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RECURSIVE FREQUENCY RESPONSE ESTIMATION

Recursive Estimation from Relay Feedback Experiments [Pg.202]

Suppose that the process to be identified is placed under relay feedback control and oscillates with some period T. Using a sampling interval of At, the number of samples within a period is AT =. The periodic square wave u k) generated by the relay output can be completely described over this period [0, T] using a discrete Fourier expansion (Godfrey, 1993) [Pg.202]

The magnitudes of the nonzero values of Ai decrease with increasing 1/.  [Pg.203]

For frequency response estimation, we set the parameter N in the FSF model in Equation (4.22) to be equal to N to capture the dominant periodic frequency components in the input and output signals. Thus the process output y(k) can be described by [Pg.203]

If u k) is a periodic and symmetric signal, the filter outputs for even values of r (r = 0, 2, 4.) are equal to zero after one complete period N. In addition, the magnitudes of the nonzero filter outputs corresponding to r = 1, 3. decrease as r increases. Therefore, in this situation, the only terms required to accurately describe the process output y k) in Equation (8.3) for processes with a monotonically decreasing frequency response may be those with r = 1, 3 and 5. However, because output disturbances and measurement noise are encountered in most practical situations, u k) is seldom an ideal periodic and symmetric signal. In many cases though, u k) would be nearly periodic and the parameter N could be chosen based on [Pg.203]


This chapter describes two new methods for obtaining frequency response and step response models from processes operating under relay feedback control. Both methods are based on the frequency sampling filter model structure and a recursive least squares estimator. [Pg.201]

The objective is to recursively estimate the process frequency response at the dominant harmonic frequencies generated under a standard relay experiment. A white noise distmrbance sequence with unit variance has been added to the output. The relay amplitude was set equal to 2 and the hysteresis level was set equal to 3 (3 times the standard deviation of the output noise). The process was sampled with a time interval of 0.67 seconds. Note that, although the hysteresis level is larger than the noise-free process output response to an input change of magnitude 2, a limit cycle still occurs due to the presence of the noise. [Pg.205]

The objective of state estimation is to estimate the system states from a limited number of response measurements (e.g., acceleration measurements) and a system model. The state vector can be determined using a deterministic approach (e.g., least squares estimation of the state vector in the frequency domain) or using a combined deterministic-stochastic approach, which mostly results in recursive time-domain algorithms which can be applied for online state estimation. The best-known recursive state estimation algorithm for linear systems is the Kalman filter algorithm (Kalman 1960), which is outlined next. [Pg.1750]


See other pages where RECURSIVE FREQUENCY RESPONSE ESTIMATION is mentioned: [Pg.201]    [Pg.203]    [Pg.205]    [Pg.201]    [Pg.203]    [Pg.205]    [Pg.8]    [Pg.204]    [Pg.208]    [Pg.1749]   


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