Proportional Control
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## 1 Introduction to Proportional Controller Design

Figure 1: Standard Block Diagram

A proportional controller provides fast response to system error. The draw back to the proportional controller is that it cannot drive the system to a 0 steady-state error. I've been told that calibration can significantly reduce the residual error left by a proportional controller but I haven't done this myself.

## 2 Proportional Control Design

The equation for a proportional controller are below

 $LaTeX: K\left(s\right)=k_{p}$

where

$LaTeX: k_{p}$ is the proportional gain.

The Pole Placement design approach to controller design makes it clear that the proportional gain can change the closed loop poles. However, a simple gain can change the closed loop poles to only a very limited set of poles. My suggestion would be to use MATLAB to plot the possible closed loop poles. From that list of possible poles pick the set that produces the best performance.