The design of simple controllers for unstable time delay systems using LQ control theory

The paper presents a new methodology of the controller design for unstable time delay systems. The proposed method based on polynomial approach and LQ control theory yields a class of CT controllers ensuring setpoint tracking as well as load disturbance attenuation. Both control configurations, a 1DOF one with a feedback controller and a 2DOF one with a feedback and feedforward ones, were considered. Moreover, the resulting controllers obtained via polynomial Diophantine equations and spectral factorization technique are stable ones. Time delay terms are approximated by two methods and they are incorporated into the control design as a perturbation. Obtained control algorithms were compared and analysed for unstable first order time delay systems.