This paper discusses the averaging, control authority, and vibrational control of mechanical control-affine systems with high-frequency, high-amplitude inputs. The inputs have different frequencies of the same order. This work is an extension of the existing averaging method for high-frequency mechanical systems with single-frequency inputs. Vibrational control authority of mechanical control-affine systems is introduced, and the effects of inputs' waveform and frequency on vibrational control authority are investigated. The results show that, in general, using multifrequency inputs may result in lower control authority of mechanical systems compared to single-frequency inputs, especially when using harmonic inputs. The results on vibrational control authority of the systems with multifrequency inputs are demonstrated using vibrational control of a horizontal pendulum with two inputs. This paper also discusses the averaging of multiple-time-scale control systems.

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