Diagnosis of Oscillations Between Controller Tuning and Harmonic External Disturbances

This paper studies the properties of linear systems described by discrete-time stochastic dynamic models and the conditions that yield an oscillatory response. Feedback loops that are oscillatory due to the controller tuning fall into this category of systems. Therefore, analyzing linear systems with oscillatory responses reveals the properties of self-oscillatory feedback loops. It is shown that in the presence of random disturbances, the oscillation due to the controller has a varying amplitude and phase even though the oscillation frequency is constant. The autocorrelation function of these types of oscillatory signals has a decay ratio and does not have a deterministic amplitude of oscillation. These properties can be utilized in distinguishing between the controller induced and externally introduced oscillations. Two hypothesis tests are developed to facilitate a solution for the above stated oscillation diagnosis problem.