing and trigger control system has been developed for the Dynamic Compression Sector (DCS) user facility located at the Advanced Photon Source (APS) at Argonne National Laboratory. The DCS is a first-of-its-kind capability dedicated to dynamic compression science. All components of the DCS laser shock station-x-ray choppers, single-shot shutter, internal laser triggers, and shot diagnostics-must be synchronized with respect to the arrival of x-rays in the hutch. A field-programmable gate array (FPGA) synchronized to the APS storage ring radio frequency (RF) clock (352 MHz) generates trigger signals for each stage of the laser and x-ray shutter system with low jitter. The system is composed of a Zynq FPGA, a debug card, line drivers and power supply. The delay and offsets of trigger signals can be adjusted using a user-friendly graphical user interface (GUI) with high precision. The details of the system architecture, timing requirements, firmware, and software implementation along with the performance evaluation are presented in this paper. The system offers low timing jitter (15.5 ps r.m.s.) with respect to APS 352 MHz clock , suitable for the 50 ps r.m.s. x-ray bunch duration at the APS.