A simple and flexible method for model simplification (Q914600)

The authors suggest the \(n+1\) model reduction method for a SISO system. The key idea consists in imposing that the reduced-order transfer function H(s) matches the original (possibly irrational) transfer function G(s) for \(m>z+p+1\) rational values of s (including \(s=0)\) where z and p are the number of zeroes and poles of H(s) respectively. Obviously this problem admits no exact solution and it results in a minimum square error problem which is easily solvable. Three examples are shown. The first one deals with a fourth-order rational transfer function (its behaviour does not match the one shown in the figure); the second one deals with an irrational transfer function and the last one deals with a discrete-time transfer function.