![]() ![]() The uncompensated error in time alignment was on the order of 7 ms. 15, curve ϕ) is an effect of misalignment between the sensors used for the tests. In this particular case, the sinusoidal shape of the output bank (Fig. The main causes of the errors are the (undetermined) mechanical misalignments between the gyroscopes and inertial systems and the (undetermined) time delays between the two sources. Three solid-state gyroscopes mounted onto the equipment provide for the local body rates (i.e., the triple ω a, ω b, ω c) at control loop sampling time T.įigure 15 shows the response to a commanded sinusoidal input, and Fig. ![]() The attitude of the motion table is properly measured and processed to derive its instantaneous attitude rates and accelerations, so as to simulate the inertial system input (i.e., the Euler angles a, b, c), fed at a 50-sample/s rate. The test bench comprises the equipment mounted on a suitable motion table. The process has been tested with real inputs too. ![]() The control loop runs at the gyroscope-module data rate, and inertial-system data are extrapolated from two subsequent samples. Inertial-system data, in digital format, are received at no more than 30 to 50 Hz gyroscope-module data, on the contrary, are available at more than ten times those rates. The predictor has also the task of aligning the inertial-system and gyroscope-module data in time. This function is indicated as the predictor (PRED) in Fig. The recovery of the position sensed by the inertial system is performed by means of a prediction algorithm, implemented in quaternion algebra, based on angles, angular rates, angular accelerations, and data time tag. The latency is supposed to be on the order of tens of milliseconds, quite significant values in the case of high platform dynamics. The implementation also takes account of inertial-system data latencies due to the transmission process (from source to equipment) or due to other factors. These differences are available as error signals from the loop. In theory the two sensors are subjected to the same motion but, on account of deformations of the structure of the host platform due to the motion itself, we have to expect that they pick up also small differences. The inertial system and the gyroscope module can be fairly distant. The use of the two aforementioned data sources is a valid means to preserve both the long-period precision in the motion measurement and a high sensitivity to the fast (local) rotations. The task for the stabilization algorithm is to recover, as well as possible, the measure of motion at the equipment location. The gyroscopes are supposed to be affected by long time drift that is a reasonable assumption when the dimensions and cost of the equipment are limited. Angular rates, picked up by gyroscopes, constitute the second source of data for the loop. It is not expected to obtain wideband performance from this source therefore a gyroscope module is mounted locally in the equipment to keep track of the higher motion frequencies. The angles are those of the platform position with respect to an inertial axis system. Angles from the inertial system, and possibly angular rates and angular accelerations with respect to the moving angles, constitute the first source of data for the loop. Aircraft and ships are typical platforms for this application. The control loop is conceived for the inertial stabilization of the line of sight of electro-optical equipment to be installed on moving platforms where precise inertial systems, characterized by long-term stability, are available. The crossover frequency can be optimized by suitably setting the gain G. If ω a, ω b, ω c are the instantaneous rates with respect to the local axes of angles a, b, c, the loop provides unit transfer function for each one of the three components, as one can verify. 7, have to be suitably transformed to quaternions, and the quaternion, at the output of the loop, has to be reconverted to angles. The aim is to have a perfect blending of the two signals, i.e., a flat frequency response of the motion measure, by properly using the features of the two sensors. This source has, on the contrary, high-pass characteristics: zero gain at zero frequency and unit gain at high frequency. The second sensor is able to measure the angular rate of the body with respect to a predefined axis system fixed in the body itself. It has low-pass characteristics, i.e., unit gain at zero frequency and decreasing gain with increasing frequency. The first source is a sensor able to provide the angular position of the body with respect to the inertial system. We need to fuse angular information coming from two different sources in order to achieve an integral value, a blending of data. ![]() Let us enter in more detail into the description of the control loop used for the tests. ![]()
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