Chemical Process Controls: PID control, part II Tuning By Peter Woolf (pwoolf@umich.edu) University of Michigan Michigan Chemical Process Dynamics and Controls Open Textbook version 1.0 Creative commons

Heater Example from last class F, Tin F, T Goal: Heat the output stream to a desired set point temperature, Tset Assumptions: All liquid in lines and tank, thus Fin=Fout=F Flow is constant Fluid does not boil No reactions Tank is well stirred Heater has no lag Heater has finite range Question: How do we choose PID control parameters?

Case: Heated CSTR Starting at 120, and Tset=130. Tfeed=100. (see PID.example.xls)

Case: Heated CSTR Starting at 120, and Tset=130. Tfeed=100. (see PID.example.xls) Here we use a smaller  to show integrator windup

Case: Heated CSTR Starting at 120, and Tset=130. Tfeed=100. (see PID.example.xls) Here  and Kc are smaller. What happened??

Case: Heated CSTR Starting at 120, and Tset=130. Tfeed=100. (see PID.example.xls) Here  and Kc are even smaller. What happened??

Possible Tuning Strategies Perturb system, see what happens and use this response to choose PID parameters Adjust PID parameters until something bad happens and then back off Numerical optimization based on data

Reaction Curve Tuning (=Open Loop) Based on a First Order Plus Dead Time (FOPDT) process model assumption time First order process delayed response to signal v

Example from http://www.controlguru.com • Change set point from 39 to 42% CO Observe delay (0.8) Observe max slope of response at T=27 Slope= Kmax= output change/ Input change=k1/k2 Max slope Units? %? Relative to what? Example from http://www.controlguru.com

i d Aside: intuition If slope is high (Kmax big) then want a small gain (Kc), as the system is sensitive If large dead time, then want a small gain because response is delayed, thus aggressive control could be dangerous. Large dead time also reduces the effect of integration, but increases derivative. Integration can cause oscillations, and with a large delay could be a problem. Derivative can still work with time delay, in most cases.

i d Advantages of open loop tuning: • fast: the experiment takes just one run • does not introduce oscillations: Oscillations can be could be dangerous in a large plant, so best avoided. • Can be done before controller is installed Disadvantages of open loop tuning: • can be inaccurate: does not take into account control dynamics or dynamics of other processes • can be difficult to implement: max slope is not always easy to find. • Terms can be ambiguous

Closed Loop Tuning i d Zeigler-Nichols (Z-N) Tuning parameters for closed loop i d

Closed Loop Tuning Advantages of closed loop tuning 1)Easy experiment 2)Incorporates in closed loop dynamics Disadvantages of closed loop tuning 1)this experiment can be slow 2)Oscillations could be dangerous in some cases, or if not at least wasteful

Model Based Tuning FOPDT is okay for a first approximation, but we know what the process is doing. Given a model and normal operating data, we can create a good model of the process. PID parameters can then be optimally selected based on this model using regression!

Model Based Tuning Set points Predicted model response for a given Kc, i, and d. temp time Goal: Use solver to find optimal values of Kc, i, and d that minimize

Model Based Tuning Advantages of model based tuning 1) Incorporates in knowledge about the physical system 2)Incorporates in closed loop dynamics 3) Incorporates in physical limitations in valves and sensors 4) Includes inherent noise in system Disadvantages of model based tuning 1) Requires a good model that takes time to produce 2) Requires significant data describing a range of operating behaviors 3) Optimization for large systems can be difficult. 4) Overkill for simple systems that are FOPD like

Light bulb control system a little bit of real data…

FLOW Light bulb (=heater) Temperature sensors Fan (=pump) Purge valve inlet

Note: valves don’t always look like valves! open closed

Thermocouple RTD

Sample Response Curve (closed loop) temp Time (sec)

Closed loop tuning? Difficult to define as we have (1) Limited control action, thus Ku tops out quickly. (2) The oscillation frequency is only somewhat stable. temp Time (sec)

Different PID tuning parameters Small i, large Kc All derivative control Open recycle temp Change set point Time (sec)

Parameterize the model based on historical data Model based tuning? Create a model Parameterize the model based on historical data If fit is poor, adjust model in step 1 and repeat. Fit PID tuning parameters to optimize performance. temp Time (sec)

Model based tuning? Create a model Parameterize the model based on historical data If fit is poor, adjust model in step 1 and repeat. Fit PID tuning parameters to optimize performance. F, Tin F, T What if this did not fit? What might be a better model?

One idea… 4 CSTRs, each with different functions. thermocouple TC2 heater TC1 RTD Flow in due to pressure balance Flow due to recycle (Look to your reactors text for many more examples of such lumped models of multiple CSTRs)

Take Home Messages PID tuning parameters can be estimated from data using a variety of methods PID tuning can be difficult and time consuming Complex physical processes can often be broken down into smaller, more familiar systems