A gimbal is a platform that can rotate about an axis. By combining two gimbals, an object on the platform can be pointed in any direction. This is useful when you want the gimballed object to continuously point at a moving target. For example, tracking radar on an aircraft is mounted on a gimbal mechanism, allowing it to maintain a fixed lock on a ground position as the airplane changes altitude, direction, and orientation.
Target-tracking radar uses a gimballed antenna along with controllers and servo-actuators to lock onto a specific target and maintain the lock as the target moves. A servo compares the commanded position from the controller to the actual measured position and rotates to correct the output angle accordingly. Should either the measured or desired angles change, then the motor rotates to compensate.
A well-designed, well-tuned tracking radar quickly turns to the desired angles and tracks the target as it moves. On the other hand, a poorly designed, poorly tuned controller “hunts” for the target (wobbles to and fro, unable to properly lock on) and cannot keep up with the moving target (lags the target’s position).
The challenge for Blue Joule was to create a controller that could determine the angle each motor should be in order to maintain a lock on the target, in a way that is fast enough to keep up as the target moves. Determining the angles using traditional modelling tools is slow and requires several iterations as the process is typically based on numeric computation techniques.
This approach is also computationally expensive, and so often is not fast enough to run in real time and keep up with a continually moving target. Using a symbolic approach makes the process much faster and presents the ability to be treated as an inverse kinematics problem – a term to describe problems where the desired end position is known, and the problem is to determine the angles needed in the mechanism to achieve the motion that will get there. Therefore, the experts from Maplesoft Engineering Solutions found an analytic, symbolic solution to the problem using MapleSim and Maple.
The team used MapleSim, the advanced system-level modelling and simulation tool from Maplesoft built on the Maple symbolic computation engine, to create a model of the aircraft, the gimbal mechanism, and the target. MapleSim’s multibody analysis tools can be used to generate the dynamic and kinematic equations of motion.
These constraint equations, when incorporated back into the model, can be used to quickly calculate the desired azimuth and elevation angles during the simulation. These values are the set-point values for the servo motors on the gimbal. Once testing is completed, code to calculate these values can be automatically generated from the formula so that it could be executed on the controller itself, in real time. As a result, a controller that keeps the tracking radar gimbal in the correct position can be developed.
“The symbolic approach to our problem, using MapleSim and Maple, allow us to deliver a more accurate, better performing solution to our customers than when using other methods,” says Neal Romine of Blue Joule Corporation. “With the help of the Maplesoft Engineering Solutions team, we are able to deliver high-quality results very quickly.”
