86 U. Musella et al. H u r e y + - continuous sweep ampl/phase estimation y(t) u(t) C time domain Fig. 13.2 MIMO swept sine feedback control, block scheme. The green blocks highlight the necessary steps of generating a continuous sine sweep from the drives spectra (continuous sweep block) and estimating the response amplitude and phase from the time recordings (ampl/phase estimationblock) Table 13.1 Different sweep modes and related sine arguments Sweepmode Frequency in Hz Sine argument in rad Linear up f(t) =fin +SRHz/st (t) =2π fint + SRHz/s 2 t 2 Linear down f(t) =fend −SRHz/st (t) =2π fendt − SRHz/s 2 t 2 Log. up flog,up(t) =fin 2 SROct/mint/60 (t) =2π 60fin SROct/min log2 2SROct/mint/60 −1 Log. down flog,up(t) =fend 2−SROct/mint/60 (t) =2π − 60fend SROct/min log2 2−SROct/mint/60 −1 13.3 Sweeping and Estimate Harmonic Estimator The idea of the on-line frequency domain MIMO control for swept sine testing proposed in this paper is closely dependent on the capability of accurately tracking the amplitude and the phase of the response (to be corrected) and the drive (to be updated) waveforms, as shown in Fig. 13.2. The idea of this paper is to use an on-line implementation of a traditional Harmonic Estimator, as currently adopted, for example, in the Siemens Simcenter Testlab Sine Control application [16]. For a general sinusoidal waveform with fundamental natural frequency 2πωf y(t) = |y(t)| sin[ωft +φ(t)]=ac cos(ωft) +as sin(ωft) (13.6) the amplitude and phase |y(t)| =.a2 c +a 2 s (13.7a) φ(t) =atan ac as (13.7b) can be calculated assuming that, withinpperiods, Eq. (13.6) holds, and therefore the parameters ac andas can be estimated in a least square sense using the acquired data (left-hand-side of Eq. (13.6)). For the on-line estimation during a continuous sine sweep, the frequency of the signals, and therefore the argument (t) +φ(t) of the sine wave in Eq. (13.6), continuously varies with a specific sweep mode (linear or logarithmic), as reported in Table 13.1.
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