Fast reference governors for second-order linear systems with constraints and an input time-delay

This note provides a solution to the constrained command tracking problem using reference governors for a class of continuous-time second order linear systems with an input delay and with pointwise-in-time state and control constraints. The reference governor modifies the command to a closed-loop system based on the prediction of whether the system response to constant commands violates the specified constraints. The solution relies on classical control results for second order linear systems and requires only checking whether predicted outputs violate the constraints at a small number of time instants (e.g., four time instants in the single output case). This greatly simplifies the online computation, especially when a reference governor is applied to system models that are (slowly) changing in time. The effectiveness of the proposed method is demonstrated by a numerical example.