Many single-axis motion systems are driven by electric machines equipped with torque-regulating power converters, and the operation of such systems is often commanded using some type of speed controller. The design of the speed controller involves choosing both the reference command shapes and the signal flow architecture. This paper provides a solution to the problem of speed controller design where the goal is to minimize the electric energy required to transition from one speed to another, for both acceleration and deceleration; this topic is inspired by applications that involve frequently occurring speed transitions. Explicit formulas are derived that characterize the energy minimizing transition time, and the corresponding torque and speed trajectories, and these trajectories are fed as reference commands into a controller architecture that incorporates both feedback and feedforward actions. For comparison, results are also derived for the case in which torque is constrained to be constant throughout the speed transition interval.