Double Integrator

In real-world applications, controllers must operate in the presence of an untold number of off-nominal conditions that either were not or could not be accounted for during formal synthesis. Engineers compensate for these real-world effects by extensive simulation and testing. Only after extensive evaluation and validation can a controller be accepted for critical applications. In addition, it should be recognized that a controller designed with certain conditions in mind may be subjected to unexpected changes in the plant or environment and may be unable to withstand these changes. A controller that can withstand unexpected changes possesses a certain flexibility; a controller that cannot may be viewed as brittle. In this article, we practice a form of controller evaluation that might 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; however, unexpectedly good performance may suggest hidden, serendipitous properties of the algorithm that were not considered in the original development of the controller. Note that this approach is distinct from robust control, which seeks to accom-