To program the Allen Bradley 1769-OW16 PLC module for controlling external devices, you would typically use Rockwell Automation's programming software, such as RSLogix 5000 or Studio 5000. Here's an overview of the programming process:

1. Hardware Configuration: Start by configuring your CompactLogix PLC system using the software. This involves creating a new project and defining the hardware configuration, including adding the 1769-OW16 module to your I/O chassis.

2. Tag Creation: Create tags in the software to represent the digital output channels of the 1769-OW16 module. Tags are essentially variables that you'll use in your program to control the outputs. Assign appropriate names and data types to the tags.

3. Program Development: Develop your PLC program using ladder logic, structured text, or any other supported programming language in the software. Use the tags you created in the previous step to control the outputs of the 1769-OW16 module.

4. Output Control Logic: Within your program, you can use various instructions and conditions to control the behavior of the digital outputs. For example, you can use energize and de-energize instructions to turn ON and OFF the respective outputs based on certain conditions or events.

5. Download and Test: Once you have completed the program, download it to the CompactLogix PLC system. Use the software's debugging and monitoring tools to test and verify the program's functionality. You can observe the behavior of the digital outputs and make any necessary adjustments.

6. Online Operation: After successful testing, you can switch the PLC system to the online mode to let it run autonomously and control the connected external devices using the 1769-OW16 module.