Naive control of the double integrator: a comparison of a dozen diverse controllers under off-nominal conditions

In naive control, a control algorithm derived under nominal, or ideal conditions is evaluated by analytical or numerical means under off-nominal, or non-ideal conditions that were not assumed in the formal synthesis procedure. Under such non-ideal conditions, the controller may or may not perform well. We consider an eclectic set of algorithms, ranging from classical to nonlinear and adaptive. Since the controllers are tuned by means of different procedures and since each controller has different capabilities, it is challenging to construct criteria that provide a useful evaluation of controller capabilities. Our approach to this problem is as follows. First, we specify nominal conditions in which the mass is given, and we tune each controller to minimize the worst case time to the origin from initial conditions located on the unit circle in the position/velocity phase plane without exceeding a peak input of unity. Next, we test each nominally tuned controller under a sequence of off nominal conditions.