Closed Loop Time Domain Gradient Methods for Parameter and Time Delay Estimation

TL;DR: This paper concentrates on the application of the algorithms to estimate the model parameters in a Smith predictor structure using Gauss-Newton gradient algorithms in the time domain.

Abstract: This paper discusses the estimation of process parameters and time delay, in a Smith predictor structure, using gradient algorithms in the time domain A number of estimation algorithms are outlined and applied in simulation to the estimation of the parameters of an appropriate process model An analytical exploration of the technique is also provided Keywords: Estimation, time delay, Smith predictor 1 Introduction Gradient methods of parameter estimation are based on updating the process model parameter vector (which includes the time delay) by a vector that depends on information about the cost function to be minimised; the cost function is normally a function that depends on the square of the error between the process and model parameters A number of such gradient algorithms have been defined (such as the Newton-Raphson and Gauss-Newton algorithms); Ljung [1] outlines these algorithms in detail Applications of these algorithms to estimate the process model parameters in both open loop and closed loop environments have appeared in the literature Open-loop applications, in both the time domain and frequency domain, have previously been dealt with by O’Dwyer and Ringwood [2], [3], amongst others; this paper concentrates on the application of the algorithms to estimate the model parameters in a Smith predictor structure Marshall [4] and Bahill [5] reduced the mismatch between the process time delay and the model time delay, in such a structure, using a Gauss-Newton gradient algorithm; just one of the modifications of this approach subsequently proposed is that defined by Romagnoli