Evaluating Vibrations and Optimizing Damper Systems

For aerial video applications, one of the most difficult aspects of a DIY gimbal system is to achieve a low level of vibrations and a well working damping system. The first reaction of most users to artefacts such as micro vibs or jello in the video seems to be "better PID tuning", while in fact the secret sauce of a well working system usually lies not in the PID tuning, which generally is "simple", but the copter vibration level and construction of the gimbal damping system.

Unfortunately, when it comes to the latter aspects the current approach available to us DIY guys is essentially trial-and-error, which at times can be frustrating. The STorM32 NT thus aims at providing tools to alleviate the situation. This is still an effort in progress, meaning that the best set of tools and/or best set of recipes to achieve the goals have not yet been established. However, some tools and procedures have emerged.

Conceptional

The basic idea of the STorM32's vibration and damping system analysis is sketched in the following picture.

Usually, the flight controller is used for analyzing the copter's vibrations, and most UAV codes provide features to do so. However, the disadvantage is immediately obvious from the picture: In most cases the flight controller doesn't see the real copter vibrations, since it is mounted with some dampers. What really matters are the vibrations at the camera, which is obviously "far away" from the flight controller. That is, in a technical language, the transfer functions for the copter's vibrations to the flight controller and the camera are substantially different. For a proper - and complete - analysis of the relevant vibrations one needs to know the vibrations on the copter, on the gimbal frame, and the camera. It is pointed out, that only with knowing the vibrations on the copter and the gimbal frame the performance of the gimbal damping system can actually be assessed.

That's the basic idea of the STorM32's three IMU setup, to provide us with a means to properly evaluate the vibrations and especially gimbal damping system, which hopefully will allow us to develop better gimbals.

It is stressed though that the offered mechanisms can be used also in other ways, e.g. for balancing motors and propellers. The possibilities are only limited by our creativity :).

Comment: In order to avoid confusion, this clarification: In the above sketch the IMU on the gimbal frame is named IMU2 and that on the copter IMU3. However, depending on the user's setup it could be also vice versa. That is because the 2nd IMU (in the terminology of the STorM32 gimbal controller) can be either located on the gimbal frame or the copter, and it is this 2nd IMU which is in the GUI, and else where, is called IMU2.

The following video explains that too, and also shows possible uses of the NTLoggerTool and Blackbox Explorer.

Basic Physics

The physics of vibrations and damper systems is very elementary. In fact, quite many aspects can be properly inferred by applying the simplest laws of physics. Yet, it seems that essentially no one is doing it. In this chapter only one simple but crucial point shall be pointed out:

The vibration dampers, as we like to call them, do not actually damp vibrations.

Before explaining that, it may be useful to first introduce the two general approaches of vibration isolation and vibration absorption (this classification seems to be generally accepted, but with varying notation):

Vibration Isolation: The system is separated from a vibrating source by some flexible pieces of something (which we call dampers). Physically it is described as to consist of a damping element, spring element, and a mass of payload.

Vibration Absorption: The system is separated from a vibrating source by some dampers, with in addition a second mass of payload attached to the primary mass via some further dampers.

The gimbal damper system by itself constitutes a vibration isolation system. However, if the stiffness of the gimbal is taken into account, the copter + gimbal frame + camera system is rather reminiscent of a vibration absorption system (but with swapped roles of the masses). Anyway, let's assume a perfectly stiff gimbal, and let's talk about the gimbal dampers as a vibration isolation system.

Physically, the item which we commonly call a damper is a combination of a damping element and a spring element. The most crucial points to realize now are these. First:

The damping coefficient of (most) vibration dampers is relatively low.

You may confirm that easily for yourself by using google. The damping coefficient of rubber e.g. is somewhere in the range of few 0.1 or less. And you may also easily confirm that by a simple test, namely tip your gimbal, and you will see it swinging back and forth a couple of times. The necessary consequence of that is, second:

The vibration damper does not always reduce the vibrations. 
In some frequency range the vibrations are actually substantially amplified.

This latter point makes the gimbal damping issue so complicated, because a good vibration reduction in some frequency range is payed for by some substantial amplification in vibrations in a lower frequency range.