Abstract
This paper investigates the preview tracking problem for discrete-time multirate systems under the scenario of the external signals with amplitude non-attenuation. Since the input and the state cannot be measured at the same time, the multirate system is first lifted into the single-rate system. Noting that the external signals are previewable and their amplitudes are unattenuated, an auxiliary system with preview information and a dynamic compensator with internal model are introduced, respectively. On this basis, the preview tracking problem can be converted to the output regulation problem of an augmented system with the aid of the state augmentation technique. Through verifying the solvability of the output regulation problem, the sufficient conditions and the corresponding controller with preview action and feedforward compensation are presented for the output regulation problem as well as the original problem. Finally, a numeric simulation result is provided to verify the validity of the proposed method.
Highlights
Multirate control system has attracted considerable attention due to a mount of sample requirements in many fields of industry
In [2], a discrete-time state space equation was established for multirate systems, where four stability criteria were derived based on two forms of a transfer matrix related to the state space equation
The controller needed for the output regulation problem and the original problem will be designed through the optimal control method
Summary
Multirate control system has attracted considerable attention due to a mount of sample requirements in many fields of industry. In [3], proper algebraic conditions were provided to ensure the desired structural properties (such as, reachability, controllability and stabilizability, etc.) of multirate systems. If the saturated communication sequences are equidistant, multirate systems and networked control system with limited bandwidth were proved to be equivalent in [4], as a result, the related conclusions of the latter on controllability and stabilizability can be applied to analyze the former. In order to simulate the dynamic characteristics in sampling interval, two different discrete lifting techniques were applied in [5] to obtain the functional space model of the multirate control systems, based on the definition of zeros and zero directions, the conditions for realizing asymptotic ripple-free tracking of multirate systems are provided
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