Analysis of linear SISO (single input single output) control systems with sample-and-hold using block pulse function (BPF) operational technique

An operational technique using block pulse functions (BPF) for the analysis of control systems with sample-and-hold (S/H) is proposed. Using this tech nique, the output in the BPF domain is obtained by means of simple matrix m ultiplication. Thus, laborious algebraic manipulations associated with the z-transform technique are avoided. Also, the method needs no inverse transf ormation, generally associated with Laplace or z-transformation. The BPF op erational matrix for differentiation D is utilised to replace the Laplace o perator s in the conventional transfer function G (s). The resulting operat ional transfer function is termed block pulse operational transfer function (BPOTF). This BPOTF is used in conjunction with a sample-and-hold matrix S to analyse a feedback control system with sample-and-hold. Since the BPOTF is always a triangular matrix, any computation involving BPOTF, e.g., matr ix inversion or multiplication, is rather simple as far as computational bu rden is concerned. The results thus obtained are compared with the exact so lution. The present operational method is simple and the accuracy of the re sults are acceptable.