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During India's PSLV-C35 launch on 26 September 2016, mission control's launch sequence events (stage separations, stage ignitions, etc.) included 'CLG INIT'. What does it mean?

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"CLG INIT" stands for "closed loop guidance initiation", and means that the launcher is switching into a mode where it actively steers based on its current trajectory rather than a fixed, unconditional program (referred to as "open loop guidance").

In the early part of flight, it is safer to use a "pitch-versus-time" or similar simple logic to guide the rocket. Weather events or errors in the measured trajectory might otherwise cause undesirable over-reactions in steering. Once out of the dense atmosphere, the launcher can correct for any difference between the desired trajectory and the actual one; the repeated process of measurement, error determination, and steering to correct the error is the "loop".

For PSLV, the CLG INIT occurs a few seconds after second stage ignition.

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