Hybrid suboptimal control of multi-rate multi-loop sampled-data systems

A hybrid state-space controller is developed for suboptimal digital control of multirate multiloop multivariable continuous-time systems. First, an LQR is designed for a continuous-time subsystem which has a large bandwidth and is connnected in the inner loop of the overall system. The designed LQR would optimally place the eigenvalues of a closed-loop subsystem in the common region of an open sector bounded by sector angles + or - pi/2k for k = 2 or 3 from the negative real axis and the left-hand side of a vertical line on the negative real axis in the s-plane. Then, the developed continuous-time state-feedback gain is converted into an equivalent fast-rate discrete-time state-feedback gain via a digital redesign technique (Tsai et al. 1989, Shieh et al. 1990) reviewed here. A real state reconstructor is redeveloped utilizing the fast-rate input-output data of the system of interest. The design procedure of multiloop multivariable systems using multirate samplers is shown, and a terminal homing missile system example is used to demonstrate the effectiveness of the proposed method.