Large Initial Errors Research Articles

Performance improvement of in-flight alignment for autonomous vehicle under large initial heading error

The paper presents a new method of in-flight alignment (IFA) for a strapdown inertial navigation system (SDINS) aided by a super short baseline (SSBL) system under a large initial heading error. To handle the large heading error, a new attitude error model is introduced in which attitude errors are divided into heading and levelling errors using a newly defined horizontal frame. Some navigation error dynamic models are derived from the attitude error model for indirect feedback filtering of the IFA system. A Kalman filter with position measurements is designed to estimate navigation errors as an indirect feedback filter. Simulation results show that the newly developed model works effectively for coarse alignment of a large heading error. The proposed IFA method very quickly decreases the heading error from more than 40° to about 5°.

Nonlinear Recursive Minimum Model Error Estimation

A novel approach is presented for nonlinear recursive estimation of dynamic discrete-time systems with model uncertainties. The formulation of this estimation problem is the same as for minimum model error estimation, but the solution of the nonlinear two-point boundary-value problem is obtained using the technique of invariant imbedding so that the resulting algorithm can be implemented in real time. The advantage of the proposed estimation over other invariant-imbedding-based sequential estimators is that the covariance constraint condition developed in the minimum model error estimation is used to choose the weighting matrix and model errors are modeled as time-varying parameters whose variations are chosen to be minimal. The simulation results show that the proposed method is effective and feasible in obtaining optimal estimation for nonlinear systems with nonlinear measurements in the face of significant model errors and large initial condition errors.

Variable structure control of a class of uncertain systems

This brief paper proposes a method for tuning the parameters of a variable structure controller. The approach presented extracts the error at the output of the controller and applies a nonlinear tuning law using this error measure. The adaptation mechanism drives the state tracking error vector to the sliding hypersurface and maintains the sliding mode. In the simulations, the approach presented has been tested on the control of Duffing oscillator and the analytical claims have been justified under the existence of measurement noise, uncertainty and large nonzero initial errors.

Rest-to-rest motion for planar multi-link flexible manipulator

In this work we consider the problem of rest-to-rest motion for planar flexible multi-link manipulators. We introduce a simple idea permitting the cancellation of end-effector residual vibration when reaching a desired angular equilibrium position, in a fixed travelling time. No internal elastic damping effect is considered and the structure of the control is simply the sum of feedforward and joint feedback terms. The new approach concerns the computation of the feedforward control, which is based on backward integration of the elastic dynamics, starting from a rest position of the flexible arms. For fast rest-to-rest motion, the feedback compensator fails to drive the system states along the desired trajectories, due to the relatively large initial elastic error. To overcome this limitation, proper joint motion is planned between the desired initial and final positions through optimization techniques. This scheme is validated via numerical tests on a two-link planar manipulator

Time-to-Go 추정기를 이용한 목표점 지향 유도 법칙 설계

In this paper, a new target pointing guidance algorithm is proposed by combining the optimal target pointing solution and a simple time-to-Go estimator. Also investigated are some properties of the guidance algorithm which include a relation to conventional PNG, convergence region and convergence trajectories of error states according to the time-to-go estimator gain. Some guidelines for designing the pointing guidance law are commented based on the convergence properties. A design example in the case of large initial heading errors is presented and its performance is investigated by simulation.

In-Flight Alignment of SDINS under Large Initial Heading Error

In-Flight Alignment of SDINS under Large Initial Heading Error

AN EXTENDED ROBUST H∞ FILTER DESIGN FOR SDINS IN-FLIGHT ALIGNMENT

In this paper, a robust filter for an in-flight alignment (IFA) is presented to effectively eliminate system errors in the case where a strapdown inertial navigation system (SDINS) has large initial attitude errors. First, an extended robust H∞ filter is proposed for a general nonlinear uncertain system. We also analyze the characteristics of the proposed filter, such as an H∞ performance criterion, using the Lyapunov function method. Analysis results show that the proposed filter has robustness against disturbances, such as process and measurement noises, and against parameter uncertainties. Then the IFA for the SDINS is designed using the presented filter. Simulation results demonstrate that the proposed filter effectively improve the performance.

Comparative studies of P and PI type iterative learning control algorithms for a class of process control problems

This paper is concerned with the application of Iterative Learning Control (ILC) to a class of process systems that can be approximated as a first order plus dead-time model. The P-type ILC with Previous Cycle Feedback (PCF) and Current Cycle Feedback (CCF) arc investigated. It is shown that ILC with PCF may not be suitable for the above mentioned system due to the large initial tracking error, which in turn results in control signal saturation, and thus degrades the control performance. On the other hand, ILC with CCF performs much better but the appropriate gain has to be searched by trial and error. To overcome this difficulty, P and PI-type ILC which are based on well established auto-tuning schemes are proposed to set the learning control gains. Experimental studies on the level control of a coupled-tank system verity the effectiveness and implementability of the proposed ILC algorithms

Entry Trajectory Tracking Law via Feedback Linearization

Asasteptowardextendingthetwo-dimensional(longitudinal)entrypredictive/trackingguidanceschemeusedby the U.S. Space Shuttle Orbitertothreedimensions, a control law fortrackinga three-dimensional entrytrajectory isdesigned. Thetrackinglawcommandstheanglesofattack and of bank thatarerequired tofollow aground track specie ed as a function of energy. Feedback linearization is used to design the tracking law. Some extensions to the existing theory are required to accommodate features of the entry tracking problem. Downrange and crossrange angles serve as output variables for the feedback linearization and lead to state and control transformations that convert the entry dynamics to an equivalent linear system in an approximate sense, which is dee ned. A feedback tracking law is then designed, taking advantage of the linear structure of the system dynamics in the transformed variables. This tracking law is shown to achieve bounded tracking of the output variables. Simulation results indicate the effectiveness of the tracking law in compensating for initial offsets from a reference trajectory. URRENT efforts to develop reusable launch vehicles (RLVs), a space station crew return vehicle, and a military spaceplane provide motivation for investigating potential improvements to the entry guidance capability for a lifting unpowered e ight vehicle.The state of the art is represented by the U.S. Space Shuttle Orbiters' entry guidance, as described by Harpold and Graves. 1 The Shuttle's longitudinal guidance combines predictive guidance, i.e., model- basedreferencetrajectoryplanningwithin-e ightupdating,withref- erence trajectory tracking. Mease and Kremer 2 revisited the Shuttle tracking law derivation in the framework of feedback linearization andshowedthattheShuttlelawisa linearized version ofthepropor- tional integral derivative (PID) type law that the feedback lineariza- tion approach can produce. By not linearizing the tracking law, the nonlinearities in the dynamics can be compensated for, provided they can be adequately modeled. Roenneke and Well 3 simulated a variety of low-lift re-entry eights and showed that the longitudinal PIDtracking lawwith feedback linearization yields uniformly good tracking performance and effectively compensates for 20% errors in air density and large initial position errors. A related nonlinear tracking law has been developed and applied to RLV guidance by Lu. 4 The entry guidance requirements for future unpowered entry ve- hicleswilllikelybe,astheyarefortheShuttle,tosteerthevehicleon afeasibletrajectory,atrajectorywithintheentrycorridor,dee nedby heating, acceleration, dynamic pressure, and controllability limits, thatachievesthe specieedtargetconditionwithin thespecie ederror margin. Additionalrequirements thatdrive our study are eying over specie edwaypointsandincreasedcrossrangecapability.Theformer may be required toavoid e ying over populated areas; the latter may be required for abort scenarios and to reduce the waiting time for returnfromorbit.TheShuttleentryguidancehandlescrossrangetar- getingbybankreversallogic.Crossrangetargetingtakessecondpri- ority todownrange targeting,and some crossrange capability issac- rie ced asa result. The additional requirements suggest that it would be desirable to extend the Shuttle longitudinal predictive/tracking guidance to longitudinal and lateral predictive/tracking guidance. The entry requirements can be met by a guidance scheme com- prising a rapid trajectory planner that generates a feasible ground

Recovery Guidance Satisfying Input and State Constraints: Rate Saturating Actuator Example

When a Ž xed regulator is used to stabilize a desired state trajectory (guidance law), large initial tracking errors can lead to input saturation,which can result in performance deterioration. A method to modify the guidance law for recovering state-trajectory tracking (without violating input and state constraints) is presented. Although it may be feasible to Ž nd such a satisfactory recovery guidance maneuver for a given initial tracking error, online development of recovery guidance maneuvers may not be computationally tractable. A technique is developed to use precomputed recovery guidancemaneuvers (precomputed for a Ž nite set of initial tracking errors) to generate recovery guidance maneuvers for other initial errors. The technique is applied to an illustrative example with a rate-limited servoactuator, and simulation results are presented.

Tropical Intraseasonal Oscillation and Its Prediction by the NMC Operational Model

In this paper, results are presented of an investigation to study the tropical intraseasonal oscillation (ISO) and its impact on the extended-range forecast in the NMC operational model during Phase II (14 December 1986–31 March 1987) of the Dynamical Extended Range Forecast (DERF). Based on principal component analysis of the velocity potential and streamfunction, evidence was found of tropical–extratropical interaction associated with the ISO. The NMC model possesses significant forecast skills for the principal streamfunction and velocity potential modes up to the first ten days. Results of the error growth analysis suggest that the principal modes of velocity potential have large initial errors comparable to the model random errors. By comparison, the initial errors in the streamfunction are much smaller. The error growth for both tropical and extratropical modes are found to be significantly suppressed during periods of strong ISO relative to periods of weak ISO. During strong ISO, a reduction of forecast error, implying a recovery of forecast skill, is also found at about three weeks into the forecast. This is presumably due to the oscillatory nature of the ISO. The overall results suggest that the forecast skill of ISO and of low-frequency extratropical modes may be considerably enhanced during a special period of DERF when the ISO was strong. The increase in extratropical forecast skill is likely due to (a) the model's ability to better capture ISO signals in the tropics and (b) the increased coupling between the tropics and extratropics during periods of strong ISO. However, because of the limited data, the applicability of the present results to a more general case needs to be ascertained by further studies.

Assembly Performance of a Robotic Vibratory Wrist

In precision assembly, even small misalignment between two mating parts can cause large reaction forces and thus make the assembly task be impossible. This paper considers a vibratory assembly method which can compensate such misalignment for successful insertion task. For this purpose a PWM controller-based pneumatic vibratory wrist is used to investigate assembly performance such as search time, assembly force and correctable error range. Since they are critically dependent upon various system parameters, they were experimentally investigated for a chamferless peg-in-hole assembly task. Experimental results show that the proposed method yields good assembly performance; compensation of large initial error, fast searching and small reaction forces.

Automatic indexing of rotation diffraction patterns

A method is described which assigns indices to a set of single-crystal reflections recorded by the rotation-oscillation technique using a fixed X-ray wavelength. It is assumed that the space group and approximate unit-cell parameters are known. The unknown crystal orientation is determined directly from the observed diffraction pattern of one or several oscillation data records. A local indexing procedure is described which tolerates large initial errors in the parameters controlling the diffraction pattern. These parameters are refined subsequently, thereby satisfying the constraints imposed by the space-group symmetry.

Adaptive, high precision, satellite attitude control for microprocessor implementation

A control system is presented for three-axis, gas jet, satellite attitude control having application to any spacecraft where precise pointing is required within stringent mass and power limitations. Several novel features are incorporated as follows: parabolic switching boundaries are employed with parameters which adapt to a disturbing acceleration estimate in order to achieve a zero offset steady-state limit cycle of preset amplitude in the arcsecond region which minimizes both fuel consumption and thruster operation frequency. The disturbing acceleration estimate is obtained from a third-order state estimator, together with angle error and rate estimates using an angle error measurement from a rate integrating gyro and a jet drive input. Time optimal recovery from large initial angle errors and rapid response to step changes in disturbing acceleration are achieved. In addition, stable control is obtained with disturbing acceleration approaching the control jet acceleration. A slew control algorithm is incorporated which enables the same control law to be utilized for fuel optimal slewing through unlimited angles, one axis at a time. Simulation results are presented, including demonstration of stochastic performance with gyro and jet noise.

An Adaptive, High Precision, Gas Jet Satellite Attitude Control System for Microprocessor Implementation

A control system is presented for three axis gas jet satellite attitude control employing parabolic switching boundaries with parameters which adapt to a disturbing acceleration estimate in order to achieve a steady state limit cycle of preset amplitude in the arc second region without zero offset, also minimizing fuel consumption and thruster operation frequency. The control law accepts angle error, rate and disturbing acceleration estimates obtained from a third order state estimator with an angle error measurement from a rate integrating gyro and an acceleration input derived from the jet drive. Time optimal recovery from large initial angle errors and rapid response to step changes in disturbing acceleration are achieved. In addition, stable control is obtained with disturbing accelerations approaching the control jet acceleration. A slew control algorithm is incorporated which enables the same control law to be utilized for fuel optimal slewing through unlimited angles, about one axis at a time. Simulation results are presented including demonstration of stochastic performance with gyro and jet noise. The technique has application to scientific spacecraft where precise pointing is required within stringent mass and power limitations. A good example is the application to ESA's EXOSAT spacecraft which carries scientific instruments with ultimate angular accuracies of about 5 arc seconds.

Automated vehicle guidance using discrete reference markers

Techniques for providing steering control for an automated vehicle using discrete reference markers fixed to the road surface are investigated analytically. Either optical or magnetic approaches can be used for the sensor, which generates a measurement of the lateral offset of the vehicle path at each marker to form the basic data for steering control. Possible mechanizations of sensor and controller are outlined. Techniques for handling certain anomalous conditions, such as a missing marker, or loss of acquisition, and special maneuvers, such as u-turns and switching, are briefly discussed. A general analysis of the vehicle dynamics and the discrete control system is presented using the state variable formulation. Noise in both the sensor measurement and in the steering servo are accounted for. An optimal controller is simulated on a general purpose computer, and the resulting plots of vehicle path are presented. Parameters representing a small multipassenger tram were selected, and the simulation runs show response to an erroneous sensor measurement and acquisition following large initial path errors.

A new method for adaptation of the dynamic transition Matrix

A new method is proposed for adaptation of the plant transition matrix of sampled data systems. Correction matrices are based on the difference between predicted and observed values of the state vector. They are constructed adaptively in a way analogous to the Davidon method for finding the Jacobians in nonlinear equation solving. Two numerical examples are presented. Convergence was obtained on a simulation of a simple two-dimensional process as well as on a six-dimensional process. Two adaptive algorithms are presented, one that is efficient for large initial error and one that converges more slowly but gives smooth behavior when initial error is small.

A comparison of self-recording and manual audiometry: Some systematic effects shown by unpractised subjects

A balanced experiment is described, the aims of which were to establish the difference of hearing thresholds by fixed-frequency self-recording audiometry and to make a contribution to further audiometric standardization. The difference is confounded with learning and order effects. Elimination of these variables results in a value of 0 dB at the first frequency tested and 3 dB at all other frequencies, self-recorded thresholds being the lower. Two distinct mechanisms in the learning process are apparent. Some subjects exhibited large initial errors in the direction of apparent hearing loss, particularly at 025 and 8 kHz by self-recording and at 6 kHz by manual audiometry. Subjects improved progressively with practice; on average the threshold shift amounted to 1 dB within the first session and ½ dB on a subsequent occasion. A further improvement occurred between the tests.

Guidance and Control Techniques for Automated Air Traffic Control

A guidance technique has been developed for flying an aircraft automatically along curved trajectories. The technique consists of a set of algorithms for automatically synthesizing flight profiles, i.e., the horizontal trajectory, the altitude and speed profiles, and a time sequence of commands. The flyability Of the synthesized profile under wind disturbances and initial condition error is verified by closing the loop around the synthesized trajectory and flying it in a computer-simul ated jet aircraft. A control law having longitudinal, lateral and heading deviation from the synthesized profile in the feedback loops is used for the simulated flight. The performance of the system is excellent, errors that are initially zero never exceed 230 ft and large initial errors are reduced rapidly. The system also behaves quite well under wind disturbance. For example, the longitudinal and lateral deviations never exceed 470 ft for a 10-knot error in estimated wind velocity. This paper presents the flight-profile synthesis algorithms, describes the control law, analyzes the overall system performance under initial errors and error in steady wind estimates, and discusses the simulation results.

On the influence of statistical field errors on the stability of longitudinal phase oscillations of a linear accelerator (flatness-problem)

The influence of random errors caused by construction and adjustment tolerances on the size of the stability region of longitudinal phase oscillations is investigated analytically and numerically. A linear approximation leads to the stability problem of an harmonic oscillator, whose frequency changes at random. No influence is found on that region of the phase-plane, which is used for acceleration, even for relatively large initial errors.