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Internal combustion engine having solenoid-operated valves and control method

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TLDR
In this paper, the exhaust valve of an internal combustion engine including solenoid-operated intake and exhaust valves is opened for a certain period of time which starts ahead of the bottom dead center.
Abstract
An internal combustion engine including solenoid-operated intake and exhaust valves is operable in a partial operating mode with at least one cylinder being deactivated, without suffering from vibration of the engine. Where particular cylinders are deactivated under cylinder deactivation control, the exhaust valve of each deactivated or inactive cylinder is opened for a certain period of time which starts ahead of the bottom dead center. The timing of opening the exhaust valve is determined so that the pressure within the inactive cylinder is lower than the atmospheric pressure when the exhaust valve is opened. The timing of closing the exhaust valve is determined so that the peak value of the pressure within the inactive cylinder becomes almost equal to the peak value of the pressure within active cylinders. Where the cylinders are successively deactivated with the engine operating on a six-stroke cycle, opening and closing actions of the exhaust valve are controlled so that an increase in the cylinder pressure due to compression of gas in the currently deactivated cylinder and an increase in the cylinder pressure due to combustion in an active cylinder do not occur at the same time.

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TL;DR: In this article, a simplified method to select cylinder and valve modes is presented for an internal combustion engine with valves that may be deactivated, and a simplified algorithm is presented to select valve modes.
References
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