Controller Stability, Performance, and Robustness
The purpose of this web-page is to provide some general understanding to the terms stability, performance, and robustness for those customers who are interested, but don't necessarily want to dive into the technical aspects of flight control system design. This information can provide potential customers with additional insight that may allow them to ask the right questions when deciding upon a control system that suites their needs.
First, lets look at simulations of simple single axis stable and unstable controllers. These controllers can all be thought of as closed loop systems, meaning that a sensor, or combination of sensors are used to feedback error to the controller. The objective of the controller, is to drive the output to the reference. In all of these examples, the reference output is 0. Figure 1 shows a simulation of an unstable controller trying to control a very small 3 degree perturbation. This perturbation could have been caused by a wind gust, for example. As is shown, this 3 deg error quickly diverges into a 30 deg error and beyond as time goes on. This vehicle is going to crash.
The rest of the figures shown on this page are simulations of stable controllers. This does not mean that they wont crash a helicopter or airplane however! Take a look at Figure 2. This is an under-damped controller trying to regain control from a 25 deg error (50 mph wind gust for example). You may notice that the controller can respond rapidly by sending the error to 0 in a short time period, but then overshoots all the way to -15 degrees. Because the controller gain is too high, it takes several oscillations and significant time to reduce the error to 0 without overshoot. During this time, it is probable that the vehicle will sustain additional wind gusts. The result will be a helicopter that never stops oscillating, and will not be able to fly in high gust conditions.
Figure 3 is a simulation of an over-damped controller. "Low Performance" is another way to describe this controller. This aerial vehicle will perform very poorly in gusty conditions (in a helicopter this translates to poor station keeping ability) and in extreme cases, will not be able to sustain flight.
Figure 4 is what might be an acceptable attitude controller. The controller exhibits rapid recovery, and acceptable overshoot to recover extreme attitude errors. The idea here is rapid recovery with very little overshoot.
Finally, Figure 5 simply shows how the same controller that was simulated in Figure 4, responds to a small 3 degree error.
Now that we have differentiated between stability and performance of a controller, what about controller design. There are several classes of aircraft control structures that guide the design of the control loops and selection of the gains. Some of these include: Optimal Control (ex. LQR, LQG), Adaptive (ex. neural network), Classical PID, and Robust Control (ex. H-infinity), along with many others. The WePilot flight control systems offered by Viking are classified as Robust and are designed based on H-infinity methods. This is a strict mathematical method that considers stability of the closed loop throughout the specified flight envelope, while optimizing performance in the mathematical sense for the required robustness.
It is important to understand that a controller is designed to handle specific dynamics, and changing these dynamics (with the addition of payload for example) can effect the performance and stability margin of the controller. This is where a controller's robustness comes into account.
As an example, a controller that does not exhibit sufficient robustness may perform very well in windy conditions. This controller, however, when introduced to a variable payload/CG will become oscillatory or unstable. To account for this, a non-robust controller must be "de-tuned" in order to have sufficient margin for uncertainties (ex. payload/CG) and will no longer exhibit high performance in gusty wind conditions. H-infinity is simply a method to optimize performance while assuring stability throughout range of uncertainty.
Designing a control system and tuning gains for aerospace vehicles is similar to tuning a carburetor that has 30 needle valves. There will surely be more than one setting that allows the motor to run. But in aerial applications, we want the settings that will exhibit the best performance without sacrificing reliability.
What does all this mean for our customers? Our vehicles' control systems are designed to perform in higher wind conditions while demonstrating great stability throughout a larger range of payload weight...