Understanding the Difference Between Open and Closed Loop Gain in Control Theory

[nbo10]

Hi all,
I've been reading up on control theory, op-amps and other electronics related items. Open loop and closed loop gain keeps poping up and I just can't get a grasp of the concept. Can anyone provide a quick and dirt explanation and maybe an example? Thanks

 

[ranger]

An open-loop controller does not use feedback to control states or outputs of a dynamic system. Open-loop control is used for systems that are sufficiently well characterized to predict what inputs are necessary to achieve the desired states or outputs. E.g. the velocity of a motor may be well characterized for the voltage fed into it, in which case feedback may not be necessary.

A closed loop is a system in which the output of one or more elements is compared to some other signal to provide an actuating signal to control the output of the loop.

So basically an open loop lacks feedback and a closed loop performs operation with feedback.

 

[berkeman]

To expand on ranger's answer in the specific case of gain, it's easiest to consider an opamp. Look at the "open loop frequency response" plot of an opamp on its datasheet. You'll typically see a maximum gain of 100+dB at DC and a few Hz, and then the dominant pole (usually around 10Hz for simple opamps) starts rolling off the open loop gain at 10dB/decade. The open loop gain gets down to unity 0dB near where the 2nd pole is located, often around 1-10MHz. There's a whole discussion about opamp stability and this gain-phase plot, but I'll skip that for this thread.

So if you hold the "-" input of the opamp steady and wiggle the + input some, the size of the output signal is determined by this open loop gain. Well, sort of ... even for -100dB signals near DC, you'll peg the output because of all the gain, etc., etc.

But opamps aren't designed to be used open-loop. They're designed to be used in various feedback configurations. So take the same opamp from the example, and close the feedback loop by tying the output to the "-" input. Now when you wiggle the "+" input, the opamp is going to drive its output to try to keep the + and - inputs at the same voltage (because of the negative feedback of the output to the - input). The closed loop gain in this "follower" configuration is +1 from the + input to the output of the opamp.

If you instead connect a resistor from the output to the - input, and connect another resistor from the - input to ground or some other reference, then you get a net gain from that feedback configuration, and your closed-loop gain is now 1 + Rf/Rd. You can also use feedback configurations that give you negative gain from Vi to Vo, and you can add reactive elements like capacitors to give you a closed-loop gain that varies with frequency.

Check out an opamp datasheet and application notes for more info. Also, check out the book "The Art of Electronics" by Horowitz and Hill for a very good intro to electronics and opamps.

 

[nbo10]

Thanks, that's what I was looking for.

 

[yopy]

So basically an open loop lacks feedback and a closed loop performs operation with feedback.

Thank you, I was also wondering the same thing.