Stability boundaries for closed-loop systems with control constraints

Constraints on the magnitudes of control variables limit the region where unstable systems can be stabilized using feedback control. Stability boundaries must be evaluated to assure satisfactory system performance. A method is presented to determine the stability boundaries for linear second-order plants with saturating control and several classes of open-loop instability. In the saddle-point case, the modal axes of the stable mode centered on the equilibrium points and the saturation boundaries establish the regions of stability. For unstable nodes and foci, the stability boundaries are represented by unstable limit cycles enclosing the stable origin. The stability regions vary with changes in feedback gain. These results have fundamental significance for determining the degree to which unstable plants can be controlled in practical application.