Controller in the feedback path? What happens if the controller of a closed-loop system is placed in the feedback path before the summation point, instead of between the summation point and the plant to control? Are we allowed to do so? If so, what are the main differences?
Thanks!
Assuming $P$ is the transfer function of your process and $C$ the transfer function of your controller.
The closed-loop transfer function of a standard control loop, with the controller in the normal path, is
$$ G(s) = \frac{C(s)P(s)}{1+C(s)P(s)}$$
while the transfer function of your alternative controller is
$$G_{alt}(s) = \frac{P(s)}{1+C_{alt}(s)P(s)}  
$$
If you set your new alternative to controller to
$$
C_{alt}(s) = \frac{1+P(s)C(s)-C(s)}{P(s)C(s)} 
$$
You will get the same closed-loop transfer function (G(s))
That being said, not sure it's a good idea for 2 reasons
1 - To get to same result as the original controller, you need to cancel poles and zeros in the alternative closed-looped transfer function. If you cancel a RHP zero with a RHP pole, your final transfer function will seem stable however your controller will not be, the output of your alternative controller could become unbounded.
2 - Even if you don't cancel RHP zeros with RHP poles, this method is way more complicated.