Control Architectures: Feed Forward, Feedback, Ratio, and Cascade By Peter Woolf (pwoolf@umich.edu) University of Michigan Michigan Chemical Process Dynamics and Controls Open Textbook version 1.0 Creative commons
Connecting Controllers & Actuators In control programming we make statements like: Adjust v3 to maintain LC1 at LC1 set We could implement this as the following PID controller: v3 = v3 offset + K c (LC1" LC1 set ) + 1 # I (LC1" LC1 set ) $ + # D d(lc1" LC1 set ) But there are other controls possible: Maintain LC1 by controlling v3 (Feedback control) Anticipate changes in LC1 by measuring FC1 and FC2 and preemptively adjust v3 (Feed forward control) Feed in a defined ratio of A and B (Ratio control) Connect LC1 to FC1 to adjust v1 (Cascade control)
Feedback Control Philosophy: Adjust for errors as they take place. Example: Maintain LC1 by controlling v3 v3 = v3 offset + K c (LC1" LC1 set ) + 1 # I (LC1" LC1 set ) $ + # D d(lc1" LC1 set ) Advantages Simple to design No process model required Disadvantages Only corrects for errors after they happen Generally only takes input from one sensor
Feed Forward Control Philosophy: Anticipate and correct for errors before they happen Example: Maintain LC1 by measuring FC1 and FC2 and preemptively adjust v3 v3 = k valves (FC1+ FC2) (assuming a linear valve) Advantages Corrects for deviations before they happen! In ideal cases can produce perfect control Disadvantages Requires infinitely accurate models Requires infinitely accurate measurements
Ratio Control Philosophy: Connect two flows to maintain a constant ratio Example: Feed in a defined ratio of A and B where A is the wild stream. v2 = k ratio k valve FC1 Advantages Links two streams to produce a defined ratio Simple--does not require a complex model Disadvantages Never measures FC2, thus assumes the flows are matched Assumes pressure from B is constant
Cascade Control Philosophy: Sensors can control the set points of other sensors to integrate information Example: Connect LC1 to FC1 to adjust v1 v1 = v1 offset + K c1 (FC1 set " FC1) + 1 d(fc1 $ (FC1 set " FC1) + # set " FC1) D1 # I1 FC1 set = FC1 offset + K c2 (LC1 set " LC1) + 1 d(lc1 $ (LC1 set " LC1) + # set " LC1) D2 # I 2 Logic: The inner loop is something that changes quickly, here possibly due to pressure changes from the A storage. Outer loop changes slowly, and influences the inner loop by controlling the set point of FC1. Inner loop (slave) Outer loop (master)
Cascade Control Example: Connect LC1 to FC1 to adjust v1 v1 = v1 offset + K c1 (FC1 set " FC1) + 1 d(fc1 $ (FC1 set " FC1) + # set " FC1) D1 # I1 Inner loop (slave) FC1 set = FC1 offset + K c2 (LC1 set " LC1) + 1 d(lc1 $ (LC1 set " LC1) + # set " LC1) D2 # I 2 controlling the set point of FC1. Advantages Controller responds quickly to high frequency changes Controller integrates multiple sensor readings together Disadvantages Controller is more complex Tuning cascade controllers is more difficult as the set point changes + more parameters Outer loop (master) Logic: The inner loop is something that changes quickly, here possibly due to pressure changes from the A storage. Outer loop changes slowly, and influences the inner loop by
Mixed Architectures Most real systems have combinations of feedback, feed forward, ratio, and cascade control. Example #1: Control LC1 using FC1 cascaded to v1 and feedback control on v3. v1 = v1 offset + K c1 (FC1 set " FC1) + 1 d(fc1 $ (FC1 set " FC1) + # set " FC1) D1 # I1 FC1 set = FC1 offset + K c2 (LC1 set " LC1) + 1 d(lc1 $ (LC1 set " LC1) + # set " LC1) D2 # I 2 v3 = v3 offset + K c 3 (LC1 set " LC1) + 1 d(lc1 $ (LC1 set " LC1) + # set " LC1) D 3 # I 3 Inner loop (slave) (feedback) Outer loop (master) Feedback
Mixed Architectures Most real systems have combinations of feedback, feed forward, ratio, and cascade control. Example #2: Maintain ratio of B using FC1 cascaded to FC2 to control v2 v2 = v2 offset + K c 4 (FC2 set " FC2) + 1 d(fc2 $ (FC2 set " FC2) + # set " FC2) D 4 # I 4 FC2 set = k ratio FC1 Outer loop (master) (ratio control) Inner loop (slave) (feedback)
Mixed Architectures Most real systems have combinations of feedback, feed forward, ratio, and cascade control. Advantages Pick and choose features to fit the problem Incorporate in any number of sensors in a rational way Disadvantages Controllers can be complex (Each I controller adds an ODE, eigenvalue, and new dimension to the problem.) Tuning is difficult - Routh stability really helps define appropriate ranges - Optimization based tuning
Example 1 TC1 T TC2set v1 Which sensor likely responds to temperature changes in the cooling water faster? TC2 Which loop would be the inner loop (slave) and which the outer loop (master)? Why? TC2 inner, TC1 outer Write out an appropriate cascade controller for this system. d(tc2 " TC2 $ (TC2 " TC2 set ) + # set ) Inner loop D1 # I1 Check signs! (slave) d(tc1 $ + # set " TC1) D 2 Outer loop (master) v1= v1 offset + K c1 (TC2 " TC2 set ) + 1 TC2 set = TC1 offset + K c 2 (TC1 set " TC1) + 1 # I 2 (TC1 set " TC1)
Example 2 Control phc1 using a single feedback PID controller. v1= v1 offset + K c (phc1" phc1 set ) + 1 d(phc1" phc1 $ (phc1" phc1 set ) + # set ) D # I Control phc1 using a single feed forward controller. v1 = k valve k ratio FC1 Control phc1 using a cascaded P-only ratio controller to balance the acid waste water. FC2 set = k valve k ratio FC1 v1= v1 offset + Kc(FC2 set " FC 2 )
Select a mixture of ratio, cascade, feedback, and or feed forward control systems to control the rectifying section of the following distillation column: One example configuration might have AC2 cascaded to TC2, cascaded to FC2 controlling V1, and LC1 cascaded to FC3 controlling V2.
To help with deciding which control schemes to use, consider the following questions: a) What is your control objective? b) Which loops are likely to be fast and which slow? c) Changes in what variables likely influence the process compositions most directly?
Other examples: The ratio of FC2 to FC3 is set by AC2. For this scheme, use a level control to set either FC2 or FC3 and determine the other flow using the ratio controller. The ratio of FC3 and FC1 Is set by AC2. For this set up, also include a level control scheme for the accumulator. AC2 is cascaded to TC2, which is cascaded to FC2 controlling V1. In addition, AC1 could be a feed forward controller on FC2 and V1. (Note here two paths control V1, so a more sophisticated logical relationship would be needed). LC1 is cascaded to FC3, which controls V2. AC2 is cascaded to TC2. TC2 is a ratio controller of FC2 and FC1, and this output is combined with FC1 to form a set point for FC2. FC2 controls V1. Also, AC1 feeds forward to FC2. LC1 is cascaded to FC3 to control V2. (Note: there are many configurations possible, depending on the control objective. Some, however don t make sense such as having FC3 control V1, or cascading AC1 to LC1 to control FC3, to control V2. )
Take Home Messages Using a combination of feedback, feed forward, ratio, and cascade control you can design flexible control systems More complex control systems are harder to tune and model, but if done right outperform simpler architectures When designing your control system, be aware of the control objective and possible conflicts