Phase (deg) Fig. 5. Amplitude-phase plot of the describing function for the vernier jet phase-plane code with r = 0.1 degls and d = 0.02 deg. A is in degrees.It is possible to numerically compute the describing function by taking the actual computer code for the phase-plane and driving it with the inputs w, = Awcos$ and Be = Asin$. The output is integrated using Simpson's rule and the results plotted in the gain-phase form.This permits the linearization, as defined by the describing function, of the exact computer code. The describing function for the vernier jet phase-plane for w = 0.04 Hz is illustrated in Fig. 5 . ffd has been set to zero for this analysis. The amplitude phase plot is qualitatively similar to the plot for the simplified phase-plane but there are several differences. In this case the phase angle never reaches -90 deg. This is due to Region 6 and Region 2 which always set the jets to off. The trajectory of the input completely encircles Regions 4 and 8 and never enters them for large values of A , but must always pass through Regions 6 and 2. This ensures that n, will always be less than zero thus causing the phase shift to be slightly more negative.In the upper left-hand comer the plot of the describing function forms a loop. This is due to the shelves formed by Region 9. This asymmetry about = x12 causes n4 to be nonzero even if the rate limits are not encountered. Because it is a function of A , it varies along with the gain, causing the loop. The numerically computed describing function produces a useful frequency-domain interpretation of the phase-plane.In the on-orbit autopilot the angular rate and attitude errors are calculated by a state estimator that derives those values from the gimbal angles of the inertial measurement unit on the orbiter. The state estimator also produces a disturbance acceleration estimate, a d . This estimate is based on a model that assumes that the external disturbance acceleration is a constant. The state estimator rate estimate has a second-order filter characteristic with a corner frequency of ~0 . 0 4 Hz. Gimbal angle measurements are input into the estimator at 6.25 Hz. The autopilot cycle time is 0.08 s. Every pass it estimates rate and disturbance acceleration. Every other pass it extrapolates attitude from the previous cycle's measurements. As a result, the rate and attitude errors are not simple functions of the measured attitude. The effects of the state estimator may be incorporated into the describing function analysis by feeding the input, Asin$, into the input of the state estimator, which drives the phase plane, and measuring the output at the output of the phase-plane logic, as was done above. The describing function for the combination state estimator and phase-plane is illustrated in Fig. 6. The primary effect of the state estimator is to increase the phase shift by 90 deg. IV. CONCLUSIONSThe use of frequency-dependent describing functions for the analysis of digital controller stability is described. This method permits the determination of li...
This paper deals with persistent oscillations in position and attitude observed in flight on a piloted VTOL during precision hover. Properties of the oscillation are shown to correlate strongly with Cooper-Harper pilot ratings. A simple yet nonlinear pilot model is developed which predicts many of the properties of the pilot-inthe-loop system behavior. Configuration 217CK+ N(E) PR ll s Tx Nomenclature = properties of the ideal relay with dead zone (Af=0.25 in., >1 =0.125 in.) = configuration C of X-22A flight 217 = error in X position, -X C -X (ft) = amplitude of sinusoidal input to nonlinear element N(E) = pilot position error gain (in./ft) = ratio of steady state x translational velocity per inch of pilot's stick position (ft/s/in.) . = minimum pilot position error gain to maintain a stable limit cycle (in./ft) = describing function gain which is a nonlinear function of sinusoidal input amplitude E = Cooper-Harper pilot rating (Ref. 1) = quantization nonlinearity, Fig.9 = Laplace operator for differentiation = equivalent path mode time constant, s = fore and aft position, ft = commanded position, ft = pilot's stick position (positive stick aft, in.) -modified stick position (positive stick forward, in.) = -d s = body-axis pitch attitude, deg = limit-cycle frequency
A287were conducted. Results: Mifamurtide, gefitinib, natalizumab and tocilizumab were included in the study. Results depict how micro-level variables influenced these decision processes. These include: managed entry agreements, ICER levels, orphan, type of evidence appraised and how it was interpreted (dealing with uncertainty). Their interface with macro-level variables was explored. These included, among others, the advisory or regulatory nature of the HTA bodies, the ability to carry out external reviews of the evidence, stakeholder involvement processes or the initiator of the HTA process. For example, patient input contributed to addressing uncertainty in countries with formal processes for patient involvement, but not in those without a formal process. ConClusions: Results demonstrate the close association between the micro and macro-level factors. Nevertheless, there were instances where no clear pattern or relationship between these two levels arose. These may relate to micro-level variables, such as the subjective interpretation of the committees making the decision, or to contextual elements, such as a country's industrial policy. We conclude that although these processes are systematic and rely on evidence-based medicine, a component of these decisions rely on judgments made during the deliberative process.
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