Achievable H∞ disturbance attenuation for mechanical systems

The problem of achieving high mechanical stiffness in an active controlled flexible structure is investigated. A wideband disturbance force is assumed to act at the effector (e.g., a cutting tool of an electromagnetically borne spindle). Explicit and quite general limits on the best possible achievable performance are found. Mechanical (or any other) systems can be divided in two basic categories. Either arbitrarily low compliance can be achieved at the cost of high controller gain or there exists a nontrivial bound on the disturbance rejection. The tradeoffs are computed explicitly for some simple systems using H_∞ techniques. They enable one to assess a given simple controller, as it can be estimated how close such a controller is to the theoretical optimum