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Limit cycles identified in systems with multiple nonlinearities and multiple paths. Feedback control system or other physical system with feedback has several forward signal paths with both linear and nonlinear elements in each path. New algorithm finds limit cycles for systems of this configuration. Applied to systems of general type.
A pole placement algorithm is proposed which uses constrained nonlinear optimization techniques on a finite dimensional model of a linear n degree of freedom system. Low order feedback control is assumed where r poles may be assigned; r being the rank of the sensor coefficient matrix. It is shown that by combining feedback control theory methods with optimization techniques, one can ensure the stability characteristics of a system, and can alter its transient response.
The objectives of this program were: to verify the model of off schedule compressor variable geometry in the T700 turboshaft engine nonlinear model; to evaluate the use of the pseudo-random binary noise (PRBN) technique for obtaining engine frequency response data; and to design a high performance power turbine speed governor using modern control methods. Reduction of T700 engine test data generated at NASA-Lewis indicated that the off schedule variable geometry effects were accurate as modeled. Analysis also showed that the PRBN technique combined with the maximum likelihood model identification method produced a Bode frequency response that was as accurate as the response obtained from standard sinewave testing methods. The frequency response verified the accuracy of linear models consisting of engine partial derivatives and used for design. A power turbine governor was designed using the Linear Quadratic Regulator (LQR) method of full state feedback control. A Kalman filter observer was used to estimate helicopter main rotor blade velocity. Compared to the baseline T700 power turbine speed governor, the LQR governor reduced droop up to 25 percent for a 490 shaft horsepower transient in 0.1 sec simulating a wind gust, and up to 85 percent for a 700 shaft horsepower transient in 0.5 sec simulating a large collective pitch angle transient.
Robotic control system causes remote manipulator to follow closely reference trajectory in Cartesian reference frame in work space, without resort to computationally intensive mathematical model of robot dynamics and without knowledge of robot and load parameters. System, derived from linear multivariable theory, uses relatively simple feedforward and feedback controllers with model-reference adaptive control.
An important issue in the control of practical systems is the effect of model uncertainty on closed loop performance. This is of particular concern when flexible structures are to be controlled, due to the fact that states associated with higher frequency vibration modes are truncated in order to make the control problem tractable. Digital simulations of a single-link manipulator system are employed to demonstrate that passive damping added to the flexible member reduces adverse effects associated with model uncertainty. A controller was designed based on a model including only one flexible mode. This controller was applied to larger order systems to evaluate the effects of modal truncation. Simulations using a Linear Quadratic Regulator (LQR) design assuming full state feedback illustrate the effect of control spillover. Simulations of a system using output feedback illustrate the destabilizing effect of observation spillover. The simulations reveal that the system with passive damping is less susceptible to these effects than the untreated case.
Powerful electromechanical linear actuator designed to replace hydraulic actuator. Cleaner, simpler, and needs less maintenance. Features rotary-to-linear-motion converter with antibacklash gearing and position feedback via shaft-angle resolvers, which measure rotary motion.
Method of designing approximately balanced, low-order linear-quadratic-Gaussian LQG compensator for use in feedback control of flexible structure devised. Low-order controller and estimator controls flexible structure efficiently.
In this report, we provide some examples of French, Russian, Chinese, and Japanese launch vehicles that have utilized fins in their designs. Next, the aerodynamic design of the fins is considered in Section 3. Some comments on basic static stability and control theory are followed by a brief description of an aerodynamic characteristics prediction code that was used to estimate the characteristics of a modified NLS 1.5 Stage vehicle. Alternative fin designs are proposed and some estimated aerodynamic characteristics presented and discussed. Also included in Section 3 is a discussion of possible methods of enhancement of the aerodynamic efficiency of fins, such as vortex generators and jet flaps. We consider the construction of fins for launch vehicles in Section 4 and offer an assessment of the state-of-the-art in the use of composites for aerodynamic control surfaces on high speed vehicles. We also comment on the use of smart materials for launch vehicle fins. The dynamic stability and control of a launch vehicle that utilizes both thrust vector control (engine nozzle gimballing) and movable fins is the subject addressed in Section 5. We give a short derivation of equations of motion for a launch vehicle moving in a vertical plane above a spherical earth, discuss the use of a gravity-turn nominal trajectory, and give the form of the period equations linearized about such a nominal. We then consider feedback control of vehicle attitude using both engine gimballing and fin deflection. Conclusions are stated and recommendations made in Section 6. An appendix contains aerodynamic data in tabular and graphical formats.
This paper considers an algorithm for synthesis of optimal controllers for full information feedback. The synthesis procedure reduces to a single linear matrix inequality which may be solved via established convex optimization algorithms. The computational cost of the optimization is investigated. It is demonstrated the problem dimension and corresponding matrices can become large for practical engineering problems. This algorithm represents a process that is impractical for standard workstations for large order systems. A flexible structure is presented as a design example. Control synthesis requires several days on a workstation but may be solved in a reasonable amount of time using a Cray supercomputer.
A paradigm for control law design for modern engineering systems is proposed: Minimize control law complexity subject to the achievement of a specified accuracy in the face of a specified level of uncertainty. Correspondingly, the overall goal is to make progress towards the development of a control law design methodology which supports this paradigm. Researchers achieve this goal by developing a general theory of optimal constrained-structure dynamic output feedback compensation, where here constrained-structure means that the dynamic-structure (e.g., dynamic order, pole locations, zero locations, etc.) of the output feedback compensation is constrained in some way. By applying this theory in an innovative fashion, where here the indicated iteration occurs over the choice of the compensator dynamic-structure, the paradigm stated above can, in principle, be realized. The optimal constrained-structure dynamic output feedback problem is formulated in general terms. An elegant method for reducing optimal constrained-structure dynamic output feedback problems to optimal static output feedback problems is then developed. This reduction procedure makes use of star products, linear fractional transformations, and linear fractional decompositions, and yields as a byproduct a complete characterization of the class of optimal constrained-structure dynamic output feedback problems which can be reduced to optimal static output feedback problems. Issues such as operational/physical constraints, operating-point variations, and processor throughput/memory limitations are considered, and it is shown how anti-windup/bumpless transfer, gain-scheduling, and digital processor implementation can be facilitated by constraining the controller dynamic-structure in an appropriate fashion.
The neighboring extremal feedback control law is developed for systems with a piecewise linear control for the case where the optimal control is obtained by nonlinear programming techniques. To develop the control perturbation for a given deviation from the nominal path, the second variation is minimized subject to the constraint that the final conditions be satisfied. This process leads to a feedback relationship between the control perturbation and the measured deviation from the nominal state.
The neighboring optimal feedback control law is developed for systems with a piecewise linear control for the case where the optimal control is obtained by nonlinear programming techniques. To develop the control perturbation for a given deviation from the nominal path, the second variation is minimized subject to the constraint that the final conditions be satisfied (neighboring suboptimal control). This process leads to a feedback relationship between the control perturbation and the measured deviation from the nominal state. Neighboring suboptimal control is applied to the lunar launch problem. Two approaches, single optimization and multiple optimization for calculating the gains are used, and the gains are tested in a guidance simulation with a mismatch in the acceleration of gravity. Both approaches give acceptable results, but multiple optimization keeps the perturbed path closer to the nominal path.
The neighboring optimal feedback control law is developed for systems with a piecewise linear control for the case where the optimal control is obtained by nonlinear programming techniques. To develop the control perturbation for a given deviation from the nominal path, the second variation is minimized subject to the constraint that the final conditions be satisfied (neighboring suboptimal control). This process leads to a feedback relationship between the control perturbation and the measured deviation from the nominal state. Neighboring suboptimal control is applied to the lunar launch problem. Two approaches, single optimization and multiple optimization, for calculating the gains are used, and the gains are tested in a guidance simulation with a mismatch in the acceleration of gravity. Both approaches give acceptable results, but multiple optimization keeps the perturbed path closer to the nominal path.
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.
This paper deals with the problem of synthesizing or designing a feedback controller of fixed dynamic order. The closed loop specifications considered here are given in terms of a target performance vector representing a desired set of closed loop transfer functions connecting various signals. In general these point targets are unattainable with a fixed order controller. By enlarging the target from a fixed point set to an interval set the solvability conditions with a fixed order controller are relaxed and a solution is more easily enabled. Results from the parametric robust control literature can be used to design the interval target family so that the performance deterioration is acceptable, even when plant uncertainty is present. It is shown that it is possible to devise a computationally simple linear programming approach that attempts to meet the desired closed loop specifications.
It is generally accepted that human bipedal upright stance is achieved by feedback mechanisms that generate an appropriate corrective torque based on body-sway motion detected primarily by visual, vestibular, and proprioceptive sensory systems. Because orientation information from the various senses is not always available (eyes closed) or accurate (compliant support surface), the postural control system must somehow adjust to maintain stance in a wide variety of environmental conditions. This is the sensorimotor integration problem that we investigated by evoking anterior-posterior (AP) body sway using pseudorandom rotation of the visual surround and/or support surface (amplitudes 0.5-8 degrees ) in both normal subjects and subjects with severe bilateral vestibular loss (VL). AP rotation of body center-of-mass (COM) was measured in response to six conditions offering different combinations of available sensory information. Stimulus-response data were analyzed using spectral analysis to compute transfer functions and coherence functions over a frequency range from 0.017 to 2.23 Hz. Stimulus-response data were quite linear for any given condition and amplitude. However, overall behavior in normal subjects was nonlinear because gain decreased and phase functions sometimes changed with increasing stimulus amplitude. "Sensory channel reweighting" could account for this nonlinear behavior with subjects showing increasing reliance on vestibular cues as stimulus amplitudes increased. VL subjects could not perform this reweighting, and their stimulus-response behavior remained quite linear. Transfer function curve fits based on a simple feedback control model provided estimates of postural stiffness, damping, and feedback time delay. There were only small changes in these parameters with increasing visual stimulus amplitude. However, stiffness increased as much as 60% with increasing support surface amplitude. To maintain postural stability and avoid resonant behavior, an increase in stiffness should be accompanied by a corresponding increase in damping. Increased damping was achieved primarily by decreasing the apparent time delay of feedback control rather than by changing the damping coefficient (i.e., corrective torque related to body-sway velocity). In normal subjects, stiffness and damping were highly correlated with body mass and moment of inertia, with stiffness always about 1/3 larger than necessary to resist the destabilizing torque due to gravity. The stiffness parameter in some VL subjects was larger compared with normal subjects, suggesting that they may use increased stiffness to help compensate for their loss. Overall results show that the simple act of standing quietly depends on a remarkably complex sensorimotor control system.
The problem of maneuvering a flexible spacecraft through a large angle while requiring the feedback control system to track a desired output state is considered. The desired output state is assumed to be provided by the corresponding open-loop maneuvering solution for the linear system model. Closed form solutions are provided for the Riccati and prefilter equations defining the optimal control. Example maneuvers are presented where control-rate penalties have been included in the performance index, in order to smooth both the open- and closed-loop control commands.
The design of scalar and multi-variable feedback control systems for the GET700 turboshaft engine coupled to a helicopter rotor system is examined. A series of linearized models are presented and analyzed. Robustness and performance specifications are posed in the frequency domain. The linear-quadratic-Gaussian with loop-transfer-recovery (LQG/LTR) methodology is used to obtain a sequence of three feedback designs. Even in the single-input/single-output case, comparison of the current control system with that derived from the LQG/LTR approach shows significant performance improvement. The multi-variable designs, evaluated using linear and nonlinear simulations, show even more potential for performance improvement.