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The AFDS and A/T do not control to a speed which is less than minimum speed for the current flap configuration. This speed is approximately 1.3Vs. Minimum speed, FMC speed, or selected speed, whichever is higher, becomes the AFS command speed. If actual speed becomes equal to or slightly less than the minimum speed the underspeed limiting symbol appears in the MCP IAS/Mach Display, and if operating in the V/S mode, the AFDS reverts to LVL CHG. The AFDS will also revert to LVL CHG from VNAV PTH, except when flying a level segment. [FCOM 4.20.36]

This paragraph is about the minimum speed reversion function of the 737 Automatic Flight system. Can anybody help me understand the first sentence? I don't understand what "control to a speed" means here. Does that mean the AFDS and A/T do not "respond" to the speed??

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It means you cannot make Autopilot/Flight Director System and Autothrottle fly a target speed below your minimum speed for the configuration. If you were trying to set e.g. 50kts as your speed target, it would be ignored and replaced with the appropriate minimum speed.

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