MULTI-RATE DIGITAL REDESIGN OF CASCADED AND DYNAMIC OUTPUT FEEDBACK SYSTEMS

In this research, new indirect digital redesign methods are presented for multi-rate sampled control systems with cascaded and dynamic output feedback controllers. Unlike the classical direct bilinear transform, which is an open-loop direct digital redesign method, the proposed digital controllers take into account the state-matching of the original continuous-time closed-loop system and the digitally redesigned sampled-data closed-loop system. Direct bilinear transform is a fairly simple method that has been widely used in industry for a long time. However, it ignores the continuous-time controllers and plant as a complete system and treats all of the controllers individually. Generally, this method might be good for short sampling periods, however the system response might become unstable for longer sampling periods. Therefore, closed-loop digital redesign methods are preferred while calculating digital controllers.
Analog controllers are often predesigned based on a desirable frequency specification, such as the bandwidth, the natural angular frequency, etc. To take advantage of the digital controllers over the analog controllers, digital implementation of analog controllers is often desirable. However, continuous-time system states might not be readily available. Therefore, an ideal state reconstructing algorithm was utilized to obtain the multi-rate discrete-time states of the original continuous-time system. By utilizing these obtained states and applying Chebyshev quadrature method, improved digital redesign method and lifting methods, multi-rate cascaded and dynamic output feedback digital controllers were constructed. Illustrative examples are provided to demonstrate the effectiveness of the developed methods