All-integrator approach to linear SISO control system analysis using block pulse functions (BPF)

The present work makes use of the block pulse domain operational matrix for differentiation D1(m) to find out an operational transfer function. Analysis of simple control systems using this Block Pulse Operational Transfer Function (BPOTF) shows that the results are not so accurate when compared with the direct expansion of the exact solution in the BPF domain. To remove this defect, one shot operational matrices for repeated integration (OSOMRI) are obtained and these matrices are used to develop a Modified Block Pulse Operational Transfer Function (MBPOTF) for linear SISO control system analysis in the block pulse function domain. linear SISO control systems are analysed using the developed MBPOTFs as illustrative examples. The results are found to match exactly with the direct BPF expansions of the exact solutions.