Posted Aug 21, 1996

H Control with Command but not Disturbance Signal Access

By J. William Helton and Wei Zhan

This paper investigates H control design where the compensator is assumed to have immediate access to the command signal (usually denoted $W_1$) but not to the disturbance signal (denoted $W_2$). While the Doyle Glover paradigm only feeds a plant output Y into the compensator, in many industrial applications the command signal at time t can be transmitted to the compensator at time t if there is any advantage to doing so. In this article we analyze both linear and nonlinear systems and find that the advantage to this control architecture is great. The results in this paper generalize those of Ball {\it et al} 1993, Doyle {\it et al} 1988, Helton {\it et al} 1992. A necessary condition is given for the general nonlinear systems. These suggest formulas for controllers. For special cases such as: when there is no disturbance signal $W_2$ or the system is linear, we have very satisfactory conclusions. In particular, for linear systems with uncertainty, we derive conditions for the solution to the robust H control problem to exist.