As a starting point, consider proportional control and look at the resulting root locus. Hence, no matter what the gain, the system will always be unstable, so we instantly conclude that proportional control is no good. We must do something to attract this branch of the root locus back to the left half of the complex plane. PID control will certainly not do this for us, since an integral term adds another pole at the origin. The pole assignment control design method uses the Diophantine equation.
B has degree at most n .
The root locus for the entire system is shown below. To illustrate this, try altering the controller in the following JAVA applet. You should try altering the noise level to see the effect of measurement noise. The scale of the graph is such that each vertical division represents 0.4m. You can try to come up with a better controller using to pole assignment method.