Instead of PI or PD if we replace the system only by I or D, what will happen?Actually I need to know what will be the effect of system response. Also in fuzzy logic controller, if we don't connect P controller with (Z-1)/Z block in simulink, there will be any deviation occur in system response.
There was a discussion on Research Gate on similar topics:
What are the separate and combined effects of increasing proportional and derivative values of P I controller in a feedback loop?
Trying to explain the physical meaning of things, assume that you have an input command u(t) and you are interested for the output y(t) to follow this input.
So, you measure the output and close the loop by measuring the error e(t)=u(t)-y(t).
This error is supplied to the system and affects the output.
If there is a positive error, it implies that the input is larger than the output and then the output will be moved in the positive direction (to increase) until it equals the input and the error is zero.
If there is a negative error, it implies that the input is smaller than the output and then the output will be moved in the negative direction (to decrease) until it equals the input and the error is zero.
If things are slow, you increase the gain P to get a faster time response that you would like.
Now, this assumes that everything stops when the error is zero. However, things have inertia and this implies that your system reaches zero error at some nonzero velocity and will continue moving beyond the desired position. This is the origin of the D term, which introduces a signal proportional to the velocity and this term opposes the velocity effect.
Also, unless P is very large, you end with a pretty large non-zero steady state error. Besides, systems have friction, which also does not allow it to reach zero tracking error. Therefore, the integral term I accumulates the error signals. So, if the error is not zero, its integral keep increasing and keeps moving the output until the error is zero.
The P portion increases system bandwidth. It is easy to see why if you plot the root locus or you just see the closed loop pole of a first order system as a function of the proportional feedback gain (the closed loop is GH/(1+GH)--1st order G=1/(s+p)--with only proportional feedback, GH/(1+GH)=k/(s+p)/(1+k/(s+p)))=k/(s+p+k). You can use high gains in some situations, provided your actuators are fast enough to respond that fast and your system does not have non-minimum phase zeros or high relative degree.
PID generally assumes that the controlled system is effectively second order, something true for most observable/detectable dynamics in the frequency range of practical closed loop operation--the integral term avoids tracking error (a consequence of the internal model principle--you can use double integrators or more complicated dynamics inside your controller) when you are tracking constant values, the Derivative term adds damping.
Look up all of the definitions of the terms I have mentioned on the web!
System bandwidth, closed loop bandwidth, actuators, relative degree, minimum phase system, unstable zeros, observability, detectability, internal model principle, tracking constant, damping.
Best,
Kartik
There was a discussion on Research Gate on similar topics:
What are the separate and combined effects of increasing proportional and derivative values of P I controller in a feedback loop?
Trying to explain the physical meaning of things, assume that you have an input command u(t) and you are interested for the output y(t) to follow this input.
So, you measure the output and close the loop by measuring the error e(t)=u(t)-y(t).
This error is supplied to the system and affects the output.
If there is a positive error, it implies that the input is larger than the output and then the output will be moved in the positive direction (to increase) until it equals the input and the error is zero.
If there is a negative error, it implies that the input is smaller than the output and then the output will be moved in the negative direction (to decrease) until it equals the input and the error is zero.
If things are slow, you increase the gain P to get a faster time response that you would like.
Now, this assumes that everything stops when the error is zero. However, things have inertia and this implies that your system reaches zero error at some nonzero velocity and will continue moving beyond the desired position. This is the origin of the D term, which introduces a signal proportional to the velocity and this term opposes the velocity effect.
Also, unless P is very large, you end with a pretty large non-zero steady state error. Besides, systems have friction, which also does not allow it to reach zero tracking error. Therefore, the integral term I accumulates the error signals. So, if the error is not zero, its integral keep increasing and keeps moving the output until the error is zero.
The PID controller parameter actions can be described as
Proportional gain KP reduces rise time, increases overshoot and decreases steady state error. Integral gain KI reduces rise time, increases overshoot and eliminates steady state error - improves steady state performance. Derivative gain KD reduces overshoot and settling time (improves transient performance along with KP). You can use Integral control action alone but not derivative control as the output of derivative control becomes zero when error becomes constant.
Hi Debottam,
in addition to all previous answers, which are quite good, let me just add a thought.
As I see it, it depends on the implementation. If it is series, the PI and I transfer functions have the same structure (only parameter values are different), the same is true for PD and D. Not so in the case of parallel implementation. The reason we separate these actions is mostly practically, because it is convenient to think in terms of tuning these terms separately. Also, commercial PIDs will come with different "knobs" for tuning.
Hope that helps.
Cheers.
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