Multi-rate control systems with multi-rate model-based holds and observers

This paper deals with the design of multi-rate control systems using multi-rate holds, which act as interfaces between the different sampling frequencies present at the control loop. Multi-rate model holds generate error signal estimation at high-frequency based on a closed-loop reference model. The paper describes first the modeling of multi-rate model-based holds and observers and later its effect in the closed-loop time response. In addition, the benefits of introducing the multi-rate holds can be studied before implementing the multi-rate solution just by analyzing the limit case, where the periodicity ratio between frequencies goes to infinite with the frame-period constant. The proposed multi-rate hold and observer are validated with a velocity control of brush-less DC motor, where improvements are performed with respect to the single-rate case at low frequency.