Inertial Angular Rate Research Articles

Inertial Stable Platforms for Precision Pointing of Optical Systems in Aerospace Applications

Both airborne and space-based high-energy laser weapon systems present interesting challenges for precision line-of-sight control. Sub-microradian to microradian pointing accuracies are required against dynamic targets. In addition, “absolute” pointing and accurate inertial angular rate measurement are required to support mission requirements. This paper addresses these unique directed-energy weapon (DEW) precision-pointing requirements and their associated implementation alternatives in the context of strapdown and stable platform inertial reference technologies. The contributions of this paper consider the broader issues of DEW requirement drivers, integration of the stabilization system with the rest of the optical system, and design tradeoffs between stable platform and strapdown stabilization mechanizations. Both types of mechanisms are mounted to the gimbal of an imaging system using gryo sensors (gyros) and accelerometers to maintain a desired orientation in inertial space independent of the craft motion. Although both can include an optical reference that propagates through the optical path for optical alignment and jitter control, only in the stable platform is the optical reference stabilized. When combined on the same platform with a stabilized inertial measurement system and closed-loop stabilization with the optical reference, the mechanism becomes a stabilized inertial reference unit, which provides a stabilized optical reference to the electro-optical/laser pointing and jitter control systems.

Impact of outgassing and its corrective methods to improve the vacuum stability in the Coriolis Vibratory Gyroscope

Coriolis Vibratory Gyroscope (CVG) is an inertial angular rate measurement sensor. CVG sensor comprises of metal coated hemispherical quartz vibrating structure as the rotation sensing element. It is forced to vibrate at one of its resonant modes by electrostatic excitation. Because of the limited flexibility of the quartz sensing element, the amplitude is limited to the submicron level. An ultra-high vacuum environment is required for the sensing element to sustain vibration for a long time. The criticality in the sensor development is to maintaining an ultra-high vacuum environment for the sensing element. Sensor suffers a problem of vacuum instability during the operation due to the outgassing from its components. This paper presents a novel approach in the identification of various outgassing sources that exist in the sensor, mitigation plan to minimize outgassing rate by selection of suitable raw material, suitable fabrication process of the components, and the surface characterization etc. The research work also presents the cost-effective experimental methodology to measure the outgassing rate from the sensor components to assess the CVG vacuum life, the requirement of the getter to maintain the ultra-high vacuum level throughout the CVG operation.

Implementation of Sensor Precision Mirror Rate using FPGA

The research contribution is increasing in the field of autonomous spacecraft. The major role contributes to the navigation methods for spacecraft. The intended control design is required precision mirror rate sensor (PMRS) to maintain positioning and stability of the satellite. One major drawback of the PMRS resides in the lock in effect, by which the sensor is not capable of sensing the rotation at low inertial angular rates. In the proposed work due to the uniqueness, it is able to sense the rotation even at the low inertial angular rates. The frequency control loop has been designed, it generates the resonance frequency using dither motor. The frequency control loop of the PMRS, is developed using a 32 bit MICROBLAZE soft core processor along with PID algorithm and same is executed using Xilinx Spartan 6 FPGA.

Modeling and Robust Continuous TSM Control for an Inertially Stabilized Platform With Couplings

Inertially stabilized platforms (ISPs), typically involving two or three axis gimbal, are extensively utilized to achieve accurate tracking of optical axis regardless of vehicle motion or vibration. Due to the complex nonlinearities induced by cross-couplings, parameter uncertainties, and external disturbances, high-performance control for ISPs is always a challenging task for practical applications, especially when the dynamic mass imbalance exists. In this brief, the situation that the mass distribution of an ISP is nonsymmetrical with respect to the mass center is emphatically analyzed, where the couplings are modeled and resolved into the known and unknown parts. To cope with the unmeasured states as well as the uncertainties composed of unknown couplings and remaining dynamics that are unmodeled, a higher order sliding mode observer (HOSMO) is developed for both the states and the lumped uncertainties estimation. By incorporating the estimated information, a robust continuous terminal sliding mode (TSM) control law is synthesized to admit the desired inertial angular rates tracking in finite time without offset. The validity of the presented control approach is demonstrated by experimental studies.

Design and implementation of continuous finite-time sliding mode control for 2-DOF inertially stabilized platform subject to multiple disturbances

Control performances of inertially stabilized platforms (ISPs) are always affected by various disturbed phenomena such as cross-couplings, mass unbalance, parameter variations, and external disturbances in real applications. To improve the dynamic response and the disturbance rejection ability of the ISP, a continuous finite-time sliding mode control (SMC) approach with cascaded control structure is proposed. By constructing a finite-time disturbance observer, the multiple disturbances are precisely estimated in real time without the complex modeling and calibration work. Under the field oriented control framework, for the stabilized loop subsystem, an improved super-twisting controller incorporating the disturbance estimates is developed whereas for the current loop subsystem, the super-twisting control method is directly employed. Finite-time convergence of the inertial angular rates is guaranteed with the continuous control action such that chattering is alleviated remarkably. Moreover, by utilizing the manner of disturbance compensation, the feedback control gains can be tuning down without sacrificing the disturbance rejection ability. Comparative experiments are performed to verify the effectiveness of the proposed control approach.

Generalized Image Navigation & Registration Algorithms for Ground and Space Segments

Ground segment image navigation and registration algorithms and space segment image motion compensation algorithm are presented. The fundamental ground algorithm is based on Kalman filter instead of least squares and does not require ranging or accurate orbit to be provided by flight dynamics. Kalman filter is used to estimate attitude correction angles, orbit position and velocity relative to ideal geostationary orbit, and internal misalignments of imagers with single mirror or two mirrors. Kalman filter measurements consist of landmarks extracted from the imaging instrument level 1A data blocks, maneuver delta V or coarse orbit from flight dynamics, and spacecraft attitude telemetry inserted in the imager wideband data. The ground algorithm is then shown how to be applied to systems with star and landmark measurements, systems with star only measurements with accurate orbit provided by flight dynamics or by the global positioning system, and systems with spacecraft inertial angular rate. Pixel location transformation from imager line of sight reference frame to GOES and CGMS fixed grid frames is also provided for on-ground image registration using resampling.

New generation precision motion simulators with inertial sensors and digital control

Precision motion simulators (controlled platforms) that use inertial angular rate sensors based on various principles (fiber optic, laser, floated, and other gyros) both for a singlemode simu� lator operating on the selftesting principle and for a wide range simulator operating in the low speed and high speed modes and equipped (to extend its functional capabilities) with triads of quartz pendu� lous accelerometers are considered. The problem is in designing digital control systems for such motion simulators that ensure highly accurate stabilization of the prescribed motions of the controlled platform. A solution of this problem is found that allows one to design digital control algorithms for the use with various angular rate sensors. The solutions are analyzed in the time and frequency domains, and the high quality of control is confirmed.

Using Fourier series to analyse mass imperfections in vibratory gyroscopes

When a vibrating structure is subjected to a rotation, the vibrating pattern rotates at a rate (called the precession rate) proportional to the inertial angular rate. This is known as Bryanʼs effect and it is employed to calibrate the resonator gyroscopes that are used to navigate in outer space, the stratosphere and under the polar cap. We study Bryanʼs effect for a non-ideal resonator gyroscope, using the computer algebra system (CAS) Mathematica to do the analysis involved, rendering this work accessible to undergraduate students with a working knowledge of college calculus and basic physics or mechanics (such as senior Engineering Mathematics students). In this paper the density of a slowly rotating vibrating annular disc is assumed to have small variations circumferentially, enabling a Fourier series representation of the density function. Using a CAS, the Lagrangian of the system of vibrating particles in the disc is calculated and, employing the CAS on the Euler–Lagrange equations, the equations of motion of the vibrating, rotating system are calculated in terms of “fast” variables, enabling us to demonstrate that the mass anisotropy induces a frequency splitting (beats). Unfortunately the fast variables are difficult to analyse (even with the aid of a CAS) and consequently a transformation from fast to slow variables is achieved. These slow variables are the principal and quadrature vibration amplitudes, precession rate and a phase angle. The transformation yields a system of four nonlinear ordinary differential equations (ODEs). This system of ODE demonstrates that the Fourier coefficients of the density function influence the precession rate and consequently a gyroscope manufactured from such a disc cannot use Bryanʼs effect for calibration purposes. Indeed, the CAS visualises that a capture effect occurs with the precession angle that appears to vary periodically and not increase linearly (Bryanʼs effect) as it would for a perfect structure. Keeping in mind that manufacturing imperfections will always be present in the real-world, the analysis shows how such density variations may be minimised. Using a symbolic manipulator such as Mathematica to do the “book-keeping” eliminates the plethora of technical detail that arises during calculations of a highly technical nature. This allows the aforementioned students to focus on the salient parts of the analysis, producing results that might have been beyond their capabilities without the aid of a CAS.

Structured MIMO [formula omitted] design for dual-stage inertial stabilization: Case study for HIFOO and Hinfstruct solvers

The paper reports on application of two available numerical solvers for structured and fixed-order controller design to a realistic laboratory MIMO electromechanical system. Namely, an experimental platform consisting of two coaxial motorized gimbals that stabilize an angular motion of an optical payload around a single axis is considered. Inertial angular rate of the payload is measured using a MEMS gyro and the mechanically constrained misalignment between the two gimbals is measured with an incremental encoder. This represents a simplified testbed for the more practically useful multi-axis line-of-sight inertial stabilization systems. The paper defends the choice of the control system structure and argues that the recent Matlab-based computational MIMO control design procedures which are capable of enforcing some structural constraints upon the controller transfer function matrix—HIFOO and Hinfstruct—constitute efficient and practical design tools. They only lose little in the optimality of the full unrestricted MIMO controllers computed by standard H∞ optimization, and yet they produce controllers which are easy to implement and fine-tune within a standard motion control infrastructure based on PID feedback and feedforward terms. Numerical simulations and laboratory experiments were used to validate the findings.

LOS Stabilization and Gyro Configuration Analysis for Roll-Pitch Seeker

Roll-pitch seeker is currently applied in particular missiles, especially in air to air missiles. A representation of the seeker gimbal forward kinematics is analysed for the roll-pitch seeker based on the product-of-exponentials (POE) formula. And by transforming the inertial angular rate into the line-of-sight (LOS) coordinate system with the aid of recursive angular velocity equations, the LOS stabilization equation is obtained, then various schemes of gyroscope configuration and control are put forward based on the gyro direct stabilization. The research provides theoretical basis for the LOS stabilization control to isolate the LOS from the disturbance and vibration of carrier.

Image-Based Pointing and Tracking for Inertially Stabilized Airborne Camera Platform

This paper describes a novel image-based pointing-tracking feedback control scheme for an inertially stabilized double-gimbal airborne camera platform combined with a computer vision system. The key idea is to enhance the intuitive decoupled controller structure with measurements of the camera inertial angular rate around its optical axis. The resulting controller can also compensate for the apparent translation between the camera and the observed object, but then the velocity of this mutual translation must be measured or estimated. Even though the proposed controller is more robust against longer sampling periods of the computer-vision system then the decoupled controller, a sketch of a simple compensation of this delay is also given. Numerical simulations are accompanied by laboratory experiments with a real benchmark system.

Alternative method for angular rate determination within the GOCE gradiometer processing

The most crucial part of the GOCE gradiometer processing is, besides the internal calibration of the gradiometer, the determination of the satellite’s inertial angular rate. This paper describes a new method for the angular rate determination. It is based on the stochastic properties of the GOCE star sensors and the gradiometer. The attitude information of both instrument types is combined at the level of angular rates. The combination is done in the spectral domain by Wiener filtering, and thus using an optimal relative weighting of the star sensor and gradiometer attitude information. Since the complete processing chain from raw measurements to gravity field solutions is performed, the results are not only analyzed at the level of gravity gradients, but also of gravity field solutions. Compared to the nominal method, already the resulting gravity gradients show a significantly improved performance for the frequencies (mainly) below the gradiometer measurement bandwidth. This can be verified by analysis of the gravity gradient trace. The improvement is propagated to the level of gravity field models, where a better accuracy can be observed for selected groups of coefficients at characteristic bands at orders k × 16, with integer k, up to high harmonic degrees.

Structured MIMO ∞Design for Dual-Stage Inertial Stabilization: Case Study for HIFOO

AbstractThe paper reports on a control design for an experimental platform that contains two aligned motorized gimbals stabilizing an optical payload around a single axis using measurements from an inertial angular rate sensor (MEMS gyro). Such a laboratory system represents a simplified testbed for the more practically useful line-of-sight stabilization. The paper defends the choice of the control configuration and argues that when using MIMO design procedures, enforcing some structure upon the transfer function matrix makes the controller implementation and fine-tuning easier. Such structural constraints were taken into consideration in the computational ∞design by using the publicly available HIFOO solver based on algorithms for non-convex and non-smooth optimization. Results are contrasted with the controllers designed with classical methods and full MIMO ∞optimization.

The influence of mass imperfections on the evolution of standing waves in slowly rotating spherical bodies

Standing waves can exist as stable vibrating patterns in perfect structures such as spherical bodies, and inertial rotation of the body causes precession (Bryan's effect). However, an imperfection such as light mass anisotropy destroys the standing waves. In this paper, an imperfection is introduced in the form of light mass anisotropy for a vibrating, slowly rotating spherical body. Assuming this light mass imperfection throughout this paper, the effects of slow rotation and light isotropic viscous damping are considered in a system of variables consisting of the amplitudes of principal and quadrature vibrating patterns, the angle of the rotation of the vibrating pattern (called the precession angle) and the phase shift of the vibrating pattern. We demonstrate how a combination of both qualitative and quantitative analysis (using, inter alia, the method of averaging) predicts that the inertial angular rate does not influence changes with time in the amplitudes of the principal and quadrature vibrations or the phase shift. The light mass imperfection causes changes with time which appear to be of a damped oscillatory nature for both the quadrature component as well as the principal component. The precession angular rate appears to depend on the inertial angular rate as well as the quadrature component of the vibration but is not influenced by the damping factor. It is not directly proportional to the inertial angular rate as is the case for a perfect isotropically damped structure. If the quadrature component is not suppressed, then a “capture effect” appears to occur, namely that the precession angle will not grow at a constant rate but is “captured” and shows periodic behaviour. It is evident that the damping factor does not influence changes with time in the phase shift and that the mass imperfection substantially influences these changes. The phase shift appears to be negative, strictly decreasing and unbounded.

Palm-Size Spy Planes

This article discusses that today’s squad leader must still risk troops to scout out what lies over the next hill, beyond the next tree line, or inside the next building. The Department of Defense is trying to help ground troops at the platoon, company, or brigade level with this crucial task by giving them tiny spy planes, called micro aerial vehicles (MAVs), to search the local terrain. Planners at the Defense Advanced Research Projects Agency (DARPA) envision equipping small combat units with their own “organic” intelligence assets that can locate and monitor possible threats. DARPA planners define a MAV as semiautonomous airborne vehicles, measuring less than 6 inches in any dimension and weighing about 4 ounces that can accomplish a useful military mission at an affordable cost. The most likely parameters to sense for MAV stabilization are inertial angular rate, differential and absolute pressure, acceleration, and the Earth’s magnetic and electrostatic fields; optical sensing could be used for angular position and rate stabilization. Developing useful micro aerial vehicles is going to be a severe design engineering challenge.

Stabilization of Undamped Gyro Platforms Using an Inertial Angular Rate Sensor

The accuracy of any gyro stabilized platform depends to a large extent upon maintaining the net torques applied to the stabilized element at a low level. This requires that the static gain of the servosystem be high in order to effectively counteract torque disturbances. Generally a basic stability problem results which requires servo lead compensation. Beyond this, the lead compensation must be effective in controlling resonant amplitudes during dynamic disturbances. This article treats the stability problem for platforms employing gyros which have negligible damping about the precession axis. The air bearing gyro is a notable example. The purpose of this paper is twofold. First, a simple analytical method is introduced to define compensation parameters which will allow control of the undamped natural frequency, and which will establish a damping factor of one half. Second, a new device is introduced which will greatly simplify the task of generating an effective compensation signal. This device is a tiny gimbal-mounted intertial angular rate sensor called ?ADA.?