Adaptive Dead-Time Estimation

Identification of a time-delayed process model using an overparameterisation method

“…The result is shown in Figure 2. In this figure, k = 5, following the advice of De Keyser [11]; other results show satisfactory tracking when k = 2.5, 10 and 20, with k = 2.5 facilitating the fastest tracking.…”

“…The simulation results show that the method of Wong and Bayoumi [7] may be expanded to estimate time delays that are multiples of 0.1 times the sample period. Other results show that the method of De Keyser [11] may also be successfully expanded. …”

“…As mentioned, the methods of Wong and Bayoumi [7] and De Keyser [11] have been considered. Wong and Bayoumi [7] suggest that, as all numerator parameters whose indices are smaller than the time delay index are close to zero, though not exactly zero in practice, the correct time delay index value may be estimated as the index of the first parameter of ( ) 1 * z B − above a defined threshold level.…”

“…A challenge is to define the threshold level, so this method best allows the estimation of an initial value of the (possibly time varying) time delay index. De Keyser [11] suggests that this initial value of time delay index may be improved by changing it according to the results of two inequality equations, which use the estimated model parameters as data: Once the parameters are estimated, the method of Wong and Bayoumi [7] is used to estimate the starting va lue of the time delay index; subsequently, the method of De Keyser [11] is used to track the variations in the time delay index. The result is shown in Figure 2.…”

“…The present paper will expand on the earlier work by reconsidering the estimation of the model parameters and time delay, both for SISO and MIMO applications. Starting with the estimation of all SISO model parameters, when the time delay is an integer multiple of the sample period, using the method of De Keyser [11], the method will be extended to the estimation of all model parameters when the time delay is not an integer multiple of the sample period. Subsequently, the method of Wong and Bayoumi [7], De Keyser [11] and modified versions of these methods, will be considered for the estimation of all model parameters of a SISO, Multiple -Input, Single -Output (MISO) and MIMO process.…”