When using quadrature encoders on a BL4S200 board, is there a way to preset the counter values on boot up?

Please read Chapter 22 of the processor manual for details on how to set up a quadrature decoder channel. Operation is as follows:

22.3 Operation
The following steps explain how to set up a Quadrature Decoder channel.

  1. Configure Timer A10 via TAT10R to provide the desired Quadrature Decoder clock
  2. Configure QDCR to select the input pins for the two channels.
  3. Reset the counters by writing to QDCSR.