As you learn about control of a first order system, it is helpful to tie together the various concepts that you need.

        Starting with a first order system

• The parameters of a first order system are the time constant and the DC gain.
• Using the parameters, you can determine a transfer function.
• Note that the pole of the system is the negative reciprocal of the time constant.
• To us proportional control in this system, you need to choose a proportional gain, K_p.
• The time response of the closed loop system will probably not match the desired response exactly.  There will be a steady state error (SSE).
• The time constant you observe in the closed loop system will not be the same as the time constant of the plant - i.e. the system you are controlling.