Naive control of the double integrator

We deal with a form of controller evaluation that may be called naive control. In naive control, a control algorithm derived under nominal (or ideal) conditions is evaluated by analytical or numerical means under off-nominal (or nonideal) conditions that were not assumed in the formal synthesis procedure. Under such nonideal conditions, the controller may or may not perform well. This approach is distinct from robust control, which seeks to accommodate off-nominal perturbations in the synthesis procedure. We consider the double integrator plant, which is one of the most fundamental systems in control applications, representing single degree-of-freedom translational and rotational motion. Applications of the double integrator include low-friction, free rigid-body motion, such as single-axis spacecraft rotation and rotary crane motion. The double integrator plant considered includes a saturation nonlinearity on the control input