Basic Design of PID Controller

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)

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,

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

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.

Ziegler-Nichols Tuning Rule

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

Example 1

Solution Imaginary part Real part K=30

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.

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.