Constraint-following control design for nonlinear underactuated belt conveyors with uncertainty

There are many mismatched uncertainties in the nonlinear underactuated belt conveyor systems which leads to challenges for designing the controllers. This paper addresses this issue based on the concept of constraint-following by establishing the dynamic model and treating the desired trajectory as a constraint. First, the nominal control portion is studied in the absence of the deviation of initial condition and uncertainties. Second, the uncertainties are decomposed into matched and mismatched parts according to the match condition. Then, the robust constraint-following control portion that is solely based on matched uncertainty is designed. By utilizing the Lyapunov method, the proposed control with two portions is able to ensure the uniform boundedness and uniform ultimate boundedness of the underactuated systems with uncertainties. Simulations are additionally carried out for the purpose of verification.