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

Abstract

An operational technique using block pulse functions (BPF) for the analysis of control systems with sample-and-hold(S/H) is proposed. Using this technique, the output in the BPF domain is obtained by means of simple matrix multiplication. Thus, laborious algebraic manipulations associated with the z-transform technique are avoided. Also, the method needs no inverse transformation, generally associated with Laplace or z-transformation. The BPF operational matrix for differentiation <i>D </i>is utilised to replace the Laplace operator <i>s </i>in the conventional transfer function <i>G</i><span style="mso-bidi-font-style:italic">(<i>s</i>)<i>. </i>The resulting

operational transfer function is termed block pulse operational transfer function (BPOTF). This BPOTF is used in conjunction with a sample-and-hold matrix <i>S </i>to analyse a feedback control system with sample-and-hold. Since the BPOTF

<span style="font-size:14.0pt;line-height:115%;font-family:" times="" new="" roman";="" mso-fareast-font-family:"times="" roman";color:black;mso-ansi-language:en-in;="" mso-fareast-language:en-in;mso-bidi-language:hi"="" lang="EN-IN">is always a triangular matrix, any computation involving BPOTF, e.g., matrix inversion or multiplication, is rather simple as far as computational burden is concerned. The results thus obtained are compared with the exact solution. The present operational method is simple and the accuracy of the results are acceptable.</span></span>