graph are the square roots of the appropriate diagonal elements from the error covariance matrix P. These elements provide a first-order approximation to the estimated variance in the states and hence ± Vi^, is an approximate measure of the standard deviation of state estimate x ,•. Increasing the running speed (and hence the excitation frequency) has little effect upon the accuracy of estimation, as shown by the results in A key assumption in producing the above results is that the values of (e/c) and <p are known exactly. Where the unbalance is introduced artificially this is a reasonable assumption, however where natural unbalance is exploited its effective magnitude and angular position would be harder to assess. Consequently a further set of tests was performed involving deliberately-induced errors in the assumed values of (e/c) and Typical results (for a running speed of 3000 rev/min) are shown in Discussion This note has discussed an approach to the identification of linearized journal bearing dynamics under normal operating conditions. Given that an effective technique is already available for estimating the four oil-film stiffness terms, a method must now be developed for extracting reliable estimates of the four damping terms, preferably without the need to conduct further experiments. We have suggested that this can be achieved by reformulating the problem so that an existing algorithm can be applied to estimate the damping terms from noisy measurements of the displacement responses to synchronous excitation. These responses are acquired automatically in any identification experiment and hence the approach could be applied retrospectively to refine estimates of the damping terms. The feasibility of the approach has been tested under controlled conditions by generating data from a linearized model of a simple rotor-bearing system and demonstrating that the governing equations can be reconstructed. In practice the effectiveness of such an approach will depend upon the robustness of the algorithm when processing actual operating data and the accuracy with which the unbalance parameters can be assessed. The effects of modeling errors (introduced by the linearization process) and other disturbances not considered in this note (for example, surface roughness of the shaft and bearings) will obviously be reflected in the eventual results. It is hoped that the results presented here will encourage experimental work to quantify such effects. 2 Holmes, R., "The Vibration of a Rigid Shaft on Short Journal Bearings," J. Mech. Eng. Set., Vol. 2, 1960, pp. 337-341. 3 Allaire, P. E., Nicholas, J. C, and Gunter, E. J., "Finite-Element Analysis of Fluid-Film Bearings," University of Virginia Report ME-543-120-75, Charlottesville, Va. 4 Stanway, R., Burrows, C. R., and Holmes, R., "Discrete-Time Modelling of a Squeeze-Film Bearing," J. Mech. Eng. Sci., Vol. 21, 1979, pp. 419-427. 5 Morton, P. G., "The Derivation of Bearing Characteristics by Means of Transient Excitation Applied Directly to a Rotating Shaft," G. E. C. Journal of Science and Technology, Vol. 42, 1975, pp. 37-47. 6 Burrows, C. R., and Stanway, R., "Identification of Journal Bearing Characteristics," ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT AND CONTROL, Vol. 99, 1977, pp. 167-173. 7 Detchmendy, D. M., and Sridhar, R., "Sequential Estimation of States and Parameters in Noisy Non-Linear Dynamical Systems," ASME Journal of Basic Engineering, Vol. 88, 1966, pp. 362-368. 8 Woodcock, J. S., and Holmes, R., "The Determination and Application of the Dynamic Properties of a Turbo-Rotor Bearing Oil-Film," Proc. I. Mech. £., Vol. 184, 1969Vol. 184, -1970. Control of Systems Subject to Introduction Although the study of linear systems receives disproportionate attention in the literature, the fact remains that nonlinear equations are necessary to adequately describe many important control processes. Linear feedback theory may still find an application even in this instance. If the nonlinear system operates near a known nominal condition, a nominal state trajectory and a nominal actuating signal can be determined. Under appropriate conditions, the deviations from the nominal path can be described by a linear model. Linear synthesis algorithms can then be applied to this perturbation model, and a regulator which causes the system to track its nominal trajectory can be deduced thereby. To be more specific about these ideas, consider the problem of synthesizing a feedwater flow rate regulator for control of a solar receiver. Certain aspects of this problem were addressed in [1] an
