A Robust Variable Structure Controller for Mixed Continuous / Bang-bang Systems

A systematic controller design procedure is developed for the class of linear time-invariant systems which use both continuous and bang-bang control effectors. The sampled-data regulator and its associated weighting matrices and cost function are extended to this class of system, and are used to modulate the bang-bang effector to achieve desired performance levels. Stability, sensitivity, and robustness are quantified, and the controller synthesis methodology is illustrated for a generic second-order plant with one continuous effector and one bang-bang effector. Results indicate that the resulting controllers are stable, not overly sensitive to the designer selected bang-bang weighting, and possesses good robustness with respect to parametric structured uncertainties. The methodology provides the designer with insight required to systematically tune closed-loop performance.