1. PD Controller 1.Find the steady-state output due to unit-step r d. 2.Find the steady-state output due to unit-step input (with r d =0). + - + - + -

2. PID Controller 1.Find the steady-state output due to unit-step r d (assume ). 2.Find the steady-state output due to unit-step (assume r d = 0). + - + - + - +

3. Selection of gains K P, K I and K D : Characteristic equation is: For stability:

4. PID Controller Design with Root- locus + - + + - 1.On s-plane, mark the plant poles and zeros. 2.Where should be controller zeros be located for a good response?

5. -5-5 Two poles at the origin (one of the system and another of the PID controller) Re s Im s

6. controller zeros Choose K D for real repeated poles.