We lay out a general framework for reverse-engineering frequency dynamics with general primary frequency control and frequency response, by showing that it is a distributed algorithm to solve a well-defined optimization problem. We further characterize the role of deadband in control, and show that if the aggregated uncontrolled load deviation is nonzero the frequencies will be synchronized, and if however it is zero the frequencies may oscillate but within the deadband. The optimization based model does not only provide a way to characterize the equilibrium and establish the convergence of the frequency dynamics, but also suggests a principled way to engineer frequency control. By leveraging the optimization problem and insights from reverse engineering, we design a distributed realtime frequency control scheme that maintains the frequency to the nominal value while achieves economic efficiency. This work presents a further step towards developing a new foundation-network dynamics as optimization algorithms-for distributed realtime control and optimization of future power networks.