Structural acceleration regulation is a means of managing structural response energy and enhancing the performance of civil structures undergoing large seismic events. A quadratic output regulator that minimizes a measure including the total structural acceleration energy is developed and tested on a realistic non-linear, semi-active structural control case study. Suites of large scaled earthquakes are used to statistically quantify the impact of this type of control in terms of changes in the statistical distribution of controlled structural response. This approach includes the impulses due to control inputs and is shown to be more effective than a typical displacement focused control approach, by providing equivalent or better performance in terms of displacement and hysteretic energy reductions, while also significantly reducing peak story accelerations and the associated damage and occupant injury. For earthquake engineers faced with the dilemma of balancing displacement and acceleration demands this control approach can significantly reduce that concern, reducing structural damage and improving occupant safety.