of 33
CHE3162 Lecture 8
Introduction To Feedback Control Loops
Chapter 7&8: Marlin Chapter 7: Seborg Chapter 6-1: Smith & Corripio
Learning Objectives
Introduce feedback control and important terms
Understand a feedback block diagram and relationship to real world
Intro to PID control
CHE3162: where are we up to?
So far, we have studied system responses A disturbance (step change,sine wave) enters
our process Shown how process responds, depending on
1st order, 2nd order, dead time, etc Ultimately, we want process control
Incoming disturbances have MINIMAL effect on process outputs Next step on to controlling the responses!
Plot
Time (sec)
0 1 2 3 4 5 6 7 8 9 10
-2.0
-1.5
-1.0
-.5
0
.5
1.0
1.5
2.0
Control benefits:Reducing variability
1 5 9
0
Plot
Time (sec)
0 2 3 4 6 7 8 10
-2.0
-1.5
-1.0
-.5
.5
1.0
1.5
2.0
Time Good
control
Control of Tank Level
Want to keep constant tank level
Flowrate of inlet stream is fluctuating
Denn. Chem Eng Intro
Control of Tank Level
Inlet flowrate initially steady at q*
Temporary step change in inlet flowrate occurs
Inlet flowrate increases by Q* then returns to original value
No Control: Tank level increases then plateaus
With Control: level increases but by less and returns to close to original level
Denn. Chem Eng Intro
Constant inlet fluctuations Inlet varying
constantly As a result, tank
level will also vary (without control)
Simple control (solid line) significantly reduces tank level changes
Inlet flowrate to tank
Tank level without and with control
Denn. Chem Eng Intro
A FEEDBACK Control System Temperature control of a heat exchanger
Cold fluid
Hot fluid
Steam Sensor & Transmitter
Steam or condensate
exhaust
Controller
Valve
Set point
Feedback loop
Temperature, flow changes are DISTURBANCES
Exercise: Find another disturbance variable
Cold fluid Steam or
condensate exhaust
Piping and Instrument Diagram (P&ID)
Heat exchanger temperature control
Field mounted instrument
Panel mounted controller
Hot fluid
Steam
TC 101
TT 101
SP
Computer control
PROCESS (Heat exchanger)
T F
Feedback Control System Block Diagram
VALVE Controller U
Measuring element (sensor)
Tm
DISTURBANCE D
+ + Ts E
+ -
All variables are functions of time. On the diagram we represent them as Laplace transforms of CHANGES
Error detector
Summing point
PROCESS (Heat exchanger)
T F
Feedback Control System Block Diagram
VALVE Controller U
Measuring element (sensor)
Tm
DISTURBANCE D
+ + Ts E
+ -
Each block is described mathematically by a TRANSFER FUNCTION
Error detector
U/E = Gc(s) Summing point
The Sensor and the Valve
A level measuring sensor usually has a fast response so its time constant is small and can be neglected (ie., = 0)
The sensor TF is just a gain: Km = Measurement Gain (or Ks)
A control valve is usually a pneumatic valve & can be represented by a 1st order TF
mm K
TT
=
sv1vK
UF
+= Typical V = 1 sec-1 min
(depends on valve size)
Closed Loop Block Diagram
TF of the
Process
Controller TF decides what to do
about the error
Error=SP-MC
TF of the final control element e.g. a 1st
order valve
Setpoint
SP
GM (s)
GD (s)
TF of the Measuring device
CV(s)
(or Y(s) T(s)etc)
D(s) TF of the disturbance
Closed loop feedback control
Marlin
Shortcut: CV = forward SP (1 + around the loop)
PROCESS Gp
CV F VALVE
Gv Controller
Gc
U
Measuring sensor Gs (or Gm)
Tm
DISTURBANCE Gd
D
+ + SP E
+ -
Controller
Process equipment
See Tute 4 Q5 for how to derive these two TF responses
Controllers
A controller calculates an output signal based on the measured error and a control algorithm Error = Setpoint Measured value
A simple controller: Proportional Control Output is proportional to the error u(t) = Kc*e(t) + u(0)
Kc is called the (proportional) gain u(0) is the output when error = 0
cKEU
=
Cold fluid T change
Hot fluid
Steam
TC 101
TT 101
SP
Proportional Temperature Control using an FODT Model
Use steam flow Fs to control T at TSP
Incoming temp disturbance TD
Assume FODT models for: T/Fs T/TD
Start with a Proportional Controller for TC101
TSP
T
TD
Fs
U
Temperature Control of a Heat Exchanger Block Diagram
Gp T Fs
Gv Kc U
Km Tm
Gd TD
+ +
TSP E +
-
oC/oC
oC/(kg/min)
oC/oC (kg/min)/%
%/oC
Fast response
Exercise: Confirm that the product of all gains around the loop is dimensionless
Temperature Control of a Heat Exchanger Block Diagram
4e-2s 1 + 15s
T Fs 0.5 1 +0.5s Kc
U
Km = 1 Tm
1e-s 1+5s
TD
+ +
Ts E +
-
Time units: minutes oC/oC
oC/(kg/min)
oC/oC (kg/min)/%
%/oC
Fast response
Exercise: Confirm that the product of all gains around the loop is dimensionless
PID response matches common sense
If a big error occurs: You need a big response Proportional P
But there is still a remaining error: Adjust until you eliminate error Integral I
Rapid change rapid response required Derivative D
+++= u(0)]dtdee(t)dt
iT1[e(t)cKu(t) d
PID algorithm
PID algorithm considers the weighting of the following types of corrections: Proportional P - Corrections based on the present error
e(t) Integral I - Corrections based on the sum of the past
errors (integral of e(t)) Derivative D - Corrections based on future predictions of
errors, using the rate of change of errors over time (de/dt)
+++= u(0)]dtdee(t)dt
iT1[e(t)cKu(t) d
PID Transfer Function
++= s
sTK
EU
dI
c 11
Laplace transform
+++= u(0)]dtdee(t)dt
iT1[e(t)cKu(t) d
U is the controller output E is the difference between SP & the measured value
Kc = controller gain TI = Integral time d = derivative time
L
Typical responses
Seborg
Feedback control loop: CV and MV responses
Marlin
Error integrals
Smith & Corropio
Definition of Open Loop
Gp Y F
Gv U
Gm Ym
+ Gc
SP E +
-
Gd D
+
Open loop = no controller Controller is either off, disconnected, or in manual
Controller
Auto and Manual Control modes
Each controller can be set to auto (on) or manual which means off
Auto mode: Controller output depends on e(t), controller constants, and type of controller used. ( PI vs. PID etc.)
Manual Mode: Controller output is adjusted manually. Manual Mode is very useful when unusual conditions exist:
plant start-up plant shut-down emergencies
Percentage of controllers "on manual ?? (30% in 2001, Honeywell survey)
Seborg
Definition of Closed Loop
Gp Y F
Gv U
Gm Ym
+ Gc
SP E +
-
Gd D
+
This is CLOSED-LOOP
With control
Setpoint Change Closed Loop Servo Control
Gp CV Fs
Gv U
GS Tm
+ Gc
SP E +
-
Gd D
+
Make a SP change, triggers error between T & TSP, so loop adjusts valve to drive T towards TSP
Disturbance Change Closed Loop Regulatory Control
Gp CV Fs
Gv U
Gm Tm
+ Gc
SP E +
-
Gd D
+
Regulates any disturbances Disturbance upsets T Results in difference between T and TSP Controller sees error, adjusts valve to fix it
Proportional Control
Controller output signal is proportional to the error input signal
u(t) = Kc*e(t) + u(0) Kc is called the (proportional) gain u(0) is the output when error = 0 Called offset (or manual reset or bias)
cKEU
=
Controller Gain Kc
Controller gain Kc is a number that we can set Used by the controller during each control calculation
can be adjusted to make the controller output changes as sensitive as desired to deviations from the set point;
the sign of Kc can be chosen to make the controller output increase (or decrease) as the error signal increases.
Positive Kc = direct acting controller ie if temp is too high, valve open the opened.
Negative Kc = reverse acting controller. If temp is too high, then close the valve.
Typical responses after a disturbance step change
Seborg
CHE3162 Lecture 8Learning ObjectivesCHE3162: where are we up to?Slide Number 4Control of Tank LevelControl of Tank LevelConstant inlet fluctuationsA FEEDBACK Control SystemTemperature control of a heat exchangerPiping and Instrument Diagram (P&ID) Heat exchanger temperature controlFeedback Control SystemBlock DiagramFeedback Control SystemBlock DiagramThe Sensor and the ValveClosed Loop Block DiagramClosed loop feedback controlControllersProportional Temperature Control using an FODT ModelTemperature Control of aHeat Exchanger Block DiagramTemperature Control of aHeat Exchanger Block DiagramPID response matches common sensePID algorithmPID Transfer FunctionTypical responsesFeedback control loop:CV and MV responsesError integralsDefinition of Open LoopAuto and Manual Control modesDefinition of Closed LoopSetpoint Change Closed Loop Servo ControlDisturbance Change Closed Loop Regulatory ControlProportional ControlController Gain KcSlide Number 35Typical responses after a disturbance step change