A coordinates and control change was designed for a class of underactuated mechanical systems to transform the dynamics into cascade nonlinear systems in strict feedforward form,and based on the derived cascade nonlinear system in strict feedforward form,the nested saturation control scheme was proposed for the class of underactuated mechanical systems.

A nonlinear control strategy based on nested saturation approach is presented for an overhead crane to achieve positioning and anti-swing control.

For a feedforward system that consists of a local input-to-state stabilizable subsystem and an input-to-state stable subsystem, a saturated controller is designed as a local input-to-state stabilizer, that is, the corresponding closed loop is input-to-state stable with restrictions on inputs.

The inertia wheel pendulum is transformed into a 4-dimensional chain of integrators with higher order nonlinearity, and a saturated control law is provided with saturation level and time delay explicitly specified.

A saturation control is presented for the chain of integrators that is an additive form.

This paper analyzes the band shift caused by the deviation of internal resonance frequency of nonlinear saturation control system.

It focuses on the effects of time delay which was ignored in the previous research on the saturation control of a flexible cantilever beam.