Admittance-Based Stability Analysis: Bode Plots, Nyquist Diagrams or Eigenvalue Analysis?
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Practical robustness measures in multivariable control system analysis
The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.
Lehtomaki, N. A.↗
Lateral control system design for VTOL landing on a DD963 in high sea states
The problem of designing lateral control systems for the safe landing of VTOL aircraft on small ships is addressed. A ship model is derived. The issues of estimation and prediction of ship motions are discussed, using optimal linear linear estimation techniques. The roll motion is the most important of the lateral motions, and it is found that it can be predicted for up to 10 seconds in perfect conditions. The automatic landing of the VTOL aircraft is considered, and a lateral controller, defined as a ship motion tracker, is designed, using optimal control techniqes. The tradeoffs between the tracking errors and the control authority are obtained. The important couplings between the lateral motions and controls are demonstrated, and it is shown that the adverse couplings between the sway and the roll motion at the landing pad are significant constraints in the tracking of the lateral ship motions. The robustness of the control system, including the optimal estimator, is studied, using the singular values analysis. Through a robustification procedure, a robust control system is obtained, and the usefulness of the singular values to define stability margins that take into account general types of unstructured modelling errors is demonstrated. The minimal destabilizing perturbations indicated by the singular values analysis are interpreted and related to the multivariable Nyquist diagrams.
Bodson, M.↗
Design and test of three active flutter suppression controllers
Three flutter suppression control law design techniques are presented. Each uses multiple control surfaces and/or sensors. The first uses linear combinations of several accelerometer signals together with dynamic compensation to synthesize the modal rate of the critical mode for feedback to distributed control surfaces. The second uses traditional tools (pole/zero loci and Nyquist diagrams) to develop a good understanding of the flutter mechanism and produce a controller with minimal complexity and good robustness to plant uncertainty. The third starts with a minimum energy Linear Quadratic Gaussian controller, applies controller order reduction, and then modifies weight and noise covariance matrices to improve multi-variable robustness. The resulting designs were implemented digitally and tested subsonically on the Active Flexible Wing (AFW) wind tunnel model. Test results presented here include plant characteristics, maximum attained closed-loop dynamic pressure, and Root Mean Square control surface activity. A key result is that simultaneous symmetric and antisymmetric flutter suppression was achieved by the second control law, with a 24 percent increase in attainable dynamic pressure.
Christhilf, David M.↗
A scheme for theoretical and experimental evaluation of multivariable system stability robustness
A scheme for theoretical and experimental evaluation of multivariable system stability robustness measures is described. The experimental scheme is based on the estimation of frequency responses from power-spectra analyses of a set of time responses due to sine-sweep excitation at each input and then computation of the appropriate singular values. The procedure can also be used on an open-loop stable system to predict the closed-loop stability before closing the loop. Classical Nyquist diagrams can also be constructed to determine one-loop-at-a-time gain or phase margins. The scheme has been implemented in a wind tunnel test for singular-value evaluation of digital flutter suppression control laws and compared with theory. The singular values at the plant input and output of the actual system and the theoretical model are qualitatively similar but have some discrepancies.
Mukhopadhyay, Vivek↗
Design, test, and evaluation of three active flutter suppression controllers
Three control law design techniques for flutter suppression are presented. Each technique uses multiple control surfaces and/or sensors. The first method uses traditional tools (such as pole/zero loci and Nyquist diagrams) for producing a controller that has minimal complexity and which is sufficiently robust to handle plant uncertainty. The second procedure uses linear combinations of several accelerometer signals and dynamic compensation to synthesize the model rate of the critical mode for feedback to the distributed control surfaces. The third technique starts with a minimum-energy linear quadratic Gaussian controller, iteratively modifies intensity matrices corresponding to input and output noise, and applies controller order reduction to achieve a low-order, robust controller. The resulting designs were implemented digitally and tested subsonically on the active flexible wing wind-tunnel model in the Langley Transonic Dynamics Tunnel. Only the traditional pole/zero loci design was sufficiently robust to errors in the nominal plant to successfully suppress flutter during the test. The traditional pole/zero loci design provided simultaneous suppression of symmetric and antisymmetric flutter with a 24-percent increase in attainable dynamic pressure. Posttest analyses are shown which illustrate the problems encountered with the other laws.
Adams, William M., Jr.↗
On panel flutter and divergence of infinitely long unstiffened and ring-stiffened thin-walled circular cylinders
A preliminary theoretical investigation of the panel flutter and divergence of infinitely long, unstiffened and ring-stiffened thin-walled circular cylinders is described. Linearized unsteady potential-flow theory is utilized in conjunction with Donnell's cylinder theory to obtain equilibrium equations for panel flutter. Where necessary, a simplified version of Flugge's cylinder theory is used to obtain greater accuracy. By applying Nyquist diagram techniques, analytical criteria for the location of stability boundaries are derived. A limited number of computed results are presented.
Leonard, Robert W↗
Stability margin analysis of the Holos-quad microreactor design
A simplified point model of the Holos-Quad microreactor is introduced. The model is based on the point kinetics equations coupled to three heat balance equations, representing the mean temperatures of the fuel particles, the graphite moderator and the helium coolant. The differential equations are converted to the frequency domain, enabling the construction of the closed-loop reactor transfer function. Using this function the stability margins of the core design is analyzed for various power levels. It is shown that the gain margins approaches infinity, demonstrating the stability of the reactor for all power levels. The phase margin at nominal power is about 60 degrees, however it shows a non-monotonous dependence on power, with minimal value obtained for about 10% of nominal power. As power level is further increased, the phase margin also increases, demonstrating the reactor becomes more stable. This behavior may be of high importance in load-follow scenarios, where the power level of the reactor changes with time. (authors)
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Application of the MNA design method to a nonlinear turbofan engine
Using nonlinear digital simulation as a representative model of the dynamic operation of the QCSEE turbofan engine, a feedback control system is designed by variable frequency design techniques. Transfer functions are generated for each of five power level settings covering the range of operation from approach power to full throttle (62.5% to 100% full power). These transfer functions are then used by an interactive control system design synthesis program to provide a closed loop feedback control using the multivariable Nyquist array and extensions to multivariable Bode diagrams and Nichols charts.
Leininger, G. G.↗
Performance of the Dsa's Subcarrier Demodulation Digital Loop
The subcarrier demodulation digital loop is part of the baseband assembly. The subcarrier demodulator is a fourth-order Costas-type loop corresponding to a type 2 analog loop in terms of steady state response. The expected value and the variance of the error signal are determined as functions of the input SNR. A Nyquist sampling rate of the input signal is assumed. From the integro-difference equations a mixed s/z domain block diagram is obtained. From the loop's transfer function a set of gains for the loop filter is obtained. Also, a set of state equations is presented for future reference. Finally, the noise-equivalent bandwidths are calculated for normalized computation times of 0, 0.25 and 0.5. The subcarrier demodulator analyzed tracks a parabolic phase input with finite steady state error. Since at each update instant the loop gains are adjusted to compensate for the variations in SNR of the input signal, the noise-equivalent bandwidth is maintained constant.
Simon, M. K.↗
The Sr and Nd isotopic record of Apollo 12 basalts - Implications for lunar geochemical evolution
Alkali, alkaline earth, and rare earth element data are reported for several Apollo 12 basalts which are representative of the four Apollo 12 magma types. Results confirm the heterogeneity of the lunar mantle and show that the Sm/Nd ratio of at least the Apollo 12 ilmenite basalts was decreased by 13-24% during magma genesis. In addition, whole mare basalt Sm-Nd data are not collinear on an isochron diagram; thus it is no longer possible to explain these data via mixing of 'primitive material' and 'early differentiates' as in the hybridization and assimilation models.
Nyquist, L. E.↗
Rb-Sr age of the Shergotty achondrite and implications for metamorphic resetting of isochron ages
The age of the Shergotty achondrite is determined by Rb-Sr isotope analysis and the metamorphic resetting of isochron ages, which is presumed to have occurred during a shock event in the history of the meteorite, is discussed. The isochron best fitting the Rb-Sr evolution diagram is found to correspond to an age of 165 million years, with an initial Sr-87/Sr-86 value of 0.72260. Different apparent ages obtained by the K-Ar and Sm-Nd methods are interpreted in terms of a model which quantifies the degree of resetting of internal isochron ages by low temperature solid state diffusion. On the basis of these considerations, it is concluded that Shergotty crystallized from a melt 650 million years ago, was shock heated to 300 to 400 C after its parent body was involved in a collision 165 million years ago, and was first exposed to cosmic rays two million years ago.
Nyquist, L. E.↗
Fast Offset Laser Phase-Locking System
Figure 1 shows a simplified block diagram of an improved optoelectronic system for locking the phase of one laser to that of another laser with an adjustable offset frequency specified by the user. In comparison with prior systems, this system exhibits higher performance (including higher stability) and is much easier to use. The system is based on a field-programmable gate array (FPGA) and operates almost entirely digitally; hence, it is easily adaptable to many different systems. The system achieves phase stability of less than a microcycle. It was developed to satisfy the phase-stability requirement for a planned spaceborne gravitational-wave-detecting heterodyne laser interferometer (LISA). The system has potential terrestrial utility in communications, lidar, and other applications. The present system includes a fast phasemeter that is a companion to the microcycle-accurate one described in High-Accuracy, High-Dynamic-Range Phase-Measurement System (NPO-41927), NASA Tech Briefs, Vol. 31, No. 6 (June 2007), page 22. In the present system (as in the previously reported one), beams from the two lasers (here denoted the master and slave lasers) interfere on a photodiode. The heterodyne photodiode output is digitized and fed to the fast phasemeter, which produces suitably conditioned, low-latency analog control signals which lock the phase of the slave laser to that of the master laser. These control signals are used to drive a thermal and a piezoelectric transducer that adjust the frequency and phase of the slave-laser output. The output of the photodiode is a heterodyne signal at the difference between the frequencies of the two lasers. (The difference is currently required to be less than 20 MHz due to the Nyquist limit of the current sampling rate. We foresee few problems in doubling this limit using current equipment.) Within the phasemeter, the photodiode-output signal is digitized to 15 bits at a sampling frequency of 40 MHz by use of the same analog-to-digital converter (ADC) as that of the previously reported phasemeter. The ADC output is passed to the FPGA, wherein the signal is demodulated using a digitally generated oscillator signal at the offset locking frequency specified by the user. The demodulated signal is low-pass filtered, decimated to a sample rate of 1 MHz, then filtered again. The decimated and filtered signal is converted to an analog output by a 1 MHz, 16-bit digital-to-analog converters. After a simple low-pass filter, these analog signals drive the thermal and piezoelectric transducers of the laser.
Shaddock, Daniel↗
Oxygen Isotope Systematics of Chondrules from the Least Equilibrated H Chondrite
Oxygen isotope compositions of bulk chondrules and their mineral separates in type 3 ordinary chondrites (UOC) show several % variability in the oxygen three isotope diagram with slope of approx.0.7 [1]. In contrast, ion microprobe analyses of olivine and pyroxene phenocrysts in ferromagnesian chondrules from LL 3.0-3.1 chondrites show mass dependent isotopic fractionation as large as 5% among type I (FeO-poor) chondrules, while type II (FeO-rich) chondrules show a narrow range (less than or equal to 1%) of compositions [2]. The .Delta(exp 17)O (=delta(exp 17)O-0.52xdelta(exp 18)O) values of olivine and pyroxene in these chondrules show a peak at approx.0.7% that are systematically lower than those of bulk chondrule analyses as well as the bulk LL chondrites [2]. Further analyses of glass in Semarkona chondrules show .17O values as high as +5% with highly fractionated d18O (max +18%), implying O-16-poor glass in chondrules were altered as a result of hydration in the parent body at low temperature [3]. Thus, chondrules in LL3.0-3.1 chondrites do not provide any direct evidence of oxygen isotope exchange between solid precursor and O-16-depleted gas during chondrule melting events. To compare the difference and/or similarity between chondrules from LL and H chondrites, we initiated systematic investigations of oxygen isotopes in chondrules from Yamato 793408 (H3.2), one of the least equilibrated H chondrite [4]. In our preliminary study of 4 chondrules, we reported distinct oxygen isotope ratios from dusty olivine and refractory forsterite (RF) grains compared to their host chondrules and confirmed their relict origins [5].
Kita, N. T.↗