Liquid feeding pump and liquid feeding method

A liquid feeding pump comprising:

• a first plunger pump that has a first plunger;
• a second plunger pump that has a second plunger and is connected to the first plunger pump in series;
• a pressure sensor that is disposed on a downstream side of the second plunger pump and is configured to measure a discharge pressure of a liquid discharged from the second plunger pump and output a discharge pressure value of the discharge pressure;
• and
• a controller configured to accept an input of said discharge pressure value1 to control driving of the first plunger and driving of the second plunger, and to control discharge of the liquid from the second plunger pump by driving the second plunger in parallel with the driving of the first plunger,
• wherein the controller is configured to
• estimate a pressure of the liquid in the first plunger pump;
• drive, when the first plunger pump pressurizes the liquid, the first plunger at a first speed until the estimated pressure of the liquid in the first plunger pump reaches a first predetermined value, then drive the first plunger at a second speed slower than the first speed while continuing to pressurize the liquid, and then temporarily stop the driving of the first plunger based on a determination that the discharge pressure value has increased, from a time of starting pressurization, by an amount equal to or larger than a predetermined threshold value, while driving the second plunger at a third speed different from the first speed and the second speed,
• based on the determination that the increased amount of the discharge pressure value is equal to or larger than the predetermined threshold value, drive the first plunger from at a fourth speed, while controlling the second plunger to suck the liquid until a lower limit point of the second plunger is reached, and
• in response to reaching the lower limit point of the second plunger, stop the driving of the second plunger and drive the first plunger at a fifth speed that is lower than the fourth speed.