Learn more. Why does a proportional controller have a steady state error? Ask Question. Asked 8 years ago. Active 6 years, 3 months ago. Viewed 48k times. Improve this question.
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Improve this answer. Guy Sirton Guy Sirton 1, 13 13 silver badges 15 15 bronze badges. If you have a system with zero friction, or a system that doesn't lose heat to the environment then a P controller could asymptotically converge on zero So you are saying that in theory with zero friction, no heat, etc there would be no offset error for P-only controller? Can you tell how this is shown by using math as Dan M's post below? That's a mathematical proof that a proportional controller can't zero the error in any system that is subject to external force heat loss, gravity, whatever which is any real world system.
Dan's math is stronger in the sense that it shows that there is always a bias even in systems that don't exist in the real world. If the error is already zero and there is no force acting on the system there is no bias. Let's express our output Y s in terms of everything else. In this example, a small change in temperature provides a large change in output. If the setting is too small for the process dynamics, oscillations will occur and will not settle at set point.
A large PB setting makes the controller act sluggish and will not respond adequately to upsets. Since proportional control does not incorporate the time that the error has existed, there will always be an offset from set point. Typically, flow or pressure controllers have a much larger proportional setting due to a possible narrower measurement range and fast process reaction to a change in the control output.
Whenever a process load change occurs and makes the process deviate from the steady state condition, the controller will respond and limit the excursion of the controlled variable.
For this to occur, and error must develop, because, for the controller output CO to be at a value other than the bias b , there must be an error, and so, if the load change continues, so will the error. While the tank level decreases, the error increases and our proportional controller increases the controller output proportional to this error. Consequently, the valve controlling the flow into the tank opens wider and more water flows into the tank.
As the level continues to decrease, the valve continues to open until it gets to a point where the inflow again matches the outflow. At this point the tank level and error will remain constant. Because the error remains constant our P-controller will keep its output constant and the control valve will hold its position. The system now remains at balance, but the tank level remains below its set point. This residual sustained error is called Offset.
Figure 6 shows the effect of a sudden decrease in fuel gas pressure to the process heater described earlier, and the response of a p-only controller. The decrease in fuel-gas pressure reduces the firing rate and the heater outlet temperature decreases. This creates and error to which the controller responds.
However, a new balance-point between control action and error is found and the temperature offset is not eliminated by the proportional controller. This is typically done by putting the controller in manual mode, changing its output manually until the error is zero, and then putting it back in automatic control. The need for manual reset as described above led to the development of automatic reset or the Integral Control Mode, as we know it today. Given enough time, integral action will drive the controller output far enough to reduce the error to zero.
A large value of T I long integral time results in a slow integral action, and a small value of T I short integral time results in a fast integral action Figure 7. If the integral time is set too long, the controller will be sluggish, if it is set too short, the control loop will oscillate and become unstable.
Figure 7. Most controllers use integral time in minutes as the unit of measure for integral control, but some others use integral time in seconds, integral gain in repeats per minute or repeats per second.
Table 2 compares the different integral units of measure. Commonly called the PI controller, its controller output is made up of the sum of the proportional and integral control actions Figure 8. Compared to Figure 6, it is clear how Integral control eliminates offset. The third control mode in a PID controller is derivative.
Derivative control is rarely used in controlling processes, but it is used often in motion control. For process control, it is not absolutely required, is very sensitive to measurement noise and it makes trial-and-error tuning more difficult. Nevertheless, using the derivative control mode of a controller can make a control loop respond a little faster than with PI control alone.
The derivative control mode produces an output based on the rate of change of the error Figure Derivative mode is sometimes called Rate. The derivative mode produces more control action if the error changes at a faster rate. If there is no change in the error, the derivative action is zero.
The derivative mode has an adjustable setting called Derivative Time T D. The larger the derivative time setting, the more derivative action is produced. A derivative time setting of zero effectively turns off this mode. If the derivative time is set too long, oscillations will occur and the control loop will run unstable.
Commonly called the PID controller, its controller output is made up of the sum of the proportional, integral, and derivative control actions Figure There are other configurations too.
This reduces the effect of a disturbance, and shortens the time it takes for the level to return to its set point. Figure 13 compares the recovery under P, PI, and PID control of the process heater outlet temperature PV after a sudden change in fuel gas pressure as described above. Figure Stay tuned! Mohd, you could take a look at this book: Process Control for Practitioners Jacques.
From mathematical, the reset action is not comprehensible. Maiti: Here is a practical example of everyday integral action. This is equivalent to proportional action. Then the temperature might be closer, but still not exactly on target. So you slowly turn the tap some more. The closer you get to the desired temperature, the slower you turn the tap.
You continue turning the tap slower and slower until the temperature is exactly on target and then you stop turning the tap. This secondary action is a pseudo integral action. The larger the error, the faster the corrective action is done, and it continues changing the controller output at a progressively slower rate until the error is zero.
Then he puts the controller in auto. It was quite nice going through it…thanks.. I have a very simple question. As in Honeywell analog outputs only having 4 points for non-linear correction.
I have been in the PID control tuning business one way or another for over 20 years. I am looking for conformation on what I consider the first and foremost property necessary to have a 1 chance in times to control the primary control Set-point in all ranges.
Thank You! Instead, the system produces a small permanent offset in reaching compromise position of controller output under new loads. Whenever there is one-to-one correspondence of controller output is required with respect to error change proportional mode will be ideal choice. The offset error limits the use of proportional mode, but it can be used effectively wherever it is possible to eliminate the offset by resetting the operating point.
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