INTRODUCTION
In the new era of technology, most of the controller in manufacturing
plants are automated control system. The mentioned control system is extended
to various industries such as food processing, refinery, chemical, and power
generation plants. The control systems consist of a single instrument or a
group of instruments which are designed, developed, installed and operated to
control a process. Control system is suffered with the issues of instability
and limited capability to resist external disturbances . It typically requires
continuous monitoring and controlling by operators so as to maintain output
response of system. Even so, the full-time availability of the operators in the
plant is unachievable due to other assigned duties and tasks that need
completion as well. Therefore, the idea of utilizing instruments to automate
the control system is becoming a popular discussion in many industries. Control
loop is exactly a feedback control loop that compares the process variable, PV
of plant to its set point, SP. This is followed by generating a
manipulated value, MV to drive PV for the new SP. At
first, control loop must utilize a sensor to measure PV. Secondly, control
loop must have a controller block with an actuator that control parameters of
the process. A typical automated control system is depicted in block diagram as
shown in Figure
Plant
is the model to be controlled. A plant incorporates a group of physical
instruments to produce the products. The plant is inherently fixed and does not
react to any changes of process parameters as well as interferences from
external environment. PV is varies relatively to any changes of
parameters in the plant. The imposed changes of PV are feedback and
compared at summing point. This is a symbol in the diagram that conceptually
adding two or more input signals, and produces a single sum output signal as
error e. The e is transmitted to the controller for generating control
signals or MV that regulates the initial changes of PV. In a
nutshell, the main objective of control loop is to regulate PV close to
SP at all times.
A reliable control loop needs a sophisticated controller, which is able
to regulate consistently any factor that destabilized PV in the plant.
There is various applied control methodologies whereas PID controller is the
most widely used because of its flexibility and simplicity to change the
settings cope with various requirements in the system. There are elements of
control actions for a PID controller] comprises proportional action, P,
integral action, I and derivative action, D.
Proportional Action P
Proportional
action P is the most common form of control action. It is depended on
magnitude of e that is generated after PV is compared with
changes of SP. In common, the P is represented as proportional
gain Kc which implies
the ratio of changes of PV to the changes of SP.
Equation shows that the output of controller, u
is equal to multiplication of Kc with e.
u(t)= Kc e(t)
The greater value of Kc means to more
magnificent control actions given for similar amount of e existed in the
process. The controller will take greater stage action for just a small amount
of PV deviated from SP. It is depicting the purpose of P
that improving capability of controller so to reduce steady state error when
the PV attains a new steady state condition. Nevertheless, Kc is unable to eliminate steady state error. There is an applied term
that is closely related to Kc, which is
known as proportional band, PB. It expresses the gain of the controller
as a percentage of the span of the instrument. In mathematical form, PB
is reciprocal to Kc as described
in equation
PB =100%/Kp
The lower value of PB means a greater Kc setting for the controller. In essence, the response is increasingly
robust when PB is reduced until the limit and eventually the controller
will become over-responsive. At this moment, the controller is reacting as an
ON/OFF controller and consequently the action of actuator is limited to fully open
and fully closed In contract, a greater PB means a smaller Kc and
subsequent control actions become ‘inaccurate’ due to a lack of responsiveness
to the e. In this extent, the actuator is not responding to minor signal
e which is just a tiny parameter change in the process. Therefore,
appropriate setting range of PB is important to allow robust and
efficient controller
Integral Action I
The
second term of control action is known as integral action I. It is
prominently to govern PV to stay tuned with SP. I reacts
by gradually shifting the PV once e existed. The action is tended
to eliminate e so that PV will attempt to converge towards SP.
The gain of integration is known as integral gain Ki. It reviews capability of the controller to overcome e versus to the SP
setting. The greater the Ki, the
controller becomes more responsive to process and typically to produce more
oscillatory output response due to changes of PV.
Mathematically,
I is the sum of the instantaneous e over time and gives the
accumulated offset that should have been corrected previously. I
responses to changes of e by multiplying Ki with net area of e from time equals to 0. The relationship
between the output of the controller, u and the e is described in
equation .
t
Ki
|
|||
u(t)
= ò
|
e(t).d (t)
|
||
0
|
The drawback of I is associated with a sort of storehouse of remembered past error that can continuously act towards e even after the PV reaches the desired value. As the PV converges back to the SP, the proportional term begins to decrease. But the I is continuing to act because of the stored e under the error curve, even though SP had been reached. I will drives the PV past through SP and to shed its accumulated e and stay continuously away from SP until accumulated e of the opposite direction accumulated and canceling the previous accumulated e. Ultimately, resultant PV is increased oscillatory and gradually contributes to “Integral Wind up”. In dealing with this issue, the controller is recommended to be temporary turned OFF once control element is saturated.
Derivative Action D
Derivative
action D is the third element in PID control system. D reacts to
the rate of change of the e at the current time. Mathematically, the
derivative of the error e is determined by computing the slope of the e
over time and then multiplying the rate of change with the gain, which is also
known as derivative gain Kd.
The
mathematical representation of D action is described in equation
u(t)
|
= K
|
de(t)
|
||
d
|
||||
where
D = Kd = Kc ∙ τd
D provides a sudden shift in output power level as the result of rate
changes (the slope of error curve) in measured value. If PV
changes, D immediately produces control signal in an attempt to correct
the perturbation before the e signal goes too far.
This immediate action reflects high sensitivity of D relatively
to the noise, which is considered as drawback of D. Any appeared noises
in the process give the slope of error a flip-flop up and down with severe
magnitudes, and consequently slight change of D. The flicking control
signals of controller drives the final control element vigorously to one
direction, and then move to another direction. As a result, PV becomes
oscillatory and unstable. In dealing with this issue, e has to be
filtered with hardware filter or a software filter prior to be compared with SP.
Process identification
A
proper controller tuning is imperatively needed for satisfactory performance of
close loop control system. Nonetheless, the presumed performance is less likely
to be achieved without a good approach to identify the dynamic of process
behavior. Identifying process behaviour typically describes the relationship in
between input and output of process, which is represented in mathematical
model. This is also known as process identification through modeling.
Modelling process is not an easy task because of complicated processes
in industries and high probability of non-linearity, causes difficulties in
tuning the controller. There are quite many literature studies had been undertaken
for process identification . Among all the studies, one the most common process
identification approach is known as Open loop method .
Flow control diagram with PI controller
A
closed loop control diagram is designed and simulated by using Matlab-Simulink
as depicted in figure.
Close loop diagram for flow rate control.
Comparison of simulation and experimental
data
The experimental data from PI controller setting is compared with simulated data as illustrated in figure. This is purposely to validate the performed physical system is in line with simulation data. The minor deviation in between simulation data with process data is possibly due to the non-linearity of system or friction of moving part such as motor fan.
Analysis for setpoint tracking and disturbance rejection performance
Set point tracking of flow control system
For a proper controlled system, the output response should
be magnificent, and should not oscillate in any new condition of set point or
applied disturbance. Robustness of controller response can be enhanced by
increasing Kc value which subsequence more oscillatory response as well.
In contrast, reducing Kc value reduces oscillatory
response. In obtaining empirical result, each correlation tuning values is
applied and then followed by a step change for recording output response
simultaneously.
Disturbance rejection performance of flow
control system
Some
systems require strong capability to resist instability of process response due
to high frequency of external disturbances rather than the SP change.
This is specifically referred to systems, which suffered from noises or
external interferences. A proper tuned control system provides reasonably
damped response with minimum overshoot and fast recovery to the set point after
imposed with disturbances. This is achievable by tuning PI controller so as to
produce consistent response with minimum oscillation.
Author: Vanshi Raina
Author: Vanshi Raina
Roll NO.14
Instru SY C
Instru SY C
