Input-state model matching and ripple-free response for dual-rate systems
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In this paper, we address the model matching problem for dual-rate systems where the controller output is generated at a faster rate than the measurement update rate. The model matching problem that has been studied in the literature requires the inputoutput properties of the closed-loop multirate system to match those of a desired single-rate linear time-invariant (LTI) system. In this paper, we consider the model matching problem from the input-state viewpoint: given a desired LTI system, find conditions and provide a controller design procedure to achieve matching between the closed-loop system and the desired system state variables at the measurement update rate. We provide a solution to this problem using a particular time-varying controller structure. In addition, we give conditions to avoid ripples in the steady-state output of the continuous-time plant; in particular, we show that some constraints on the input matrix of the desired system have to be posed. Numerical examples are given to illustrate the proposed method. 2011 Elsevier B.V. All rights reserved.
