Babji Srinivasan

Time-delay estimation in closed-loop systems is of critical value in the tasks of system identification, closed-loop performance assessment and process control, in general. In this work, we introduce the application of mutual information (MI) theory to estimate process delay under closed-loop conditions. The hallmark of the proposed method is that no exogenous (dither) signal is required to estimate the delay. Further, the method allows estimation of time-delays merely from the step response of the system. The method is based on the estimation of a quantity known as the average mutual information (AMI) computed between the input and output of the system. The estimation of AMI involves estimation of joint probability distribution of the input-output pair and therefore is a superset of the existing correlation-based methods, which only compute second-order moments of the joint distribution. Simulation studies are presented to demonstrate the practicality and utility of the proposed method.

Two of the most important sources of degradation of control loop performance are (i) valve stiction and (ii) tight controller tuning, both of which lead to oscillations in closedloop outputs. A factor that distinguishes these two sources is the nonlinear signature of the valve stiction; a tightly tuned controller produces oscillations due to a linear source. Detection and isolation of nonlinear fault sources is essential to correctly determine the cause of poor loop performance of control loops. Despite a rich research activity in this area, there is hardly a method which can isolate the simultaneous effects of these two sources. Moreover, the traditional spectral analysis based on Fourier Transforms is largely restricted by the assumption of stationarity in the data to detect and quantify valve nonlinearities. In this work, Hilbert-Huang Transform (HHT) is used to (i) detect valve nonlinearities and (ii) isolate linear and nonlinear fault sources. The key characteristic of HHT is that it represents nonlinearities as intra-wave frequency modulations allowing it to distinguish it from linearities which do not exhibit such modulations. The advantages of HHT-based methods are that (i) nonlinearities translate to a unique signature (ii) nonstationarities in data can be handled in a natural way. It is observed that nonlinearity is captured by a Intrinsic Mode Functions (IMF) obtained from the Empirical Mode Decomposition (EMD) of the process output. The Hilbert-Huang spectrum of these IMFs exhibits intra-wave frequency modulation. The power spectrum of the IMFs shows the presence of harmonics which is used to characterize the valve stiction nonlinearity. Subsequent to detection, quantification is done using the power spectrum of the IMFs. The proposed method is sensitive enough to detect low levels of valve stiction nonlinearities. Results from simulation using one-parameter valve stiction model are presented in support of the proposed methodology. The results demonstrate the advantage and potential of the HHT-based method. © 2009 World Scientific Publishing Company.