Control Logic for Parameter Insensitivity and Disturbance Attenuation

An approach to the synthesis of control logic that is both insensitive to system parameters and attenuates response to input disturbances (sometimes called robust control logic) is presented and is applied to a simple system with an uncertain vibration frequency. A conclusion drawn from this study is that the lower the order of the compensator dynamics, the lower the sensitivity of the closed-loop system performance to parameter variations. It follows that estimated-state feedback is undesirable when there are large uncertainties in the system parameters. However, quadratic performance indices are minimized with estimated-state feedback, so the designer must trade off parameter insensitivity against disturbance attenuation. This is done here by minimizing the expected value of a sum of quadratic performance indices, each one of which is evaluated with different values of the system parameters; the decision variables in the minimization are parameters in a compensator of specified order that is less than or equal to the order of the system model.