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

In summary, the conversation discussed the concepts of open loop and closed loop control in control theory and electronics. It was explained that open-loop control does not use feedback, while closed-loop control uses feedback to control the output of a dynamic system. An example using an opamp was provided to illustrate the difference between open and closed loop gain.
  • #1
nbo10
418
5
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
 
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  • #2
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.
 
  • #3
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.
 
  • #4
Thanks, that's what I was looking for.
 
  • #5
ranger said:
So basically an open loop lacks feedback and a closed loop performs operation with feedback.

Thank you, I was also wondering the same thing.
 

1. What is the difference between open and closed loop gain?

Open loop gain refers to the gain of an amplifier without any feedback, while closed loop gain refers to the gain of an amplifier with feedback. In other words, open loop gain is the gain of the amplifier itself, while closed loop gain takes into account the effects of the feedback circuit on the overall gain.

2. How does feedback affect the gain of an amplifier?

Feedback has a negative effect on the gain of an amplifier, reducing it from the open loop gain. This is because the feedback circuit introduces a portion of the output signal back into the input, which acts to counteract the original input signal. The amount of feedback determines the amount of reduction in gain.

3. Which type of gain is more stable - open or closed loop gain?

Closed loop gain is more stable than open loop gain. This is because feedback helps to reduce the effects of changes in component values, temperature, and other factors that can affect the gain of an amplifier. Closed loop gain is more consistent and predictable, making it the preferred choice for most applications.

4. How does open vs closed loop gain affect the frequency response of an amplifier?

Open loop gain typically has a flatter frequency response compared to closed loop gain. This is because the feedback circuit can introduce phase shifts and other distortions that affect the frequency response. However, closed loop gain can be designed to have a desired frequency response by carefully selecting the feedback components.

5. What are some practical applications of open vs closed loop gain?

Open loop gain is often used in high-gain amplifiers, such as in instrumentation and audio applications. Closed loop gain is commonly used in audio amplifiers, where stability and predictable gain are important. It is also used in feedback control systems, such as in motor control and temperature regulation, to achieve precise and stable operation.

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