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The computer program known as QR is described. Classical control systems analysis and synthesis (root locus, time response, and frequency response) can be performed using this program. Programming details of the QR program are presented.
The synthesis and experimental validation of a control law for an active flutter suppression system for the Active Flexible Wing wind-tunnel model is presented. The design was accomplished with traditional root locus and Nyquist methods using interactive computer graphics tools and with extensive use of simulation-based analysis. The design approach relied on a fundamental understanding of the flutter mechanism to formulate understanding of the flutter mechanism to formulate a simple control law structure. Experimentally, the flutter suppression controller succeeded in simultaneous suppression of two flutter modes, significantly increasing the flutter dynamic pressure despite errors in the design model. The flutter suppression controller was also successfully operated in combination with a rolling maneuver controller to perform flutter suppression during rapid rolling maneuvers.
The design of a control law for simultaneously suppressing the symmetric and antisymmetric flutter modes of a sting mounted fixed-in-roll aeroelastic wind-tunnel model is described. The flutter suppression control law was designed using linear quadratic Gaussian theory, and it also involved control law order reduction, a gain root-locus study, and use of previous experimental results. A 23 percent increase in the open-loop flutter dynamic pressure was demonstrated during the wind-tunnel test. Rapid roll maneuvers at 11 percent above the symmetric flutter boundary were also performed when the model was in a free-to-roll configuration.
This paper presents the design of digital rebalance loops for a tuned-rotor gyro which is intended to be an attitude sensor in a strapdown inertial measurement unit. A tuned-rotor gyro is a two-degree-of-freedom gyro which has two input axes, with cross-coupling between them. The rebalance loop of the gyro serves for two purposes. First, it restores the position of the rotor to its null position after experiencing an attitude input. Second, the rebalancing signal, which is proportional to the attitude change, is calibrated to give the desired attitude information. Since the gyro has more than one input and one output, a multivariable control technique is needed for designing the rebalance loop. The analytic model for the gyro is described and the available design methods are examined. A new root-locus design technique specially developed for the present problem is outlined. The design of the rebalance loop using the new technique is given. The computer simulation result of the designed system is presented and discussed.
Interactive controls analysis (INCA) program developed to provide user-friendly environment for design and analysis of linear control systems, primarily feedback control. Designed for use with both small- and large-order systems. Using interactive-graphics capability, INCA user quickly plots root locus, frequency response, or time response of either continuous-time system or sampled-data system. Configuration and parameters easily changed, allowing user to design compensation networks and perform sensitivity analyses in very convenient manner. Written in Pascal and FORTRAN.
The interactions of control system and distributed flexible structural dynamics is explored for mechanical arms. A modeling process using 4 x 4 transfer matrices is described which permits the closed loop response of many current arm configurations to be evaluated. Root locus, frequency response, modal shapes, and time impulse response have all been obtained from the digital computer implementation of this model, which is oriented to arm design and allows for easy variation of the arm configuration through data cards. The model corresponds with experimentally observed natural frequencies with an average error of less than 5% in the first three flexible modes in the seven cases considered. The model was used to explore the limits imposed by structural flexibility on a nondimensionalized two link arm with one and two joints for planar motion.
A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.
An analytical model has been used to study the problem of integrated control system/structural dynamic design. This model utilizes the traditional typical section lifting surface with a control surface attached in 2-D unsteady incompressible flow. The studies have as their purpose the examination of the use of the location of the elastic axis of the airfoil as a design variable in the search for an actively controlled configuration that has a specified flutter margin. Items of interest include the determination of flutter speed and divergence speed as functions of a nondimensional parameter, a sub c, that measures the location (in semi-chords) of the elastic axis with respect to the airfoil midchord. All other parameters are fixed. The behavior of velocity root locus curves with changes in a sub c is illustrated. Also shown is an example of the use of sensitivity derivatives to reposition poles of the open loop system. The behavior of the actively controlled or closed loop system is also discussed. A set of examples are presented to indicate how the shear center parameter, a sub c, affects the design of the controlled system.
A users guide to the Sampled Data Stability Analysis Program (SADSAP) is provided. This program is a general purpose sampled data Stability Analysis Program capable of providing frequency response on root locus data.
Stochastic robustness, a simple numerical procedure for estimating the stability robustness of linear, time-invariant systems, is applied to a forward-swept-wing aircraft control system. Based on Monte Carlo evaluation of the system's closed-loop eignevalues, this analysis approach introduces the probability of instability as a scalar stability robustness measure. The related stochastic root locus provides insight into robustness characteristics of the closed-loop system. Three Linear Quadratic controllers of decreasing robustness are chosen to demonstrate the use of stochastic robustness to analyze and compare control designs. Examples are presented illustrating the use of stochastic robustness analysis to address the effects of actuator dynamics and unmodeled dynamics on the stability robustness of the forward-swept-wing aircraft.
A propulsion controlled aircraft (PCA) system has been developed at NASA Dryden Flight Research Center at Edwards Air Force Base, California, to provide safe, emergency landing capability should the primary flight control system of the aircraft fail. As a result of the successful PCA work being done at NASA Dryden, this project investigated the possibility of incorporating the PCA system as a backup flight control system in the design of a large, ultra-high capacity megatransport in such a way that flight path control using only the engines is not only possible, but meets MIL-Spec Level 1 or Level 2 handling quality requirements. An 800 passenger megatransport aircraft was designed and programmed into the NASA Dryden simulator. Many different analysis methods were used to evaluate the flying qualities of the megatransport while using engine thrust for flight path control, including: (1) Bode and root locus plot analysis to evaluate the frequency and damping ratio response of the megatransport; (2) analysis of actual simulator strip chart recordings to evaluate the time history response of the megatransport; and (3) analysis of Cooper-Harper pilot ratings by two NaSA test pilots.
The translational and attitude control of a drag-free, rotating satellite are usually designed to be independent of each other. However, coupling may exist which can produce instability. The different types of coupling and the stability conditions are studied, using root locus type techniques. The resulting root loci have unusual shapes due to the nonlinearity of the characteristic polynomial in terms of the coupling parameters. It is possible, however, to use standard root loci techniques by appropriate factoring and subsequent superposition of loci. The effect of the main parameters upon the overall stability of the system is studied. Both, attitude and translation instabilities eventually arise - the former being more critical for typical satellite designs. An analytical expression for the stability boundary is developed.
By using traditional control concepts of gain root locus, the active suppression of a flutter mode of a flexible wing is examined. It is shown that the attraction of the unstable mode towards a critical system zero determines the degree to which the flutter mode can be stabilized. For control situations where the critical zero is adversely placed in the complex plane, a novel compensation scheme called a 'Dipole' filter is proposed. This filter ensures that the flutter mode is stabilized with acceptable control energy. The control strategy is illustrated by designing flutter suppression laws for an active flexible wing (AFW) wind-tunnel model, where minimal control effort solutions are mandated by control rate saturation problems caused by wind-tunnel turbulence.
A modified linear quadratic Gaussian (LQG) synthesis procedure has been used to design low-order robust multiloop controllers for a flexible airplane. The introduction of properly constructed fictitious Gauss-Markov processes in the control loops allowed meeting classical frequency-domain stability criteria using the direct synthesis procedures of modern time-domain control theory. Model reduction was used to simplify the control laws to the point where they could be easily implemented on onboard flight computers. These control laws provided excellent gust load and flutter mode control with good stability margins and compared very favorably to other control laws synthesized by the classical root-locus technique.
It is argued that the design of a single input single output (SISO) control system is simplified if the designer has direct control over the closed loop poles. A space-laser-communications design example utilizing a two-transform algorithm that constructs a generic discrete compensator is presented. The plant in the example has an anti-aliasing filter, a double integrator, a torquer time constant, and a sample-and-hold as continuous elements, and a discrete proportional plus integral module. This fifth-order system is representative of many instrument pointing control systems. Poles resulting from the compensator are placed near the origin of the Z-plane so that the response is dominated by the closed loop poles from the plant. Root locus, time response, and frequency response data are given. Normalization by the sample interval is used to provide a dimensionless example.
The constant lift rotor (CLR) employs a control input of pitch moment to several airfoil sections which are free to pivot on a continuous spar, allowing them to change their pitch to obtain the desired lift. A flap-lag-torsion flutter analysis of a constant lift rotor blade in hover was developed. The blade model assumes rigid body flap and lead-lag motions at the root hinge and each strip undergoes an independent torsional motion. The results are presented in terms of root locus plots of complex eigenvalues as a function of thrust. The effects of several parameters (including structural damping, center of gravity and elastic axis offset from aerodynamic center, compressibility pitch-lag and pitch-flap coupling) on the blade dynamics are examined. With a suitable combination of lag damper and pitch-flap coupling, it is possible to design a constant lift rotor blade free from flutter instability.
Design procedures and supporting data necessary for configuring light aircraft to obtain desired responses to pilot commands and gusts are presented. The procedures employ specializations of modern military and jet transport practice where these provide an improvement over earlier practice. General criteria for riding and handling qualities are discussed in terms of the airframe dynamics. Methods available in the literature for calculating the coefficients required for a linearized analysis of the airframe dynamics are reviewed in detail. The review also treats the relation of spin and stall to airframe geometry. Root locus analysis is used to indicate the sensitivity of airframe dynamics to variations in individual stability derivatives and to variations in geometric parameters. Computer programs are given for finding the frequencies, damping ratios, and time constants of all rigid body modes and for generating time histories of aircraft motions in response to control inputs. Appendices are included presenting the derivation of the linearized equations of motion; the stability derivatives; the transfer functions; approximate solutions for the frequency, damping ratio, and time constants; an indication of methods to be used when linear analysis is inadequate; sample calculations; and an explanation of the use of root locus diagrams and Bode plots.
A real time adaptive controller was designed and tested successfully on a fourth order laboratory dynamic system which features very low structural damping and a noncolocated actuator sensor pair. The controller, implemented in a digital minicomputer, consists of a state estimator, a set of state feedback gains, and a frequency locked loop (FLL) for real time parameter identification. The FLL can detect the closed loop natural frequency of the system being controlled, calculate the mismatch between a plant parameter and its counterpart in the state estimator, and correct the estimator parameter in real time. The adaptation algorithm can correct the controller error and stabilize the system for more than 50% variation in the plant natural frequency, compared with a 10% stability margin in frequency variation for a fixed gain controller having the same performance at the nominal plant condition. After it has locked to the correct plant frequency, the adaptive controller works as well as the fixed gain controller does when there is no parameter mismatch. The very rapid convergence of this adaptive system is demonstrated experimentally, and can also be proven with simple root locus methods.