More Fun with PID Controllers

Exploring Just How Flexible and Powerful the PID Controller Can Be

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Greg McMillan and Stan Weiner bring their wits and more than 66 years of process control experience to bear on your questions, comments, and problems. Write to them at controltalk@putman.net.

McMillan & WeinerBy Greg McMillan and Stan Weiner

Stan: We continue exploring just how flexible and powerful the PID controller can be. The concept of setpoint (SP), process variable (PV), controller output (CO) and mode have been used since the inception of the PID in the 1930s. The modern-day DCS has all the modes, such as manual (MAN), automatic (AUTO), cascade (CAS), remote cascade (RCAS) and remote output (ROUT), developed for the electronic analog controllers in the 1970s. The RCAS mode is used for supervisory or model-predictive control, and the ROUT mode is used to position outputs for batch operation, transitions, start-up, shutdown and abnormal conditions.

Greg: You want the operator to be able to set a target (setpoint), monitor the control error, put a control system in manual and position the valve to deal with unforeseen situations, and to check out valve operation. The PID provides this familiar and effective interface, and has the flexibility to do just about anything within its framework. In the future, the operator will also be able to see trajectories of the PID SP, PV and CO intelligently scaled and time spanned to show where the process has been and where the process is going. The use of smart PID trajectories can overcome the problems introduced by digital displays, and provide a better perception of loop dynamics and tuning as discussed in "Are We Misleading Our Operators" (http://tinyurl.com/6xd3buf). For example, the delay between a change in the SP or CO and a change in the PV can make the operator aware of dead time, which is the most important and difficult dynamic parameter to understand.

Stan: In this third of a four-part series, we continue our interview with Mark Congiundi of Sasol, who has done an incredible job of using the PID, so the operator is not intimidated or out of touch with advanced applications—a common problem with supervisory, model-predictive, batch and field control systems.

Greg: When we use a variable-frequency drive (VFD) we have the opportunity to use tachometer feedback for greater rangeability and precision of speed adjustment. The speed control is very fast, and is best done in the drive rather than the DCS to avoid introducing a delay and lag due to signal transmission and DCS execution. For fast process loops manipulating a speed loop, slowing down the speed loop by putting it in the DCS can cause a violation of the cascade rule, which stipulates the secondary loop (speed loop) should be five times faster than the primary loop (process loop). Also, the vendor has the knowledge of internal drive operation to make the speed loop do its job. Keeping the speed loop in the VFD avoids the transfer of the responsibility for speed loop tuning and performance from the manufacturer to the user. The downside is the loss of operator access and visibility. How do you address the lack of an operator interface for a speed loop in a VFD?

Mark: I use a pass-through speed controller. The operator sees a speed PID loop that he can monitor and select modes. If the speed loop is put in the cascade mode, the PID uses a setpoint that is the output of the process PID. The speed-indicating controller (SIC) PV is the actual speed. A zero-gain PID with an external feedback signal that is the speed setpoint is used, so there is no response to the speed PV; the SIC functions to provide the flexibility of a hand-indicating controller (HIC), even though it looks like a conventional SIC. The bumpless transition to cascade, process PID features and equipment coordination are provided as if the SIC was doing speed control in the DCS. For example, the speed setpoint is automatically set to a minimum when the motor is off, so the motor can start at minimum speed.

Stan: The tuning settings for best setpoint response and disturbance rejection are quite different. The settings for minimum integrated error from unmeasured disturbances will typically cause overshoot and excessive oscillation for a setpoint change. This problem is prevalent in batch loops and automated start-up and transitions of continuous loops. How do you get the best setpoint and load response?

Mark: I use proportional action on PV rather than on error, so the controller gain does not provide a kick from the setpoint change. I then add to the PID output a feed-forward signal that is simply the change in setpoint multiplied by a gain factor. I can control the size of the step change in controller output from the step change in setpoint without affecting the disturbance response.

Greg: Some control systems offer a PID structure with factors built in to allow tuning for setpoint response without affecting the load response. For example, in a "two degrees of freedom" structure, the user can specify beta and gamma factors for the response to setpoint changes of the proportional and integral mode. The beta and gamma factors do not affect the reaction to disturbances. For loops with low controller gains and little-to-no rate action due to excessive dead time or noise, setpoint feed-forward can still be useful for a standard PID, since these factors have a 1.0 high limit. For these cases, where you effectively have proportional action on setpoint changes limited by a gamma setting of 1.0 and a low controller gain setting, the setpoint feed-forward factor would be the inverse of the process gain minus the controller gain. For example, if the process gain was 1.25 and the controller gain was 0.2, the setpoint feed-forward factor would be 0.6, so that the sum of feed-forward and proportional action on setpoint immediately puts the output to its final resting value, corresponding to PV = SP (feedforward gain = 1/1.25 - 0.2 = 0.6). The enhanced PID developed for wireless operation allows the controller gain to be set equal to the inverse of the process gain for loops dominated by an analyzer cycle time or wireless measurement update time as discussed in "Wireless PID Benefits" (http://tinyurl.com/644pt82). This immediately puts the PID output at the final resting value for self-regulating loops.

For batch operation of loops with large process time constants, it is desirable to get to setpoint as fast as possible. The PID temperature controller is often entitled to a high controller gain by virtue of the extremely large process time constant or slow integrating process gain compared to the dead time. To reduce batch cycle time, it is extremely important that the closed-loop time constant be much faster than the process time constant. It is not uncommon to have a Lambda factor (ratio of closed-loop time constant to process time constant) that is less than 0.02. For a process-time constant of 200 minutes, a dead time of two minutes, and a small setpoint change where the controller output does not hit an output limit, the closed-loop time constant can be less than four minutes approaching the process dead time. The savings in batch cycle time is 196 minutes compared to a lambda of 1.0 or a combination of feedback or feed-forward action that puts the controller output immediately at its final resting value.

However, noise may prevent the use of a high controller gain and low Lambda factor. A threshold sensitivity limit can be set just larger than the noise so proportional and derivative action does not amplify noise. When used in conjunction with the enhanced PID for wireless, the threshold sensitivity limit prevents integral action from chasing noise.

For the fastest possible rise time (time to get within a control band of setpoint), a smart bang-bang logic can be used where the controller output is positioned immediately to a limit. When the PV value one dead time into the future is predicted to be close to setpoint, the controller output is set and held at the final resting value for one dead time, and then released for feedback correction. While this logic applies best to integrating process responses as encountered in batch temperature, it is also applicable to self-regulating processes with large time constants that behave as "near-integrating" processes as seen in continuous temperature control on large well-mixed vessels. For more information on setpoint feed forward and smart bang-bang control check out Deminar #7 (http://tinyurl.com/6xzbrhv). 

July 2011 Comic

Believe It or Don't

  • A pH control valve was sized so it never rides the seat.
  • Slip-stick near seat was considered in split-range control.
  • Static head was considered in stated variable-speed drive (VSD) pump rangeability.
  • The vortex meter size max flow matched the max process flow, giving max rangeability.
  • Noise at low flow was considered in stated differential head meter's rangeability.
  • Noise was considered in the stated sensitivity and repeatability of a measurement.
  • Noise was nonexistent in a pH loop with a setpoint between 4 pH  and 10 pH.
  • Noise was nonexistent in an agitated, boiling or aerated level.
  • The dead time in a process loop was constant.
  • The process time constant in a process loop was constant.
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