A CA D method is presented for converting existing continuous-data control systems into digital control systems by means of a digital controller. The digital controller is synthetized by matching the frequency response of the digital control system to that of the continuous-data system with a minimum weighted mean-square error. A formula for computing the parameters of the digital controller is obtained as a result. The design technique is illustrated with a numerical example and a comparison with previous methods is also presented.
Recent developments in digital technology have renewed interest in analysing and designing sampled-data control systems. During the past few years, digital devices have been incorporated into control systems because they are more compact, reliable and economical than analogue elements. There is also a need for converting existing continuous-data systems into digital or sampled-data systems with similar performances.
Tabak i presented a method for converting existing continuous control systems into sampled-data control systems by means of digital controllers. This method converts continuous compensators into digital controllers using bilinear transformation, and it only takes into consideration the frequency responses of the digital controllers, not the overall system. Although the method is straightforward and easy to use, the sampled-data control system obtained by this method approximates the continuous system only if the sampling frequency is sufficiently high compared with the highest frequency of the continuous system. Thus the capabilities of the digital controller are not fully utilized, In recent papers, Kuo et aL 2 , Yackel et al. 3 and Singh et al. 4 proposed methods for converting a continuous control system into a sampled-data control system with the output or state trajectories matched at all sampling instants or at multiples of sampling instants. The matching requirements are satisfied by changing the input and feedback gains of the system instead of using a digital controller. However, such matching holds only for unit step inputs. Thus the performances of the sampled-data system obtained by their method approximates that of the continuous model only when the input frequency is sufficiently low in comparison with the sampling frequency. For higher input frequencies, the approximation is poor.
Hence there is a need for developing a method which does not require an excessively high sampling frequency Department of Physiology and Biophysics (formerly with Department of Electrical Engineering),