1. Outline Control structure design (plantwide control)
A procedure for control structure design
I Top Down
Step 1: Degrees of freedom
Step 2: Operational objectives (optimal operation)
Step 3: What to control ? (self-optimizing control)
Step 4: Where set production rate?
II Bottom Up
Step 5: Regulatory control: What more to control ?
Step 6: Supervisory control
Step 7: Real-time optimization
Case studies

2. II. Bottom-up
Determine secondary controlled variables and structure (configuration) of control system (pairing)
A good control configuration is insensitive to parameter changes
Step 5. REGULATORY CONTROL LAYER
5.1 Stabilization (including level control)
5.2 Local disturbance rejection (inner cascades)
What more to control? (secondary variables)
Step 6. SUPERVISORY CONTROL LAYER
Decentralized or multivariable control (MPC)?
Pairing?
Step 7. OPTIMIZATION LAYER (RTO)

3. Step 5. Regulatory control layer
Purpose: “Stabilize” the plant using a simple control configuration (usually: local SISO PID controllers + simple cascades)
Enable manual operation (by operators)
Main structural issues:
What more should we control? (secondary cv’s, y2, use of extra measurements)
Pairing with manipulated variables (mv’s u2)
y1 = c
y2 = ?

4. H H2 Optimizer (RTO) PROCESS y ny d Stabilized process CV1s
Supervisory controller (MPC)
Regulatory controller (PID) H2 H
CV1
CV2s y ny d
Stabilized process
CV1s
CV2
Physical
inputs (valves)
Optimally constant valves
Always active constraints
Degrees of freedom for optimization (usually steady-state DOFs), MVopt = CV1s
Degrees of freedom for supervisory control, MV1=CV2s + unused valves
Physical degrees of freedom for stabilizing control, MV2 = valves (dynamic process inputs)

5. Objectives regulatory control layer
Allow for manual operation
Simple decentralized (local) PID controllers that can be tuned on-line
Take care of “fast” control
Track setpoint changes from the layer above
Local disturbance rejection
Stabilization (mathematical sense)
Avoid “drift” (due to disturbances) so system stays in “linear region”
“stabilization” (practical sense)
Allow for “slow” control in layer above (supervisory control)
Make control problem easy as seen from layer above
The key decisions here (to be made by the control engineer) are:
Which extra secondary (dynamic) variables y2 should we control?
Propose a (simple) control configuration (select input-output pairings)

6. Main objectives control system
Implementation of acceptable (near-optimal) operation
Stabilization
ARE THESE OBJECTIVES CONFLICTING?
Usually NOT
Different time scales
Stabilization fast time scale
Stabilization doesn’t “use up” any degrees of freedom
Reference value (setpoint) available for layer above
But it “uses up” part of the time window (frequency range) 6

7. Why simplified configurations?
Fundamental: Save on modelling effort
Other:
easy to understand
easy to tune and retune
insensitive to model uncertainty
possible to design for failure tolerance
fewer links
reduced computation load

8. Use of (extra) measurements (y2) as (extra) CVs: Cascade control
Primary CV y1
y2s K u2 G y2
Secondary CV
(control for
dynamic reasons)
Key decision: Choice of y2 (controlled variable)
Also important (since we almost always use single loops in the
regulatory control layer): Choice of u2 (“pairing”)

9. Degrees of freedom unchanged
No degrees of freedom lost by control of secondary (local) variables as setpoints become y2s replace inputs u2 as new degrees of freedom
Cascade control: G K
y2s u2 y2 y1
Original DOF
New DOF

10. Example: Distillation
Primary controlled variable: y1 = c = xD, xB (compositions top, bottom)
BUT: Delay in measurement of x + unreliable
Regulatory control: For “stabilization” need control of (y2):
Liquid level condenser (MD)
Liquid level reboiler (MB)
Pressure (p)
Holdup of light component in column
(temperature profile)
Unstable (Integrating) + No steady-state effect
Variations in p disturb other loops
Almost unstable (integrating) Ts TC
T-loop in bottom

11. Cascade control distillation ys y Ts T Ls L z With flow loop +
T-loop in top y XC Ts T TC Ls L FC z XC

12. Hierarchical control: Time scale separation
With a “reasonable” time scale separation between the layers
(typically by a factor 5 or more in terms of closed-loop response time)
we have the following advantages:
The stability and performance of the lower (faster) layer (involving y2) is not much influenced by the presence of the upper (slow) layers (involving y1)
Reason: The frequency of the “disturbance” from the upper layer is well inside the bandwidth of the lower layers
With the lower (faster) layer in place, the stability and performance of the upper (slower) layers do not depend much on the specific controller settings used in the lower layers
Reason: The lower layers only effect frequencies outside the bandwidth of the upper layers

13. QUIZ: What are the benefits of adding a flow controller (inner cascade)?qs
Extra measurement y2 = q q z
Counteracts nonlinearity in valve, f(z)
With fast flow control we can assume q = qs
Eliminates effect of disturbances in p1 and p2

14. What are the benefits of adding a flow controller (inner cascade)?qs
Extra measurement y’ = q q z
f(z)
Counteracts nonlinearity in valve, f(z)
With fast flow control we can assume q = qs
Eliminates effect of disturbances in p1 and p2
(FC reacts faster than outer level loop) 1
linear valve z
(valve opening) 1

15. Counteracting nonlinearity using cascade control: Process gain variation -> Time constant variation
Proof:
Slave controller with u = z (valve position) and y=q (flow)
Nonlinear valve with varying gain k: G = k / (τs+1)
PI-controller with gain Kc and integral time τI= τ.
With slave (flow) controller: Transfer function from ys to y (for master loop):
T = L/(1+L) = 1/(τCL s + 1)
where τCL = τ/(k Kc)
So variation in k translates into variation in τCL
In practise this gives a variation in the effective time delay in the master loop
Low gain k for valve gives large effective time delay (bad)

16. Objectives regulatory control layer
Allow for manual operation
Simple decentralized (local) PID controllers that can be tuned on-line
Take care of “fast” control
Track setpoint changes from the layer above
Local disturbance rejection
Stabilization (mathematical sense)
Avoid “drift” (due to disturbances) so system stays in “linear region”
“stabilization” (practical sense)
Allow for “slow” control in layer above (supervisory control)
Make control problem easy as seen from layer above
Implications for selection of y2:
Control of y2 “stabilizes the plant”
y2 is easy to control (favorable dynamics)

17. 1. “Control of y2 stabilizes the plant”
A. “Mathematical stabilization” (e.g. reactor):
Unstable mode is “quickly” detected (state observability) in the measurement (y2) and is easily affected (state controllability) by the input (u2).
Tool for selecting input/output: Pole vectors
y2: Want large element in output pole vector: Instability easily detected relative to noise
u2: Want large element in input pole vector: Small input usage required for stabilization
B. “Practical extended stabilization” (avoid “drift” due to disturbance sensitivity):
Intuitive: y2 located close to important disturbance
Maximum gain rule: Controllable range for y2 is large compared to sum of optimal variation and control error
More exact tool: Partial control analysis

18. Recall maximum gain rule for selecting primary controlled variables c:
Controlled variables c for which their controllable range is large compared to their sum of optimal variation and control error
Restated for secondary controlled variables y2:
Control variables y2 for which their controllable range is large compared to their sum of optimal variation and control error
controllable range = range y2 may reach by varying the inputs
optimal variation: due to disturbances
control error = implementation error n
Want large
Want small

19. What should we control (y2)? Rule: Maximize the scaled gain
General case: Maximize minimum singular value of scaled G
Scalar case: |Gs| = |G| / span
|G|: gain from independent variable (u2) to candidate controlled variable (y2)
IMPORTANT: The gain |G| should be evaluated at the (bandwidth) frequency of the layer above in the control hierarchy!
If the layer above is slow: OK with steady-state gain as used for selecting primary controlled variables (y1=c)
BUT: In general, gain can be very different
span (of y2) = optimal variation in y2 + control error for y2
Note optimal variation: This is often the same as the optimal variation used for selecting primary controlled variables (c).
Exception: If we at the “fast” regulatory time scale have some yet unused “slower” inputs (u1) which are constant then we may want find a more suitable optimal variation for the fast time scale.

20. Minimize state drift by controlling y2
Problem in some cases: “optimal variation” for y2 depends on overall control objectives which may change
Therefore: May want to “decouple” tasks of stabilization (y2) and optimal operation (y1)
One way of achieving this: Choose y2 such that “state drift” dw/dd is minimized
w = Wx – weighted average of all states
d – disturbances
Some tools developed:
Optimal measurement combination y2=Hy that minimizes state drift (Hori) – see Skogestad and Postlethwaite (Wiley, 2005) p. 418
Distillation column application: Control average temperature column

21. 2. “y2 is easy to control” (controllability)
Statics: Want large gain (from u2 to y2)
Main rule: y2 is easy to measure and located close to available manipulated variable u2 (“pairing”)
Dynamics: Want small effective delay (from u2 to y2)
“effective delay” includes
inverse response (RHP-zeros)
+ high-order lags

22. Rules for selecting u2 (to be paired with y2)
Avoid using variable u2 that may saturate (especially in loops at the bottom of the control hieararchy)
Alternatively: Need to use “input resetting” in higher layer (“mid-ranging”)
Example: Stabilize reactor with bypass flow (e.g. if bypass may saturate, then reset in higher layer using cooling flow)
“Pair close”: The controllability, for example in terms a small effective delay from u2 to y2, should be good.

23. Cascade control (conventional; with extra measurement)
The reference r2 (= setpoint ys2) is an output from another controller
General case (“parallel cascade”)
Special common case (“series cascade”)

24. Series cascade
Disturbances arising within the secondary loop (before y2) are corrected by the secondary controller before they can influence the primary variable y1
Phase lag existing in the secondary part of the process (G2) is reduced by the secondary loop. This improves the speed of response of the primary loop.
Gain variations in G2 are overcome within its own loop.
Thus, use cascade control (with an extra secondary measurement y2) when:
The disturbance d2 is significant and G1 has an effective delay
The plant G2 is uncertain (varies) or nonlinear
Design / tuning
First design K2 (“fast loop”) to deal with d2
Then design K1 to deal with d1

25. Partial control
Cascade control: y2 not important in itself, and setpoint (r2) is available for control of y1
Decentralized control (using sequential design): y2 important in itself

26. Partial control analysis
Primary controlled
variable y1 = c
(supervisory control layer)
Local control of y2
using u2
(regulatory control layer)
Setpoint y2s : new DOF
for supervisory control
Assumption: Perfect control (K2 -> 1) in “inner” loop
Derivation: Set y2=y2s-n2 (perfect control), eliminate u2, and solve for y1

27. Partial control: Distillation
Supervisory control:
Primary controlled
variables y1 = c = (xD xB)T
Regulatory control:
Control of y2=T
using u2 = L (original DOF)
Setpoint y2s = Ts : new DOF
for supervisory control
u1 = V

28. Limitations of partial control?
Cascade control: Closing of secondary loops does not by itself impose new problems
Theorem 10.2 (SP, 2005). The partially controlled system [P1 Pr1]
from [u1 r2] to y1
has no new RHP-zeros that are not present in the open-loop system [G11 G12]
from [u1 u2] to y1
provided
r2 is available for control of y1
K2 has no RHP-zeros
Decentralized control (sequential design): Can introduce limitations.
Avoid pairing on negative RGA for u2/y2 – otherwise Pu likely has a RHP-zero

29. Selecting measurements and inputs for stabilization: Pole vectors
Maximum gain rule is good for integrating (drifting) modes
For “fast” unstable modes (e.g. reactor): Pole vectors useful for determining which input (valve) and output (measurement) to use for stabilizing unstable modes
Assumes input usage (avoiding saturation) may be a problem
Compute pole vectors from eigenvectors of A-matrix

32. Example: Tennessee Eastman challenge problem

39. ”Summary Advanced control” STEP S6. SUPERVISORY LAYER
Objectives of supervisory layer:
1. Switch control structures (CV1) depending on operating region
Active constraints
self-optimizing variables
2. Perform “advanced” economic/coordination control tasks.
Control primary variables CV1 at setpoint using as degrees of freedom (MV):
Setpoints to the regulatory layer (CV2s)
”unused” degrees of freedom (valves)
Keep an eye on stabilizing layer
Avoid saturation in stabilizing layer
Feedforward from disturbances
If helpful
Make use of extra inputs
Make use of extra measurements
Implementation:
Alternative 1: Advanced control based on ”simple elements” (decentralized control)
Alternative 2: MPC

40. Summary of some simple elements
Feeforward control with Multiple feeds etc. (extensive variables).: Ratio control
Ratio setpoint usually set by feedback in a cascade manner
Feedback
Use of extra measurements for improved control;: Cascade control
Cascade control is when MV (for master) =setpoint to slave controller
MV1 = CV2s
Switch between active constraints: Selectors
Make use of extra inputs
Dynamic (improve performance): Input resetting = valve position control = midranging control
Steady state (extend operating range): Split range control
Reduce interactions when using single-loop control: Decouplers (including phsically based)

41. Control configuration elements
Control configuration. The restrictions imposed on the overall controller by decomposing it into a set of local controllers (subcontrollers, units, elements, blocks) with predetermined links and with a possibly predetermined design sequence where subcontrollers are designed locally.
Some control configuration elements:
Cascade controllers
Decentralized controllers
Feedforward elements
Decoupling elements
Input resetting/Valve position control/Midranging control
Split-range control
Selectors

42. Most important control structures
Feedback control
Ratio control (special case of feedforward)
Cascade control

43. Ratio control (most common case of feedforward)
General: Use for extensive variables (usually flows) with constant optimal ratio
Example: Process with two feeds q1(d) and q2 (u), where ratio should be constant.
Use multiplication block (x): x
(q2/q1)s
(desired flow ratio) q1
(measured
flow
disturbance) q2
(MV: manipulated variable)
“Measure disturbance (d=q1) and adjust input (u=q2) such that
ratio is at given value (q2/q1)s”

44. Usually: Combine ratio (feedforward) with feedback
Adjust (q1/q2)s based on feedback from process, for example, composition controller.
This is a special case of cascade control
Example cake baking: Use recipe (ratio control = feedforward), but adjust ratio if result is not as desired (feedback)
Example evaporator: Fix ratio qH/qF (and use feedback from T to fine tune ratio)

45. Cascade control Example Hs Hs H H LC LC MV=z MV=qs q FC z
Controller (“master”) gives setpoint to another controller (“slave”)
Without cascade: “Master” controller directly adjusts u (input, MV) to control y
With cascade: Local “slave” controller uses u to control “extra”/fast measurement (y’). “Master” controller adjusts setpoint y’s.
Example: Flow controller on valve (very common!)
y = level H in tank (or could be temperature etc.)
u = valve position (z)
y’ = flowrate q through valve
flow in Hs
flow in Hs H LC H LC
MV=z
valve position
MV=qs q FC
measured
flow z
flow out
flow out
WITHOUT CASCADE
WITH CASCADE

46. What are the benefits of adding a flow controller (inner cascade)?qs
Extra measurement y’ = q q z
f(z)
Counteracts nonlinearity in valve, f(z)
With fast flow control we can assume q = qs
Eliminates effect of disturbances in p1 and p2 1
linear valve z
(valve opening) 1

47. Example (again): Evaporator with heating
qF [m3/s]
TF [K]
cF [mol/m3]
From
reactor
evaporation
level measurement ∞ H
temperature measurement T
q [m3/s]
T [K]
c [mol/m3]
Heating fluid
qH [m3/s]
TH [K]
concentrate
NEW Control objective
Keep level H at desired value
Keep composition c (rather than temperature T) at desired value
BUT: Composition measurement has large delay + unreliable
Suggest control structure based on cascade control

48. Split Range Temperature Control

49. Split Range Temperature Control
Note: adjust the location er E0 to make process gains equal

50. Use of extra measurements: Cascade control (conventional)
The reference r2 (= setpoint ys2) is an output from another controller
General case (“parallel cascade”)
Not always helpful…
y2 must be closely related to y1
Special common case (“series cascade”)

51. Series cascade
Disturbances arising within the secondary loop (before y2) are corrected by the secondary controller before they can influence the primary variable y1
Phase lag existing in the secondary part of the process (G2) is reduced by the secondary loop. This improves the speed of response of the primary loop.
Gain variations in G2 are overcome within its own loop.
Thus, use cascade control (with an extra secondary measurement y2) when:
The disturbance d2 is significant and G1 has an effective delay
The plant G2 is uncertain (varies) or nonlinear
Design / tuning (see also in tuning-part):
First design K2 (“fast loop”) to deal with d2
Then design K1 to deal with d1
Example: Flow cascade for level control
u = z, y2=F, y1=M,
K1= LC, K2= FC

52. Pressure control distillation
Need to stabilze p using Qc
But want Qc to be max
Use cascade with backoff on Qc (
Another similar example: reactor temperature control (stabilization) closed to Qmax.

53. Use of extra inputs Two different cases
Have extra dynamic inputs (degrees of freedom)
Cascade implementation: “Input resetting to ideal resting value”
Example: Heat exchanger with extra bypass
Also known as: Midranging control, valve position control
Need several inputs to cover whole range (because primary input may saturate) (steady-state)
Split-range control
Example 1: Control of room temperature using AC (summer), heater (winter), fireplace (winter cold)
Example 2: Pressure control using purge and inert feed (distillation)

54. Extra inputs, dynamically
Exercise: Explain how “valve position control” fits into this framework. As en example consider a heat exchanger with bypass

55. QUIZ: Heat exchanger with bypass
closed qB
Thot
Want tight control of Thot
Primary input: CW
Secondary input: qB
Proposed control structure?

56. Use primary input CW: TOO SLOW
Alternative 1 qB
Thot
closed TC
Use primary input CW: TOO SLOW

57. Advantage: Very fast response (no delay)
Alternative 2 qB
Thot
closed TC
Use “dynamic” input qB
Advantage: Very fast response (no delay)
Problem: qB is too small to cover whole range
+ has small steady-state effect

58. Alternative 3: Use both inputs (with input resetting of dynamic input)qB
Thot
closed
qBs FC TC
TC: Gives fast control of Thot using the “dynamic” input qB
FC: Resets qB to its setpoint (IRV) (e.g. 5%) using the “primary” input CW
IRV = ideal resting value
Also called: “valve position control” (Shinskey) and “midranging control” (Sweden)

59. Too few inputs Must decide which output (CV) has the highest priority
Selectors
Implementation: Several controllers have the same MV
Selects max or min MV value
Often used to handle changes in active constraints
Example: one heater for two rooms. Both rooms: T>20C
Max-selector
One room will be warmer than setpoint.
Example: Petlyuk distillation column
Heat input (V) is used to control three compositions using max-selector
Two will be better than setpoint (“overpurified”) at any given time

60. Divided wall column example

61. Control of primary variables
Purpose: Keep primary controlled outputs c=y1 at optimal setpoints cs
Degrees of freedom: Setpoints y2s in reg.control layer
Main structural issue: Decentralized or multivariable?

62. Decentralized control (single-loop controllers)
Use for: Noninteracting process and no change in active constraints
+ Tuning may be done on-line
+ No or minimal model requirements
+ Easy to fix and change
- Need to determine pairing
- Performance loss compared to multivariable control
- Complicated logic required for reconfiguration when active constraints move

63. Multivariable control (with explicit constraint handling = MPC)
Use for: Interacting process and changes in active constraints
+ Easy handling of feedforward control
+ Easy handling of changing constraints
no need for logic
smooth transition
- Requires multivariable dynamic model
- Tuning may be difficult
- Less transparent
- “Everything goes down at the same time”