Fault diagnosis of discrete time linear systems using transmission zeros and zero directions

In this paper, we present a new algorithm to generate a class of input signals corresponding to which the combination of outputs of a discrete time plant in its output zero direction is always zero irrespective of time. Using the above mentioned result and the output zeroing result of Tokarzewski (1999) we propose two tests to find the fault indicating row and fault indicating column of the plant transfer function matrix. Our fault detection scheme is based on the following triple: the output zero direction of the plant, the transmission zero of the plant, and the input zero direction of the plant. Based on the fault indicating rows and columns we identify those elements of the plant transfer function matrix which have undergone changes. The test is also applicable to those cases which have multiple fault indicating rows, columns and elements of the plant transfer function matrix. A system of four interconnected water tanks with two multivariable zeros was used to illustrate the results.