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

A hybrid state-space control scheme for suboptimal digital control of a cascaded continuous-time system using dual rate sampling is presented. First, an optimal regional-pole placement technique is utilized to find an optimal state-feedback control law for a subsystem connected in the inner loop of the overall system. Next, the designed analogue control law is converted into an equivalent fast-rate digital control law using the recently developed digital redesign technique. Then, the digitally redesigned subsystem is converted into an equivalent continuous-time model. As a result, the overall continuous-time model can be formulated from the converted analogue subsystem and the rest of the analogue subsystems to be designed. Moreover, the optimal regional-pole placement technique is applied again to the overall continuous-time model in order to obtain the overall analogue state-feedback control law. Finally, the digital redesign technique is employed again to convert the overall analogue control law obtained to an equivalent slow-rate digital control law. For practical implementations of the developed digital control laws with various sampling rates, the existing ideal state reconstructor method is redeveloped to construct the ideal discrete-lime states using multi-rate input-output data. A practical semi-active terminal homing missile is used as an illustrative example to demonstrate the proposed design method.