Discrete LQ optimal control with integral action: A simple controller on incremental form for MIMO systems

A simple Linear Quadratic (LQ) optimal controller of velocity (incremental) form with approximately the same properties as a conventional PID controller of velocity form is presented, i.e. integral action. The proposed optimal controller is insensitive to slowly varying system and measurement trends and has the ability of stabilizing any linear dynamic system under weak assumptions such as the stabilizability of the system and the detectability of the system seen from the performance index.