Which mode of control complements automatic and remote manual in the automatic boiler control system?

Local manual mode is the correct answer because it allows operators to control the boiler system directly at the equipment's location. This mode is particularly important for situations that may require immediate attention or adjustment that cannot be adequately handled by automatic or remote control systems. Local manual control provides a hands-on approach, ensuring that operators can respond to changes or issues in real time.

In the context of an automatic boiler control system, local manual mode serves as a valuable complement to automatic and remote manual modes by providing an additional layer of control. This can be crucial during system maintenance, troubleshooting, or emergencies, where quick and direct intervention is needed. Other modes like emergency or optical do not fulfill the same direct operational role within the scope of standard boiler control practices.