PID has served the process control industry for well over a decade and has solidified itself as the primary technique for feedback control systems. Over the years, the technique has seen a number of upgrades and improvements, giving way to pneumatic, electronic, and computer-based devices, ensuring tighter control over processes.
One of the first breakthroughs in PID systems was the integral action, also known as automation reset, which significantly improved the performance of controllers equipped with proportional action. A “P-only” controller applies a corrective effort proportional to the difference between measured value and the setpoint, which can be summed up as:
- If the difference or error increases, the P-only controller responds with a positive control effort to reduce the difference.
- If the difference decreases, the controller injects a negative control effort.
The entire implementation is easy to understand and maintain but holds the flaw of longevity, meaning as the error decreases so does the control effort. This slows down the rate at which the error is diminished, increasing the overall time taken for the error to cease. But the error never ceases to exist as well, with the P-controller leaving the process with a slight offset.
This steady-state error is corrected through integral action that operates in parallel to the P-controller, ensuring that the control effort remains for as long as the error has a non-zero value. This makes up for the PI controller. While this controller ensures a consistent effort to eliminate the error, it gives rise to other problems. The most important problem that arises is closed-loop instability, with the integral action causing the process variable to overshoot the desired setpoint. This problem becomes exceptionally harmful if the control process is highly sensitive, causing the overshoot to create an even larger error in the opposite direction. This kicks off yet another error-elimination process.
To rectify this, engineers use analytical techniques to determine integral and proportional gains that would fit perfectly for the process.
The Reset Windup Error
If a large control effort is used to mitigate an error of significant magnitude for a process whose actuator is too small, the result is reset windup. The actuator gets saturated at a specific value corresponding to its maximum output, unable to affect the process any further. The operator can try to mitigate the problem by reducing the setpoint’s value so that it falls within the range the actuator can achieve, but this won’t work. Why? Because by this time the integrated error would have achieved a huge value, and the controller would continuously try to get the actuator to generate a response higher than its upper limit.
However, if the setpoint is dropped low enough, the integrated error will start to decrease. This would have to be combined with a string of negative errors to cancel out the effect of positive errors accumulated during the time the actuator had been in the saturated state.
Another way of getting rid of this error is by installing an actuator that’s large enough to produce a change required for the process without saturating.
The Pre-Loading Fix
Reset windup can also take place if the actuator is off while the controller is on. For instance, in the case of a cascade controller, if the inner loop is in manual mode, it would have no effect over the outer-loop controller. If the outer-loop controller continues to operate, its integral action would “wind up”.
A simple solution to this problem is that whenever the actuator isn’t running, the controller’s integrator should be turned off. Another solution is to adjust the setpoint to the process variable’s value in-between batches. But, there are better methods of fixing reset windup.
In a pre-loading scenario, the controller’s integrator output is fixed so that the process will start the next batch with the error it acquired from the preceding batch. With pre-loading, the reset can continue right from the previous batch, cutting down the time required to settle to a constant state.
This works best if the batches are identical so that the controller has to obtain the same setpoint every time. If the batches aren’t identical, then a mathematical model must be used to predict the integral action required for the next round. This approach works for a continuous process if modeled before starting up the process.
The Bumpless Transfer Fix
However, pre-loading can lead to a few hiccups. One potential issue is the abrupt adjustment to the actuator’s output once each round starts, which can damage the actuator. Similarly, when the controller is switched from automatic to manual mode and vice versa, any attempt by the operator to modify the control effort can also damage the actuator.
Bumpless Transfer uses artificial pre-loading to resolve these hiccups. The integrator is loaded with the value required to restart operators, eliminating the need to change the control effort. The controller would still have to account for changes in the process variable or setpoint, but there would be less of a bump when shifting to automatic mode.
Deadtime is the time taken by the process variable to adjust after a change in the control effort. This happens when the variable sensor is too downstream from the actuator. No matter how hard the controller tries, it cannot alleviate the error until the sensors’ physical parameters change.
As the controller attempts to correct the errors, both the error and the process variable stop moving, resulting in a wound-up integral action like if the actuator was turned off. One solution to this is decreasing the integral gain, which would lower the maximum integral action due to windup and eliminate deadtime.
The problem can also be solved by issuing the integral action with a deadtime, giving the windup buffer time to ease down. One way to enhance this technique is by adding intermittent intervals to the integral action. Letting the proportional action work for some time and then turning on the integral action can shorten the time required for the error to be zero.
This is just one example of PID usage. PID algorithms have been greatly modified to take into account velocity-limited actuators, process variable measurement noise, time-varying process models, and so on.
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