Gimbal Axis Research Articles

Inverse-Kinematics Steering Laws for Double-Gimbal Scissored-Pair Control Moment Gyros

The generalized singularity robust inverse steering law (GSRISL) is widely used to avoid singularity problems in control moment gyroscopes (CMGs). However, GSRISL tends to generate perturbation torques near singularities, which hinder highly accurate attitude tracking control. Model predictive steering control can eliminate the necessity of considering singularities, but its implementation in satellites remains challenging because of its high computational cost. Therefore, the development of a steering law that avoids explicit consideration of internal singularities and costly calculations is critical. The inverse-kinematics steering law (IKSL) is one such law removing the need for the calculation of the inverse matrix. The double-gimbal scissored-pair CMG (DGSPCMG) addresses the singularity problem as it does not have internal singularities except along the outer gimbal axis. To enhance the attitude control by removing the need for the calculation of the inverse matrix, this study proposes the combining of IKSL with DGSPCMG. Additionally, to mitigate the risk of gimbal mechanical failure, the IKSL for inner or outer gimbal axes failure was designed by relaxing the identical steering constraint of the scissored-pair gimbal angles. Numerical simulations were performed to evaluate the effectiveness of the combination of IKSL and DGSPCMG in terms of settling time and maneuvering axis accuracy.

Stabilization of Two Axis Gimbal System with Self Tuning PID Control

Gimbal is a system that provides locking and tracking of the seeker on the target in missiles and increases the angle of view with its mobility in two axes. In this study, stabilization of a two-axis gimbal system used in the missile was carried out. In gimbal stabilization, adaptive controllers are preferred instead of classical controllers due to unbalance, cross-coupling, and unmeasurable disturbances. A Self Tuning PID controller based on Fuzzy Logic was developed for axis controls in the stabilization algorithm. Thanks to this controller, which works with the principle of choosing the most appropriate coefficient at every step, it was possible to control with less than 3% errors in the tests performed with the flight simulator. In addition, a PID controller whose coefficients are optimized with Particle Swarm Optimization is designed for comparison purposes. In experimental studies, it was seen that PID with adjustable coefficients gave better results than the fixed PID.

Gimbal Axes Control with PID Controllers

Gimbal is a system in missiles that allows the seeker to lock onto the target and follow it and increases the angle of view with its mobility in two axes. In this study, the control of the axes of a two-axis gimbal system used in the missile was carried out. PID controller tuned with Particle Swarm Optimization (PSO) is used in the control algorithm. In the optimization, a smoother controller is aimed by using the multi-objective objective function, which also includes the controller output with the position error. At the same time, the bandwidth of the system is also included as a constraint. The Butterworth Polynomial Method (BPM), which can adjust the coefficient according to the bandwidth criterion, was used for comparison purposes. As a result of the experimental studies show that the PID tuned with PSO can control the system with a lower positional error by responding faster to external factors than the PID designed with BPM.

Calibration method for misalignment angles of a fiber optic gyroscope in single-axis rotational inertial navigation systems.

In a fiber optic gyroscope rotational inertial navigation system (RINS), attitude errors may change after vibration due to the change of misalignment angles. There are two kinds of misalignment angles which can cause the same attitude errors: the one is misalignment angles of gyroscopes, and the other is misalignment angles between input axis of gyroscope and rotating gimbal axis. Thus, it is difficult to calibrate any kind of misalignment angles by attitude errors alone. Self-calibration methods can separate and calibrate the two kinds of misalignment angles. But single-axis RINSs rely on a turntable to realize the rotation scheme. And misalignment angles may change during repeated removal. Therefore, it is necessary to study an efficient and convenient method to analyze which kind of misalignment angles leads to the change of attitude errors and calibrate these misalignment angles. According to the different influences of two kinds of misalignment angles on navigation errors and fine alignment errors, this paper proposes a calibration method based on fine alignment algorithm to calibrate the gyroscopes' misalignment angles. Its accuracy is proven by simulations and experiments. From experimental results, position errors have decreased at least 21.4% with the proposed method.

Simulating microgravity using a random positioning machine for inducing cellular responses to mechanotransduction in human osteoblasts.

The mechanotransduction pathways that mediate cellular responses to contact forces are better understood than those that mediate response to distance forces, especially the force of gravity. Removing or reducing gravity for significant periods of time involves either sending samples to space, inducing diamagnetic levitation with high magnetic fields, or continually reorienting samples for a period, all in a manner that supports cell culturing. Undesired secondary effects due to high magnetic fields or shear forces associated with fluid flow while reorienting must be considered in the designof ground-based devices. We have developed a lab-friendly and compact random positioning machine (RPM) that fits in a standard tissue culture incubator. Using a two-axis gimbal, it continually reorients samples in a manner that produces an equal likelihood that all possible orientations are visited. We contribute a new control algorithm by which the distribution of probabilities over all possible orientations is completely uniform. Rather than randomly varying gimbal axis speed and/or direction as in previous algorithms (which produces non-uniform probability distributions of orientation), we use inverse kinematics to follow a trajectory with a probability distribution of orientations that is uniform by construction. Over a time period of 6 h of operation using our RPM, the average gravity is within 0.001 23% of the gravity of Earth. Shear forces are minimized by limiting the angular speed of both gimbal motors to under 42 °/s. We demonstrate the utility of our RPM by investigating the effects of simulated microgravity on adherent human osteoblasts immediately after retrieving samples from our RPM. Cytoskeletal disruption and cell shape changes were observed relative to samples cultured in a 1 g environment. We also found that subjecting human osteoblasts in suspension to simulated microgravity resulted in less filamentous actin and lower cell stiffness.

Model predictive steering control law for double gimbal scissored-pair control moment gyros

To overcome the singularity problem of control moment gyros (CMGs) and simultaneously provide a lightweight, agile, and simple dynamical system, a CMG system called a double-gimbal scissored-pair control moment gyro (DGSPCMG) was recently proposed. The DGSPCMG is a hybrid mechanism that combines scissored-pair CMGs and a double-gimbal mechanism; further, the outer singularities in this system (saturation singularities) can be escaped by steering the scissored-pair gimbals. This system generates less perturbation torque and has almost no inner singularities except at the origin and the line along the outer gimbal axis. This paper proposes model predictive control (MPC) based steering laws for the mentioned CMG system. The proposed MPC based steering laws can directly provide the optimal gimbal rate under the nonlinear constraints in real time without using the inverse of the CMG Jacobian matrix, and hence, the singularities do not have to be considered when determining the gimbal steering rate of this system. Three objective functions are considered in the steering law design: fast maneuver-weighted type, minimum control energy type, and a hybrid of these two types. The control performances of these three MPC-based steering laws are compared via numerical simulations. Results demonstrate that the hybrid type can achieve both a short rise time of the angular velocity at the initial stage of control, and smooth stabilization to the target attitude; moreover, its settling time and control effort is between those of the other two types.

Stability Criterion for Stationary Solutions of Multi-Current Model Equations for a Synchronous Gimbal-Mounted Gyroscope. Part 1

We study the dynamics of a gimbal-mounted gyroscope, which has a vertical external gimbal axis and is equipped with a synchronous electric drive that rotates a gyroscope (electric motor rotor). A mathematical model of the electric motor that includes differential equations for electric currents in the rotor windings is used. Both friction and control torques on the gimbal axes are assumed to be absent. Friction torque on the rotor axis is a nonlinear function of the angular velocity of its rotation relative to the stator. The differential equations of motion for such an electromechanical system have an infinite set of stationary (steady-state) solutions that describe its stationary motions, namely, regular precessions and uniform rotations of the rotor. Due to the verticality of the outer axis of the gimbal suspension, the considered system of differential equations has a first integral, which expresses the constancy of the projection of the angular momentum of the device onto the vertical axis. In the present article we have proved that the presence of an isolated minimum of the total reduced potential energy is the necessary and sufficient condition for the stability of stationary (steady-state) motions. Thus, the previously obtained result using a simplified non-current model of a synchronous electric motor is generalized to the case of the multi-current model. Content of the study is presented in two articles. In the first part, we consider the cases when the mechanical reduced potential energy is not identical constant with respect to the internal gimbal angle. In the second part, we analyze the case of constancy for the mechanical reduced potential energy.

Predictive Functional Control-Based Zenith Pass Controller Design for Roll-Pitch Seeker

A roll-pitch seeker has a wide field of view but suffers from a singularity as the sightline coincides with the outer gimbal (OG) axis. In the vicinity of the singularity, the tracking effectiveness is often degraded or even lost due to the high actuation demand on OG, which is known as the zenith pass problem. To solve this problem, this paper first proposes a novel motion model of sightline to predict the singularity in a receding horizon, where the model parameters are identified using a modified recursive least square estimator. And with the singularity predictions as set points, a predictive functional controller is then designed for the OG position control to minimize the tracking error. This novel combination control scheme is validated in MATLAB/Simulink. Simulation results have confirmed that the proposed scheme can significantly mitigate the zenith pass problem and be applied to the real-time tracking process.

Stereovision Tracking System for Monitoring Loader Crane Tip Position

This paper presents the idea and experimental tests of a non-stationary stereovision system used for supervision of a loading crane. The system based on two independent gimbals, equipped with cameras, allows simultaneously to measure and track a group of individual spatial points. The four steps calibration procedure is required for each gimbal axis, camera optics, gimbals positions, and loading crane position. Modern camera systems have been widely applied in several fields of the industry allowing for accurate measurements and real-time quality control. The systems based on stereo camera models and appropriate image analysis algorithms can measure a group of spatial points, complex surfaces, small displacements, or vibrations. There are also several vision systems such as laser tracker, camera mounted on fully controlled rotating head (called gimbal), or TOF camera, which can be used to follow and measure real-time object displacements. Unfortunately, they all have significant individual limitations explained in this paper. Accuracy tests of 3D measurements including active tracking of length pattern and crane tip have been performed within a selected working area. Based on reconstructed 3D data points, different types of geometric errors have been presented. The results revealed effects of accuracy degradation on the workspace boundaries and for higher observation angles, as well as 3D data bias suggesting mechanical issues. Several improvements in calibration and gimbal construction might result in far enough accuracy for normal operations of the crane.

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.

Gimballed Camera Control for On-Point Target Tracking

Detailed design of tracking system that enable a Micro Aerial Vehicle (MAV), equipped with a pan-tilt gimbaled camera to be stabilized and to track the target, with target asin center of image. The algorithm performs automatic tracking of target while camera gimbal is moved according to the target position in image.2- Axis gimbal camera set up is made with servo motors and FPV 10x zoom camera.Gimbal camera set up is integrated with APM and XBee to replicate real set up of MAV in laboratory. And it is controlled with GCS set up made of joystick, XBee, Matlab and Mission Planner software. Thus, closed loop for control of gimbal camera designed. Image processing algorithm is used to track the target and to compute the position of target in image. Accordingly, control algorithm will generate control PWM signal for control of camera gimbal.

Dynamic Modeling and Coupling Characteristic Analysis of Two-Axis Rate Gyro Seeker

A dynamic model of a two-axis rate gyro-stabilized platform-based seeker with cross-coupling, mass imbalance, and disturbance torque is developed on the basis of the working principle of seeker two-loop steady tracking theory; coordinate transformations are used to analyze the effects of seeker servo control mode on missile guidance and control systems. Frequency domain is used to identify the servo motor transfer function. Furthermore, a block diagram of the two-gimbal-coupled system is developed, and the coupling characteristics of gimbal angle are analyzed with different missile body inputs. Simulation results show that the analysis conforms with the actual movement rule of seeker gimbal and optical axis, and cross-coupling exists between the two gimbals. The lag compensation network can increase the open loop gain and increase the capacity for disturbance rate rejection. Simulations validate the theory and technology support for developing the seeker servo control model in engineering.

MEMS 3D Scan Mirror with SU-8 Membrane and Flexures for High NA Microscopy.

We demonstrate a MEMS beam scanner capable of biaxial scanning with simultaneous focus control, for integration into a handheld confocal microscope for skin imaging. The device is based on a dual axis gimbal structure with an integrated largestroke deformable mirror. SU-8 polymer is used to construct both the deformable membrane as well as the torsional hinges for biaxial scanning. The 4 mm diameter mirror can perform raster pattern scanning with a range of +/- 1.5 degrees and Lissajous scanning with a range of +/- 3 degrees (mechanical scan angle), and has a maximum deflection of 9 um for focus control. The design, fabrication and characterization of the opto-mechanical performance of the MEMS device are presented in this paper.

Indirect Measurement of Rotor Dynamic Imbalance for Control Moment Gyroscopes via Gimbal Disturbance Observer.

The high-precision speed control of gimbal servo systems is the key to generating high-precision torque for control moment gyroscopes (CMGs) in spacecrafts. However, the control performance of gimbal servo systems may be degraded significantly by disturbances, especially a dynamic imbalance disturbance with the same frequency as the high-speed rotor. For assembled CMGs, it is very difficult to measure the rotor imbalance directly by using a dynamic balancing machine. In this paper, a gimbal disturbance observer is proposed to estimate the dynamic imbalance of the rotor assembled in the CMG. First, a third-order dynamical system is established to describe the disturbance dynamics of the gimbal servo system, in which the rotor dynamic imbalance torque along the gimbal axis and the other disturbances are modeled to be periodic and bounded, respectively. Then, the gimbal disturbance observer is designed for the third-order dynamical system by using the total disturbance as a virtual measurement. Since the virtual measurement is derived from the inverse dynamics of the gimbal servo system, the information of the rotor dynamic imbalance can be obtained indirectly only using the measurements of gimbal speed and three-phase currents. Semi-physical experimental results demonstrate the effectiveness of the observer by using a CMG simulator.

Convex Optimization for Power Tracking of Double-Gimbal Variable-Speed Control Moment Gyroscopes

This Paper addresses an integrated power/attitude control system for a spacecraft with two double-gimbal variable-speed control moment gyroscopes. Double-gimbal variable-speed control moment gyroscopes are of interest because a single device is a three-degree-of-freedom attitude actuator. A double-gimbal variable-speed control moment gyroscope has two gimbal axes and one variable-speed wheel. A primary advantage of adopting this actuator is to reduce the number of actuators, which leads to reducing the total mass and volume allocation within the spacecraft. In this Paper, first, the dynamical equations of motion of a spacecraft equipped with multiple double-gimbal variable-speed control moment gyroscopes are developed. Then, two types of steering laws are proposed for two double-gimbal variable-speed control moment gyroscopes. These steering laws attain three-axis attitude control and power tracking by using the wheels as energy storage devices while considering both singularity avoidance and wheel spin equalization. The controller design applies multiobjective gain scheduling with linear parameter-varying control theory, which can evaluate both optimality and robustness. Finally, numerical simulation examples of the orbiting spacecraft attitude tracking problem demonstrate the effectiveness of the proposed gain-scheduling controller and two steering laws for the integrated power/attitude control system.

A compensation approach for nonlinear gimbal axis drift of a control moment gyroscope

This paper investigates the axial drift phenomenon of a gimbal system of a Control Moment Gyroscope (CMG) system and proposes a solution to tackle the problem. A CMG is an indirect actuator to generate a torque in the desired direction by using a gyroscopic effect for the attitude control of dynamical systems. CMGs are easily subject to drift gradually against one direction resulting in the instability of the system. The fast repositioning control of the gimbal axis to the origin should be ensured to maximize the induced gyroscopic force. Since the position control for repositioning the gimbal axis takes time, the axial drift compensator is designed for the nonlinear drift model in the inverse dynamic control framework to shorten the repositioning time. Comparison studies with disturbance observer (DOB)-based control scheme are conducted to the same problem. Advantages and disadvantages of the proposed scheme are analysed. Experimental studies confirm that the proposed compensation method can dramatically improve the performances of the returning time to the origin and the torque regulation by compensating for the axial drift of the gimbal system compared with the conventional position control.

Research on Measurement Accuracy of Laser Tracking System Based on Spherical Mirror with Rotation Errors of Gimbal Mount Axes

Abstract This paper presents a novel experimental approach for confirming that spherical mirror of a laser tracking system can reduce the influences of rotation errors of gimbal mount axes on the measurement accuracy. By simplifying the optical system model of laser tracking system based on spherical mirror, we can easily extract the laser ranging measurement error caused by rotation errors of gimbal mount axes with the positions of spherical mirror, biconvex lens, cat’s eye reflector, and measuring beam. The motions of polarization beam splitter and biconvex lens along the optical axis and vertical direction of optical axis are driven by error motions of gimbal mount axes. In order to simplify the experimental process, the motion of biconvex lens is substituted by the motion of spherical mirror according to the principle of relative motion. The laser ranging measurement error caused by the rotation errors of gimbal mount axes could be recorded in the readings of laser interferometer. The experimental results showed that the laser ranging measurement error caused by rotation errors was less than 0.1 μm if radial error motion and axial error motion were within ±10 μm. The experimental method simplified the experimental procedure and the spherical mirror could reduce the influences of rotation errors of gimbal mount axes on the measurement accuracy of the laser tracking system.

A Simple Integrated Geometrical Error Model for Laser Tracer

Geometrical errors of 2D gimbal mount axes are studied for laser tracer for the sake of realizing rapid detection for numerical control equipment. The high precision reference sphere, which serves as the reflection unit and is set on the base, avoids the influence on measurement accuracy caused by the movements of rotatory axes, and ensures that laser tracer owns large tracing angle. The nonlinear coupling relationship between the geometrical errors and the measurement accuracy of laser tracer is analyzed; the integrated geometrical error model of 2D gimbal mount axes and laser interferometry system is established; the error map of the measuring system is brought. The simulation results demonstrate that the measurement error of the laser tracer is certain and unique after the value and direction of all the geometrical errors determined.

Analysis of the Dynamics of a Honing Gimbal by using Two Friction Models in Long Stroke Honing

Honing is a precise machining process with high standards for the resulting form, dimensions and surface quality. Additionally, the achieved geometrical tolerances can be even further reduced by the application of a honing process. Essential for the resulted surface integrity, is the coaxial interaction between the honing tool and the work piece, attached to a honing gimbal. Therefore, the process kinematics and dynamics of the honing gimbal during the long stroke honing were closely investigated in this article. Based on a substituted mechanical system, mathematical differential equation system was prepared in order to characterize the four degrees of freedom of the honing gimbal in relation to the honing tool. A MATLAB/Simulink simulation was applied to analyze the friction states in the gimbal axis in relation to the displacement and tilting compensation movements. The used friction models Stribeck and LuGre were presented and compared. Experimental investigations of the dynamics of the honing gimbal were used to compare to the simulation results.

High-Precision Anti-Disturbance Gimbal Servo Control for Control Moment Gyroscopes via an Extended Harmonic Disturbance Observer

In control moment gyroscopes (CMGs), the gimbal is expected to rotate at a low speed with high precision so that high-precision gyroscopic torque can be generated to realize high-precision spacecraft attitude control. However, there are complex and multiple disturbances in the gimbal servo systems, which may deteriorate the gimbal control performance to a great extent. In this paper, an extended harmonic disturbance observer (EHDO)-based composite controller is proposed to reject the effects of multiple disturbances on the control performance of gimbal servo systems. Firstly, an EHDO is developed for an mth-order model describing disturbance dynamics in which the rotor dynamic imbalance torque along gimbal axis is modeled as a harmonic, and the others are approximated as a polynomial. Compared with conventional extended disturbance observers, EHDO can estimate multiple disturbances with high precision even with a lower bandwidth. Secondly, a backstepping-based composite controller is designed to achieve high-performance gimbal control for CMGs. Finally, simulation and experimental results are presented to demonstrate the effectiveness of the proposed method.