1. Basic Design of PID Controller

2. What is PID Controller A PID controller ,
P – Proportional
I – Integral
D- Derivative
The transfer function of the basic form of PID controller:
C(s) = KP + KI/s + KDs
=(KD s2+ KPs + KI)/s
C (s)

3. Basic PID Controller C (s) where KP = Proportional gain
Ki = Integral gain
KD = Derivative Gain
In the figure above, the controller is used in a unity closed loop feedback controller . The control signal from the controller to the plant is equal to the proportional gain, KP times the magnitude of the error plus the integral gain KI, times the integral of the error plus the derivative gain KD times the derivative of the error,

4. Why we use PID Controller
Due to simplicity and excellent if not optimal performance
Use in many applications in control industry
No extensive background need to be tuned by operators
Can be tune on-site, practicable

5. How do the PID parameters affect system dynamics?
The most interested in major characteristics of the
closed-loop step response are
1. Rise Time: the time it takes for the plant output y to rise
beyond 90% of the desired level for the first time.
2. Overshoot: how much the the peak level is higher than
the steady state, normalized against the steady
state.
3. Settling Time: the time it takes for the system to
converge to its steady state.
4. Steady-state Error : the difference between the steady-state
output and the desired output.

7. Ziegler-Nichols Tuning Rule

8. The Ziegler-Nichols tuning Rule Table
Using the parameters L and T, the values of
is set according to the formula shown in the table below.
The parameters above give a response of overshoot about 25% with good settling time. The fine-tuning of the controller should use the basic rules relate each parameter to the response characteristics

9. Example 1

10. Solution
Imaginary part
Real part K=30

12. Example 2
Design a PD controller that has 20% steady-state error due to step input. The system also requires that the overshoot percentage is less than 5% and settling time of less than 2 seconds. Also determine the range of controller constants for stability. State the dominant poles on the s-plane that satisfies these design requirements.

13. Summary
Relations between Kp, Ki and KD and important response characteristics
Use Kp to decrease the rise time
Use KD to reduce the overshoot and settling time
Use KI to to eliminate steady state error
The Ziegler-Nichols tuning rule (action curve method) is used to estimate the initial of the parameters.