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# PID controller, Lead/Lag, Type 2 and Type 3 controller2

## PID controller, Lead/Lag, Type 2 and Type 3 controller

(OP)
Hi guys,

I have a doubt:

I am trying to understand the controller to control a smps and from what I have seen, in power electronics book they talk about the type 1, 2 and 3 controller. I had online classes about this topics where the controller that was used to control a smps was a PID type. However I have heard about the lag/lead compensator and then after all this I became confused!

What are the differences between PD, PI and PID to the lead/lag lead-lag compensator? Moreover where those types 1, 2 and 3 of controllers fits on the PD, PID, PI, lead/lag?

I so confused!

Kind regards.

### RE: PID controller, Lead/Lag, Type 2 and Type 3 controller

P Proportional
I Integral (Old school, reset)
D Derivative (Old school pre-act)
Depending on the application, the reset and/or derivative functions may not be used although they are usually included in the controller.

Bill
--------------------
"Why not the best?"
Jimmy Carter

### RE: PID controller, Lead/Lag, Type 2 and Type 3 controller

None of the controllers you mentioned are the same. Here are some basics, though in most cases, I'm neglecting to discuss the DC gain term or individual tuning terms that accompany each controller.

A lag controller is a single pole, single zero controller where the pole is at lower frequency than the zero. It usually is used to reduce steady-state error by adding low frequency gain.

A lead controller is a single pole, single zero controller where the pole is at higher frequency than the zero. It usually is used to improve stability margins by adding low frequency phase lead from the zero.

A lead/lag controller has two poles and two zeros, with the poles sandwiching the zeros. This is essentially a lag and lead compensator in series.

Type 1 is pure integral control. This will eliminate error to a step function disturbance, but reduces stability margins. In some systems, it works fine, but is usually slow to respond because it's reduction of stability margins means it has to be used with a low gain.

Type 2 is a controller with two poles (one an integrator) and one zero. It is essentially a Type 1 in series with a lead controller.

Type 3 is a controller with three poles (one an integrator) and two zeros, where the additional pole and zero are often placed at the same location as those in a Type 2 controller (i.e., a Type 3 is a controller with an integrating pole, a double pole, and a double zero). It is essentially a Type 1 in series with two identical lead controllers.

A PD consists of a single zero, and is usually used in systems that have integration already to provide better stability margins. It is often used in the feedback path acting on the plant output rather than on the error signal.

A PI compensator consists of a single pole (an integrator) and a single zero. The integrator removes steady-state error to steps, and the zero improves the stability margins.

A causal PID compensator consists of two poles (one an integrator, one at high frequency to cutoff the derivative to prevent amplifying noise and step signals to infinity), and two zeros between them.

xnuke
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### RE: PID controller, Lead/Lag, Type 2 and Type 3 controller

Anybody else think it would be a good idea to combine those last two answers into a FAQ?

A.

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