# Effects of feedback

After doing some exercises in control theory I realized that one don't really need feedback to fulfill a lot of specifications. One could in principal introduce a controller giving us stability etc for any reference signal to the system.

How does the idea of feedback become relevant in situations such as following a signal or get a stable system? To me it looks like a open loop controller does the job as well.

• Give us an example. – Leon Heller Feb 25 '18 at 11:01
• Open-loop control drifts over time: if you drive a mechanism 10cm one way then 10cm the other way with 0.1mm error each time, after a thousand cycles it could be entirely in the wrong place. – pjc50 Feb 25 '18 at 11:13
• @LeonHeller suppose we want the output to be constant = C then we use a controller defined for the reference say a PID for instance u(r) such that we get the constant we want for any reference. We can do alot of "tweeks" and "tuning" changing the paramaters of the PID or adding some Lead-Lag getting the system to do all sorts of things also for responding to changes in the choice of constant C. – user21312 Feb 25 '18 at 11:19

Reasons to use feedback:

1. The system characteristics are not well known enough. Most models are appoximations. Sometimes the system is too complex to fully model accurately enough. Sometimes the exact parameters of the system aren't known well enough.

For example, consider cruise control in a car. You can try to model the slope, the power of the engine at various speeds and throttle settings, the engine temperature, the type of fuel used, etc. However, there will be parameters you really can't measure realistically. What about tire inflation level, the total weight? Then there will be other parameters that matter but you fail to take into account.

2. The characteristics of the system change due to external conditions. You can't measure everything. In the cruise control example, consider wind, road surface condition, momentum lost due to hitting rain, etc.

3. The characteristics of the system change over time. The engine produces less power as the pistons seals get worn. The injectors wear and don't squirt out exactly the same amount of fuel for the same length pulse. Bearings wear and present more or less friction.

4. The characteristics of the system differ between units. No two units off the production line are going to be identical. Even if you calibrate the controller for each unit during production, the drift from that starting point won't be identical per unit.

5. Errors accumulate. Imagine controlling the steering open-loop instead of the speed. Even if you were only off by 0.1° coming out of the last turn, that adds up with distance. After 10 m you are only off by 17 mm. After 100 m, you're off by 175 mm sideways. After a mile you're off sideways by 9 feet. Now you're in the oncoming lane or in the ditch off the side of the road.

This example my sound absurd, but that's exactly what you are proposing to do.

In short, closed loop feedback is necessary to maintain accuracy in many cases by correcting for the inevitable errors that can't be known or that would be too impractical to know.

• ah, so one benefit is that one could "counter" the offset that is mentioned in 5 ariseing due to 1-4, in the right direction some sense? – user21312 Feb 25 '18 at 18:41
• @user21312 it's not just "one benefit" - try to work with any real system that is strictly dependent on numerical models (e.g. engine controller) or has to remain stable during variable conditions (e.g. power supply) and you'll see that what Olin said is just that - without a feedback loop, the circuit will often go haywire as soon as the conditions change, even if the changes are slight. It's, from my experience, mostly due to the nonlinear behaviour of those circuits - if there's any path that can amplify and/or accumulate the error, you'll get erroneous results quickly. – vaxquis Feb 25 '18 at 19:40
• @user: #5 doesn't always apply since errors don't always accumulate, depending on which integral or derivative you get to control. Still, the point is that feedback allows for accurate control despite various inevitable errors. Some errors you don't know, some you can't model, some you don't even know about at all. Stuff happens. Not all control systems need or use feedback, but it is certainly common and important. Controlling the position with a stepper motor is a example of something that is often done open loop. – Olin Lathrop Feb 25 '18 at 19:41
• @user21312 as for the science behind it: en.wikipedia.org/wiki/Stability_theory , en.wikipedia.org/wiki/Resonance , en.wikipedia.org/wiki/Thermal_runaway#Electrical_engineering etc. – vaxquis Feb 25 '18 at 19:41

Well you could be sitting at your table with a cup of tea. Then you could ask yourself, would it work if I closed my eyes and reached my arm over to pick up the cup. You could try it of course and possibly get a burnt leg or arm so, using feedback via your eyes is usually safer and gives a higher precision result compared to blind open loop.

You could be sailing a boat and aiming for a harbour then along comes a sideways tide that could drive you onto the rocks (if you didn’t use some means for correcting the boats position).

• So you are saying a bad model or disubances are countered? But still stabalizing a system could be done using a open loop right? – user21312 Feb 25 '18 at 10:56
• Disturbances, wear and tear, friction, stiction all contribute to an error when using open loop controllers. You can partially overcome some of these things with a brute force controller but that wastes power and still may not provide the degree of accuracy that closed loop gives you. – Andy aka Feb 25 '18 at 11:00
• Actually even with your eyes closed you have tons of sensors which give your brain feedback about where all your body parts are located (proprioception). It is suprisingly accurate (try tapping both your index fingertips together behind the back of your head), we actually use nested loop(s) feedback with vision as the outermost loop... – peufeu Feb 25 '18 at 13:21
• @user21312 Using an open loop how do you know if the system is stable or not? – user253751 Feb 25 '18 at 22:03
• @immibis it stay bounded or behaves niceley for all inputs – user21312 Feb 26 '18 at 6:56

You could conceivably design an open-loop controller that does exactly what you want to when you first build it but then there is a change in temperature, humidity or sign of the zodiac (kidding) and everything is different. In electronics for example, the trans-conductance of transistors is heavily temperature dependent. Furthermore, it is often very difficult to model a system accurately and it may be next to impossible to control the parameters of your system exactly during manufacturing. To use another transistor example, the Beta parameter of a transistor exhibits a wide spread for a given transistor model, you could measure each transistor individually I suppose but then again the parameter will vary with temperature etc.

Closed-Loop feedback always you to build predictable circuits out of unpredictable components. The same goes for any control system.

How does the idea of feedback become relevant in situations such as following a signal or get a stable system? To me it looks like a open loop controller does the job as well.

Well, let's say you want to follow a signal without using any feedback at all.

Let's say you got something in this configuration, no feedback. The output will be about $\text{input}-V_{be}$, it is a follower with some offset. But notice how the offset is not a constant, it is dependent on the input voltage.

So you might be thinking that you can solve the offset by cascading a P-based follower. Well that looks like the following schematic:

The largest offset of around 600 mv, the $V_{be}$, was removed. But the non-linearity from the $V_{be}$ got worse. This is all fine and dandy if you are okay with an offset that is dependent on the input voltage and that is only going in the range of -676 mV to 100 mV. The 100 mV happens when the input is set to 5 V, the -676 mV happens when the input is 0 V.

So sure, you can live without feedback if you are okay with relatively large errors. But how on earth would you make something more advanced than a follower? Let's say you would want something that multiplies with a gain of 2. In order for the output to know that it is twice as large, then it has to know how wrong it is. In other words, you need feedback if you are going to do anything that has any specific amplification, or you need to calibrate your amplifier 24/7 due to noise, like temperature for an example.

It's like you've been spun around blindfolded and then asked to point to north, you have no idea where north is. But if you have a compass and take off the blindfold, then you can see how much wrong you are and point accurately at north.