Controller for internal combustion engine

A controller for an internal combustion engine including at least one of a port injection valve that injects fuel into an intake passage of a cylinder and a direct injection valve that injects fuel into a combustion chamber of the cylinder, the controller comprising:

• processing circuitry configured to perform:
• a first fuel injection process injecting fuel by operating the port injection valve,
• a second fuel injection process including one of a process operating the port injection valve when the first fuel injection process is completed and an intake valve is open and a process operating the direct injection valve,
• a division process variably setting a division ratio, which divides a request injection amount of the internal combustion engine into a first request amount for the first fuel injection process and a second request amount for the second fuel injection process, based on an operating point of the internal combustion engine, and
• a gradual increase process, wherein when the first request amount corresponding to the division process does not exist, the gradual increase process specifies the first request amount to be zero, and when the first request amount is increased, the gradual increase process sets an instruction value of a fuel injection amount of the first fuel injection process to gradually increase to the first request amount based on a decreased amount from the first request amount and also sets an instruction value of a fuel injection amount of the second fuel injection process based on an increased amount of the second request amount to compensate for a shortage amount of a sum of the decreased amount and the second request amount with respect to the request injection amount.