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Feedback Control System
Error
+
-
* Error = Set value - Measured value
•Control function gives the signal to the actuator which is feeding energy to the process. Only input for
control function is the error.
•The controlled value is measured and compared to the set value.
•The basic idea of the closed loop control is to get error signal so small as possible, (zero).
Heating process
Tin
Heater
Output power =
losses
Energy
W = ∫ P dt
Tout
Thermal energy
Input power
Q = c m dT
1 2
3
0
Heat capasity =
c [ kJ/kg K ]
230 V
Many common processes can store the energy.
The phenomenon is named for capacity
Because of the capacity the state of the process can not been altered very fast.
It is needed time to alter the state of the process. This is the time delay of the process.
EXAMPLES:
If solid mass is heated by certain power, the temperature of this
mass is warming slowly. The capacity affects the delay of the process.
Correspondingly we need time to move the mass on the ground and increase the velocity.
So the moving body is storing energy.
Rotating mass is similar process, but mass is changed to mass of inertia.
In electrical circuits capacitors can store voltage energy and inductors have current
energy.
.
Output of the control function block has normally only two states: on or off.
Output is on, if the set point is bigger then measured value (error > 0).
Output is off, if the set point is smaller than measured value (error < 0).
Often the turn-on and turn-off points are deliberately made to differ by a small
amount, known as the hysteresis. This moderates the switching frequency.
Typical for on-off controller is the simple construction and the actuator is type:
open/closed.
On-off system is also oscillating all the time !
.
Test functions are profitable, if we need more knowledge of unknown dynamic process.
Process input is the test signal and output is the response.
The response gives us very useful data for tuning the system and making decisions.
.
Impulse function
Ramp function
t
t
Step function
Sine function
t
t
Control block is the amplifier, which has constant gain.
The error signal is multiplied by constant = Kp = P-control gain
We can say that P-block is “exaggerating” the error.
Drawback is that P-control is normally not able to do the job without error !
Bigger gain Kp gives smaller error. If the gain is too large the feedback
system starts to oscillate.
If P-controller could have: Set point = controlled value. It gives the error = 0
and output of the controller is also zero. This means: there are no power
to the process (in most cases impossible to support).
Advantage is rapid function. There are no delay between controller input
and output. Any changes in the control system gives fast response.
Control block is integrator, KI = 1/TI = I- gain , TI = integration time
Output is integral of the error.
If error is positive, output signal is increasing. Bigger error gives
faster increasing output.
If error is negative, output signal is decreasing.
If error is zero, output keep constant (“memory”).
Integrator is able to eliminate control error.
Drawbacks are rather slow response and saturation.
Very often P- and I-control are used together.
Control block differentiates error signal. Kd = D-gain.
If the error signal increases fast, the output signal has big
positive value.
If the error signal decreases fast, the output signal has big
negative value.
D- block is able to accelerate or put the break to process (forecast).
Processes with large dead time or noise cannot utilize D- block.
D block is not used alone.
Cascade control
SET
VALUE
CONTROLLED VARIABLE
+
Control block
2
Control block
1
+
-
PROCESS
PROCESS
fast loop
Main feedback (slow loop)
Cascade Control uses the output of the primary controller
to manipulate the setpoint of the secondary controller as if
it were the final control element.
Reasons for cascade control
• Allow faster secondary controller to handle
disturbances in the secondary loop.
• Allow secondary controller to handle nonlinear valve and other final control element
problems.
• Allow operator to directly control secondary
loop during certain modes of operation
(such as startup).
Requirements for cascade control
• Secondary loop process dynamics must be
at least four times as fast as primary loop
process dynamics.
• Secondary loop must have influence over
the primary loop.
• Secondary loop must be measured and
controllable.