This paper presents a multi-rate state-space control scheme for digital control of a cascaded continuous-time system with fractional time delays. First, a discrete-time state-space representation of a continuous-time system with a fractional input delay is established. Based on the time-delay digital modelling, an ideal state reconstructor is also presented such that system states are exactly reconstructed via the measurement histories of inputs and outputs without a state observer. Next, a time-delay subsystem (designated subsystem 1) with a fast sampling rate is designed to form the inner loop of the overall system, then the designed closed-loop subsystem 1 is cascaded with a time-delay open-loop subsystem 2 with a slow sampling rate. A digital modelling of the time-delay open-loop subsystem 2, based on a fast-rate sampling, is also formed for obtaining the digital modelling of the overall cascaded continuous-time system by using the block-pulse function approximation. Then, the fast-rate overall system is converted into a slow-rate model via the newly developed model conversion technique. Furthermore, subsystem 2 is separated from the slow-rate overall system via a linear transformation for achieving a reduced-order subsystem design. As a consequence, a digital control law is determined on some specific goals for the overall system. The proposed method is suitable for digital control of a multivariable, multi-rate, time-delay system in which state variables are not accessible.
|Number of pages||14|
|Journal||Journal of the Chinese Institute of Engineers, Transactions of the Chinese Institute of Engineers,Series A/Chung-kuo Kung Ch'eng Hsuch K'an|
|Publication status||Published - 1991 Sep|
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