Controller Fusion
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## 1 Introduction to Controller Fusion

What I am calling controller fusion is a version of simple Sensor Fusion for controllers. The idea was spurred by work on a Reaction Cancellation proposal. The idea never matured enough to be useful to that application so I don't think I'm giving away any proprietary information here.

For this proposal we need a very fast response time which required a proportional controller. The unfortunate byproduct of a proportional controller is a non-zero steady-state error. So I was trying to devise a means of controlling the system with a proportional controller when the error was large while employing PI-Lead controller when the error was small. The point of the PI-Lead controller being to drive the steady-state error to zero.

## 2 Basic Implementation for Controller Fusion

The basics of controller fusion are similar to that of sensor fusion. In controller fusion though I used the relative magnitude of high and low frequency portions of the error to scale the proportional controller and PI-Lead controller outputs.

In my implementation I filtered the error signal with a Low Pass Filter (LPF) and a High Pass Filter (HPF). The outputs of these filters were used as a form of automatic gain control.

 $LaTeX: \frac{LPF}{\left \| HPF \right \| + \left \| LPF \right \|}$ Gain for PI-Lead Control Output

 $LaTeX: \frac{HPF}{\left \| HPF \right \| + \left \| LPF \right \|}$ Gain for Proportional Control Output

where:

$LaTeX: LPF$ is the output of the LPF,
$LaTeX: HPF$ is the output of the HPF and
the input to both filters is the error signal.

The idea being that a large step command will pass through the HPF untouched and barely come through the LPF at all. Then, after the system has settled from the step command, the non-zero steady-state error passes through the LPF but not the HPF. The values seen in the equations above are fed into the 2 controllers as their respective inputs. The outputs of both controllers are summed together and fed to the plant.

## 3 Early Results

The early results showed promise or I wouldn't bother writing an article on controller fusion. However, this was a proposal effort which means you have very limited hours to work on a lot of design iterations. So during this proposal I never had the time to sit down and mature this control technique. It may lead nowhere but I find it an interesting concept.