Optimal tradeoff between H2 performance and tracking accuracy in servocompensator synthesis

The problem of optimal H₂ disturbance rejection while tracking uncertain constant or sinusoidal reference commands is considered. The internal model principle is used to ensure that the tracking error approaches zero asymptotically. Necessary conditions are given for controllers that minimize an H₂ disturbance rejection cost plus a worst-case integral square tracking error for transient tracking performance. The necessary conditions provide expressions for the gradients of the cost with respect to each of the control gains. These expressions are then used in a quasi-Newton gradient search algorithm to determine the optimal feedback gains. Numerical examples demonstrate the tradeoff between the two competing objectives in the cost function.