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Setpoint tracking with actuator offset and sensor bias - Probing the limits of integral control

In SISO systems, a servo-loop architecture with a forward-and backward-path controller cannot be used to achieve asymptotic setpoint tracking when both an actuator offset and sensor bias are present. We provide results for SISO systems that illustrate the limits of integral control in achieving setpoint tracking. Although the results in this article are confined to the case of SISO transfer functions, extensions to the MIMO case based on state-space models are of interest. In particular, a MIMO treatment of the problem of command following in the presence of actuator offset is given in (Davison and Smith, 1971). For the case of actuator and sensor disturbances that are both measured, setpoint tracking using feedforward control is considered in (Davison, 1973). Consequently, our results on actuator offset are a special case of (Davison and Smith, 1971), whereas our results on sensor bias are not addressed by (Davison, 1973) due to the additional assumption in (Davison, 1973) of measured offsets