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This brief solves critical long-standing numerical stability issues for solutions to the sinusoidal robust servomechanism problem implemented as discrete-time linear time-invariant transfer functions; new closed-form results for direct form I and direct form II implementations now enable such forms to be used indefinitely in open-loop autonomous, or feedforward, configuration, and also provide difference equation initialization and servocompensator output parameter estimation methods that can be quickly calculated and used to enhance transient system performance and to assess harmonic control components. Simulation and real-time experimental results presented, respectively, exhibit expected concordance and robust effectiveness, and therefore highlight the method whereby such linear configurations can be pragmatically applied to further reduce computational implementation requirements relative to their mathematically intensive nonlinear time-varying counterparts.