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Eigenvalue/eigenvector assignment using output feedback

The problem of eigenvalue assignment in a linear time-invariant system using output feedback is considered. New sufficient conditions are derived to assign an almost arbitrary set of minimum (n,m + r - 1) distinct eigenvalues where n, m, and r are the number of states, inputs, and outputs, respectively. These conditions precisely identify the class of systems where such an assignment is impossible. The synthesis technique also highlights the freedom in selection of closed-loop eigenvectors under output feedback. The utility of eigenvalue/eigenvector assignment in transient response shaping is illustrated by the design of a controller for the lateral dynamics of an aircraft.

Srinathkumar, S.

Computation of output feedback gains for linear stochastic systems using the Zangwill-Powell method

Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell.

Kaufman, H.

Cold-air investigation of a 4 1/2 stage turbine with stage-loading factor of 4.66 and high specific work output. 2: Stage group performance

The stage group performance of a 4 1/2 stage turbine with an average stage loading factor of 4.66 and high specific work output was determined in cold air at design equivalent speed. The four stage turbine configuration produced design equivalent work output with an efficiency of 0.856; a barely discernible difference from the 0.855 obtained for the complete 4 1/2 stage turbine in a previous investigation. The turbine was designed and the procedure embodied the following design features: (1) controlled vortex flow, (2) tailored radial work distribution, and (3) control of the location of the boundary-layer transition point on the airfoil suction surface. The efficiency forecast for the 4 1/2 stage turbine was 0.886, and the value predicted using a reference method was 0.862. The stage group performance results were used to determine the individual stage efficiencies for the condition at which design 4 1/2 stage work output was obtained. The efficiencies of stages one and four were about 0.020 lower than the predicted value, that of stage two was 0.014 lower, and that of stage three was about equal to the predicted value. Thus all the stages operated reasonably close to their expected performance levels, and the overall (4 1/2 stage) performance was not degraded by any particularly inefficient component.

Whitney, W. J.

On the power output of some idealized source configurations with one or more characteristic dimensions

The calculation of power output from a (finite) linear array of equidistant point sources is investigated with allowance for a relative phase shift and particular focus on the circumstances of small/large individual source separation. A key role is played by the estimates found for a twin parameter definite integral that involves the Fejer kernel functions, where N denotes a (positive) integer; these results also permit a quantitative accounting of energy partition between the principal and secondary lobes of the array pattern. Continuously distributed sources along a finite line segment or an open ended circular cylindrical shell are considered, and estimates for the relatively lower output in the latter configuration are made explicit when the shell radius is small compared to the wave length. A systematic reduction of diverse integrals which characterize the energy output from specific line and strip sources is investigated.

Levine, H.

Recent results on output feedback problems

Given a real linear system sigma = (A, B, C) with m inputs, p outputs and degree n, the problem of generic pole placement by output feedback is studied, which is to compute the constant C(m,p) such that the inequality C(m,p) not less than n is necessary and sufficient for generically positioning the poles of the generic linear system by constant output feedback. A constant C prime (m,p) is determined, which gives a sufficient condition for generic pole placement and which, to the best of the author's knowledge, is at least as good an estimate of C(m,p) as any in the literature. Some results on the construction of solutions in case mp = n are announced, based on the degree formula of Brockett and Byrnes and the Galois theory. In particular, a question raised by Anderson, Bose, and Jury, on the existence of a rational procedure for computing the feedback law from the desired characteristic polynomial is answered.

Byrnes, C. I.

Design of hydraulic output Stirling engine

A hydraulic output system for the RE-1000 free piston stirling engine (FPSE) was designed. The hydraulic output system can be readily integrated with the existing hot section of RE-1000 FPSE. The system has two simply supported diaphragms which separate the engine gas from the hydraulic fluid, a dynamic balance mechanism, and a novel, null center band hydraulic pump. The diaphragms are designed to endure more than 10 billion cycles, and to withstand the differential pressure load as high as 14 MPa. The projected thermodynamic performance of the hydraulic output version of RE-1000 FPSE is 1.87 kW at 29/7 percent brake efficiency.

Toscano, W. M.

Algorithms for output feedback, multiple-model, and decentralized control problems

The optimal stochastic output feedback, multiple-model, and decentralized control problems with dynamic compensation are formulated and discussed. Algorithms for each problem are presented, and their relationship to a basic output feedback algorithm is discussed. An aircraft control design problem is posed as a combined decentralized, multiple-model, output feedback problem. A control design is obtained using the combined algorithm. An analysis of the design is presented.

Halyo, N.

Research on output feedback control of systems with ill-conditioned dynamics

The accuracy of a two time scale approach to the output feedback regulator design problem is examined. An approximate quadratic performance index which reflects a two time scale decomposition of the system dynamics is developed. A sequential numerical algorithm is defined which obtains output feedback gains minimizing a broad class of performance indices, including the standard LQ case. A procedure for optimally zeroing selected gain elements in an output feedback gain matrix is developed and demonstrated. A summary of conference and journal publications from this research is also provided.

Calise, A. J.

Pole placement by static and dynamic output feedback

This paper gives new results concerning pole-assignability by static and dynamic output feedback, based on the interpretation of transfer functions, feedback laws, poles and zeroes in terms of the incidence geometry of m-planes and p-planes in (m+p)-space. As an illustration of the most basic ideas, a short proof of the Brasch-Pearson theorem is given. A more careful analysis of this proof yields a significant extension of this theorem, which is considerably sharpened in the case of pole-assignment by constant gain output feedback. As a final application, a root-locus design technique for non-square systems is introduced: zero placement by pre- or post-compensation. This zero placement problem is then analyzed by methods similar to those developed for pole placement by output feedback.

Byrnes, C. I.

Multiple-Winding Output Inductors for Power Converters

Design procedure developed for dc-to-dc power converters with multiple outputs having inductors wound on common core. With common core, minimum load current consistent with good output regulation is lower, output regulation is improved, and total inductor size and weight is reduced.

Mclyman, W. T.

Input-output characterization of an ultrasonic testing system by digital signal analysis

Ultrasonic test system input-output characteristics were investigated by directly coupling the transmitting and receiving transducers face to face without a test specimen. Some of the fundamentals of digital signal processing were summarized. Input and output signals were digitized by using a digital oscilloscope, and the digitized data were processed in a microcomputer by using digital signal-processing techniques. The continuous-time test system was modeled as a discrete-time, linear, shift-invariant system. In estimating the unit-sample response and frequency response of the discrete-time system, it was necessary to use digital filtering to remove low-amplitude noise, which interfered with deconvolution calculations. A digital bandpass filter constructed with the assistance of a Blackman window and a rectangular time window were used. Approximations of the impulse response and the frequency response of the continuous-time test system were obtained by linearly interpolating the defining points of the unit-sample response and the frequency response of the discrete-time system. The test system behaved as a linear-phase bandpass filter in the frequency range 0.6 to 2.3 MHz. These frequencies were selected in accordance with the criterion that they were 6 dB below the maximum peak of the amplitude of the frequency response. The output of the system to various inputs was predicted and the results were compared with the corresponding measurements on the system.

Williams, J. H., Jr.

Validation and application of single breath cardiac output determinations in man

The results of a procedure for estimating cardiac output by a single-breath technique (Qsb), obtained in healthy males during supine rest and during exercise on a bicycle ergometer, were compared with the results on cardiac output obtained by the direct Fick method (QF). The single breath maneuver consisted of a slow exhalation to near residual volume following an inspiration somewhat deeper than normal. The Qsb calculations incorporated an equation of the CO2 dissociation curve and a 'moving spline' sequential curve-fitting technique to calculate the instantaneous R from points on the original expirogram. The resulting linear regression equation indicated a 24-percent underestimation of QF by the Qsb technique. After applying a correction, the Qsb-QF relationship was improved. A subsequent study during upright rest and exercise to 80 percent of VO2(max) in 6 subjects indicated a close linear relationship between Qsb and VO2 for all 95 values obtained, with slope and intercept close to those in published studies in which invasive cardiac output measurements were used.

Loeppky, J. A.

Reliability of voting in fault-tolerant software systems for small output spaces

Under a voting strategy in a fault-tolerant software system there is a difference between correctness and agreement. An independent N-version programming reliability model is proposed for treating small output spaces which distinguishes between correctness and agreement. System reliability is investigated using analytical relationships and simulation. A consensus majority voting strategy is proposed and its performance is analyzed and compared with other voting strategies. Consensus majority strategy automatically adapts the voting to different component reliability and output space cardinality characteristics. It is shown that absolute majority voting strategy provides a lower bound on the reliability provided by the consensus majority, and 2-of-n voting strategy an upper bound. If r is the cardinality of the output space it is proved the 1/r is a lower bound on the average reliability of fault-tolerant system components below which the system reliability begins to deteriorate as more versions are added.

Mcallister, David F.

Nonlinear input-output systems

Necessary and sufficient conditions that the nonlinear system dot-x = f(x) + ug(x) and y = h(x) be locally feedback equivalent to the controllable linear system dot-xi = A xi + bv and y = C xi having linear output are found. Only the single input and single output case is considered, however, the results generalize to multi-input and multi-output systems.

Hunt, L. R.

Input-output characterization of fiber composites by SH waves

Input-output characterization of fiber composites is studied theoretically by tracing SH waves in the media. A fiberglass epoxy composite is modeled as a homogeneous transversely isotropic continuum plate. The reflection of an SH wave at a stress-free plane boundary in a semi-infinite transversely isotropic medium is considered first. It is found that an incident SH wave reflects only a similar SH wave back into the medium. It is also established that the angle of reflection of the reflected wave is equal to the angle of incidence of the incident wave. The phase velocity of the SH waves and the delay time of the SH waves in reaching the receiving transducer are computed as functions of a reflection index, defined as the number of reflections of the SH waves from the bottom face of the continuum plate. The directivity function corresponding to the shear stress associated with the SH waves in the continuum plate is also derived as a function of the reflection index. A theoretical output voltage from the receiving transducer is calculated for a tone burst (a periodic input voltage of finite duration). The output voltage is shown for tone bursts of duration 60 microseconds and center frequencies of 0.75, 1.00, and 1.25 MHz. The study enhances the quantitative and qualitative understanding of the nondestructive evaluation (NDE) of fiber composites which can be modeled as transversely isotropic media.

Renneisen, John D.

Output-Isolation And Protection Circuit

Output-isolation circuit couples precise analog signals (-10 to +10 V, 0 to 20 kHz) from computer or from other electronic equipment to external electronic equipment that may be at different ground potential. Circuit functions in presence of common-mode voltages up to 2,500 Vac or 3,500 Vdc. To prevent damage from accidental connection of output leads to powerlines or other sources of high voltage, circuit includes features that protect input and output signal lines against normal-mode overvoltages up to 120 V ac or dc.

Wagner, Charles A.

Output Control Using Feedforward And Cascade Controllers

Report presents theoretical study of open-loop control elements in single-input, single-output linear system. Focus on output-control (servomechanism) problem, in which objective is to find control scheme that causes output to track certain command inputs and to reject certain disturbance inputs in steady state. Report closes with brief discussion of characteristics and relative merits of feedforward, cascade, and feedback controllers and combinations thereof.

Seraji, Homayoun

Output model-following control synthesis for an oblique-wing aircraft

Recent interest in oblique-wing aircraft has focused on the potential aerodynamic performance advantage of a variable-skew oblique wing over a conventional or symmetric sweep wing. Unfortunately, the resulting asymmetric configuration has significant aerodynamic and inertial cross-coupling between the aircraft longitudinal and lateral-directional axes. Presented here is a decoupling control law synthesis technique that integrates stability augmentation, decoupling, and the direct incorporation of desired handling qualities into an output feedback controller. The proposed design technique uses linear quadratic regulator concepts in the framework of explicit model following. The output feedback strategy used is a suboptimal projection from the state space to the output space. Dynamics are then introduced into the controller to improve steady-state performance and increase system robustness. Closed-loop performance is shown by application of the control laws to the linearized equations of motion and nonlinear simulation of an oblique-wing aircraft.

Pahle, Joseph W.