Analysis and design of control systems by means of time-domain matrices

The paper presents a method of engineering analysis and design for complex control systems, the time-domain infinite-matrix method. The formulation of the infinite matrix follows from the convolution summation of sampled-data systems. The mathematical basis of the time-domain matrix formulation is related to the applicable concepts of infinite matrices and sequence spaces. The method is applicable to both continuous-data and sampled-data systems. For continuous systems it is necessary to introduce a fictitious sampler and `hold¿ of sufficient sampling rate to effect an accurate approximation. The time-domain-matrix method is presented and illustrated as a method of analysis and design of linear, non-linear, and time-varying systems of the continuous-data or sampled-data class. The investigation of non-linear systems is greatly simplified by the time-domain approach. Multi-loop systems may be investigated, and the signals at intermediate points throughout the loops are readily available. Also, systems with multiple non-linearities may be investigated. Two methods of design of a discrete compensator for a sampled-data system are presented. These methods are accomplished directly in the time domain and allow for a compromise of specifications in the time domain. In one design procedure the response between sampling instants is also accounted for. The time-domain-matrix method may be readily programmed on a digital computer, and therefore provides a rapid analysis and design technique.