In this problem you are to investigate steady state error in a proportional control system.  The system is shown below.  You will investigate the behavior of the closed loop system for different kinds of controlled systems with different forms for G(s).

        First, we will examine a situation in which the controlled system - with a transfer function G(s) - is a motor and we are controlling the speed..  The motor has a time constant of one second.  (That number is chosen for convenience, but it can be in the ball park.  Imagine a motor starting up, and you are listening to the speed change as the system reaches a constant speed.  If you can hear the sound in your mind, you probably do that with a system that has a time constant of around one second.)  Anyhow, the transfer function we will use is:

For this system, an input of 1.0 volt to the amplifier that drives the motor produces 1000 rpm as the steady state speed, and the output is in thousands of rpm.  Now, with that in mind, do the following.

• Determine the gain, K, that will produce a SSE of 1% or less.
• Plot the response of the system for that gain.  You may use the first order simulator to see the response.  Click here to get the simulator in another window.

• Is the response as accurate as claimed?