Hi Sarathi

Integrating a constant voltage gives a ramp voltage which will continue to grow with time. As such, in a normal inverting operational amplifier integrator this will continue until you reach the limits of the power supply, i.e. the output will saturate to the rail voltage. I will attach a few pages from my filters book on PSpice which should help you.

Regards

Paul

The integrator gives a zero voltage, if the mean value of the input signal is zero.

Even at zero input voltage is real integrator (for some time) in saturation - thanks to the input voltage unbalance of OPA.

As said by Paul, the time integral of a constant is a ramp, so an opamp-based integrator with a constant input saturates to either the negative or the positive power supply voltage. Nonetheless I want to stress that this is its normal behavior and it is not a problem for a properly designed PID controller designed to operate at DC (e.g in a DC power supply), since the integrator in the PID controller is part of a negative feedback loop, in which the actual input of the integrator is intrinsically set by the loop within its linear region. As a matter of fact, even a single opamp in itself with its frequency compensation network can be regarded as an integrator, nonetheless it does not saturate when it operates in negative feedback configurations. The case of the PID controller is very similar and such controller is therefore useful and effective also for DC signals.

Your problem could be just to test the controller outside the feedback loop. To this purpose, you can add feedback just for testing. The best would be to measure (or to simulate) the controller with a circuit reproducing the feedback characteristics of the plant at DC, while not loading the controller at higher frequencies. A model of the plant connected to the PID controller at DC via the inductance of an LC coupling-decoupling network (with very large L and C values), and connected to the AC signal source through the capacitor, can be used in simulations to this purpose.

Dear Paul, Joseph & Paolo,

                                                       Thanks for your kind reply.

• Currently i am doing a reverse engineering of a product.
• As i said early, the product should maintained a constant D.C voltage ( as equal to set voltage). The objective of the product is similar to boost converter.
• In that product they had used PID controller for controlling a D.C voltage.
• My doubt is, If we give any periodic signal as input for a PID Controller,the ouput will be periodic because the capacitor in the feed back loop need some time to discharge. But here the input  is error between the Set Voltage and the input voltage ( which is D.C), how the product works very fine? it doesn't get saturated (+Vcc / -Vcc)? 
• My simulation (matlab simulation) is working fine, but while i am trying in Analog Circuits instead of using microcontroller, the systems gets saturated.

Dear  Sarathi Kannan,

In order that your circuit wok properly, you must subtract your measured value from your set value. only the difference is input to the integrator. Since the difference is fluctuating around the zero, the integrator will not go saturation. Basically, the error signal that must be filtered. The problem is not with the integrator as this is its nature.as the colleagues pointed out. The solution is in correcting the loop such that the error and not the measured value are entered to loop filter including the integrator. Therefore, your error is  a basic one.

wish you success.

Dear Abdelhalim Zerky,

                                            Sir, thanks for your kind reply. If i passes the error through a low pass filter, the error will be D.C voltage (it wont fluctuate), then naturally integrator will saturate.

Dear sarathi,

Taking the difference between the measured value and the set value will differentiate the signal and make it free from the DC component. The residual will be the fluctuations around the set value. The low pass filter will pass only the low frequency fluctuations. Do not forget that the integrator in the loop acts as the low pass filter. To limit the gain of the integrator at low frequency you have to make it lossy by shunting its capacitor by a suitable resistance.

It seems me now that you have to avoid saturation of the integrator by limiting its gain. This is accomplished by shunting the integrator capacitor by a suitable resistance since the gin of the it will be excessive at very low frequency. You have to adjust the value of the capacitor.

Dear Abdelhalim,

                                  Sir, now i got your point and the main thing is the output of the PID control of that product is Sine wave.  Is it the residual will be a triangle or ramp signal??

Sarathi Kannanو

The residual my  be  of complex waveform. The most important thing is that it fluctuates

around the zero or it may decay monotonically to zero. In the second order system which is under damped the fluctuations will be in form of damped oscillations So, the shape of the error signal will be exponential decaying  signal. Well adjusted systems are under damped with a damping factor of about 0.7.

The analogue PID circuit has to be within an active control loop otherwise it won't work.

Also the sign/polarity of the control output and the input have to be correct, getting one inverted will drive the integrator to one of the rails.

You don't say what sort of time constants you are looking for - uS, mS or Seconds?

Show the schematic please. 

Let me add some insights about the basic idea behind a DC driven integrator...

Its output quantity is an integral of the constant input one; so it will continuously changing... like the water level inside a vessel when opening the tap... or a moving car... This can continue endlessly only in two ways.:

• the supply voltage is infinitely high (a theoretical assumption) or we change it simultaneously with the voltage variations (following supply voltage)
• we reverse the direction of the "movement" when the output voltage reaches the power rails (the basic idea of relaxation oscillators)

The latter is the clever trick to get an endlessly continuous movement in this world...

feedback is positive! change it to negative, and if oscillations occur stabilize the loop!