Limits of Disturbance Rejection for Indirect Control

In many practical problems, the primary controlled variable is not available for feedback and is needed to be controlled indirectly using secondary measurements. We derive bounds on the H2and H∞optimal achievable performance for systems under indirect control, which have all scalar signals. These bounds are useful for gaining insights into the factors posing limitations on the achievable performance. As compared to direct control, the unstable poles can severely limit the control quality for indirect control. The limiting effect of the unstable poles can be reduced using an additional feedforward controller, when the disturbance is measurable.