APPROXIMATE POLE PLACEMENT APPROACH

A recently developed design method is applied to the benchmark problem. The design method may be viewed as a numerical loop-shaping method that also permits approximate assignment of the dominant poles of the closed-loop system. Solutions with different properties are obtained depending on the choice of closed-loop poles. Three different designs are given. The first is a a high-gain solution, the second gives a controller with relative degree 2, and the last one gives a controller with relative degree 1. The controllers satisfy the given design criteria. The chosen design method also makes it possible to tune a controller for structured parameter variations. A special controller, which admits a wide range of variations in the spring constant, is designed. It is also shown that the design method can easily be extended to deal with disturbances with known frequencies.