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Once you are able to control your lunge in isolation then you can start to develop your technique under more pressure.
Have a feeder throw shuttles into the forecourt area for you to hit. Concentrate on the quality of the movement rather than hitting the shuttle to targets.
Start from base, split step and lunge on your racket leg to meet the shuttle. Perform 10-12 repetitions and rest before repeating the set.
The easier the feed the earlier you should try and intercept the shuttle. When you are forced to take the shuttle late in the forecourt, then your lunge will have to be deeper.