Fault detection optimization for controllable dynamic systems

Abstract

Introduction: When diagnosing the deviations of controllable dynamic system parameters, it is convenient in terms of control simplicity to apply the Schreiber method which uses a set of rectangular pulses of equal duration as a test signal. Since for a single object you can construct many test signals which differ in the number of pulses, the problem arises how to minimize the number of test pulses when using the Schreiber method. Purpose: Simplification of test control and diagnostics of linear controllable dynamic systems. Results: It has been shown that a set of test pulse amplitude vectors is a kernel of the controllability matrix of a discrete analogue of the object under test. The problem is formulated of finding the optimal length of a test pulse in order to minimize the number of pulses in the test signal. For a given pulse length, the pulse amplitudes of an optimal test signal are equal to the coefficients of the control vector minimal polynomial for the discrete analog of the object relative to its system matrix. The number of test pulses can be reduced by choosing the pulse duration calculated from the imaginary component of the object poles. In particular, if an object has at least one pair of complex-conjugate poles, the number of test pulses does not at least exceed the order of the object. An algorithm has been developed for calculating a test signal for linear controllable object FDI by the Schreiber method. The input to the algorithm is the system matrix of the object, and the output is the length of the test pulse and the pulse amplitude vector. The efficiency of the algorithm is illustrated by FDI for two technical objects. Practical relevance: The results of the study can be applied to static parameter FDI of controllable dynamical objects which allow a linear description in their state space.