Mechanical Systems and Signal Processing (1988) 2(3), 265-277 FREQUENCY VERSUS TIME DOMAIN PARAMETER ESTIMATION: APPLICATION TO A SLOT MILLING OPERATION O. TURKAY Department of Mechanical Engineering, Bogazici University, Bebek, lstanbul, Turkey AND A. G. ULSOY Department of Mechanical Engineering, G. G. Brown Building, University of Michigan, Ann Arbor, MI 48109, U.S.A. (Received April 1987, accepted April 1988) The time domain recursive least squares estimation of parameters in the presence of additive output noise of harmonic form leads to biased estimates. However, frequency domain least squares parameter estimation, where the frequency range contaminated by the noise is eliminated, can be used to obtain good parameter estimates. Both the time domain and frequency domain methods are described, and applied to the example of a slot milling operation. A model of the resultant force response to feedrate changes in slot milling, based on previously reported experimental studies, is presented. The force measurement is corrupted by harmonic noise arising from runout on the milling cutter. Simulation studies are performed, using a fiat band width multi-frequency test signal to persistently excite the system. The time domain approach leads to poor estimates as expected, while the frequency domain approach gives good parameter estimates. The advantages and disadvantages of both methods are discussed. 1. INTRODUCTION This paper considers time domain vs. frequency domain parameter estimation in linear systems with additive harmonic output noise. The study was motivated by the particular problem of adaptive control in a slot milling operation as described below, and this example is used as a basis for comparing the time domain vs. frequency domain parameter estimation approaches. The conclusions and results, however, should be relevant to a wide variety of parameter estimation problems with additive harmonic output noise. Numerically controlled (NC) and computer numerically controlled (CNC) machine tools are used extensively for machining operations to reduce operator input, resulting in significant improvements in productivity. However, further improvements in metal removal rates, and in the tool life can be achieved by on-line manipulation of the feeds and speeds [1], [2]. This can, for example, be achieved by using a process controller where the resultant cutting force can be measured and fed back to manipulate the feed in order to maintain a constant, optimum, force level. Such process control strategies have generated considerable research interest in recent years, particularly in light of difficulties due to process parameter variations [2]-[5]. Adaptive controllers, which combine on-line parameter estimation and control [6]-[8], have been proposed and implemented to address these difficulties [3]-[5], [9], [10]. In adaptive control of the force during a milling operation, difficulties in parameter estimation arise due to runout noise [4]. The runout noise comes from small geometric 265 0888-3270/88/030265+ 13 $03.00/0 (~ 1988 Academic Press Limited