Abstract: Aiming at the control problem of nonlinear underactuated unstable systems, a virtual full actuated control method based on auto coupling PID control theory is proposed. This method will define the known or unknown internal dynamics of each input channel as a total disturbance, and in the first input channel is introduced into the corresponding virtual control, thus the nonlinear underactuated equivalence of unstable system for virtual full drive system of linear disturbance, and based on the auto coupling PID control theory to establish the first virtual controller, input channel to form virtual instruction, then the controller of the next input channel is established according to the obtained virtual instruction and the auto coupling PID control theory to realize the effective control of nonlinear underactuated unstable system. The simulation results verify the effectiveness of the proposed control theory and have wide application prospects in the control field of nonlinear underactuated unstable systems.

Key words: nonlinear underactuated system, unstable system, ACPID control, virtual instruction, total disturbance