This study presents an untethered magnetic manipulation technique for controlling a microrobot position under high rate laminar flows up to 4.5 mL/min. An increase in flow rate exponentially increases the drag force on the microrobot and negatively impacts its positioning accuracy. Increasing the longitudinal force generated by the microrobot's driving apparatus helps in overcoming the disruptive effects of the fluid flow and increases longitudinal motion stability. To this end, we propose a magnetic configuration with two ring-shaped magnets, one above and the other below the microfluidic channel. This configuration causes the magnetic field lines emanating from the ring-shaped magnets to converge on both sides of the microrobot. Thus, the magnetic trapping forces that hold the microrobot in position are increased. To the best of our knowledge, no prior study exists on investigating the longitudinal motion for high flow velocities (>5 mm/s). Investigating the longitudinal forces (along the x-axis) that affect a magnetically-driven microrobot is a novel research topic that has many potential application areas such as cell research, micromanipulation, and lab-on-a-chip systems. The microrobot's dynamical motion is modeled as a second-order system, and using this model as a guideline, we demonstrate the ability of a microrobot in a square-shaped microfluidic channel 900 m 900 m to follow a linear trajectory with a relative velocity up to 132.6 mm/s. A straight and longitudinal trajectory of 4000 m has been successfully followed in the same and opposite directions to the flow for different flow rates (1-4.5 mL/min) and different robot speeds (10-50 mm/s).