1 Chapter - 1 Introduction There are dramatic changes in the power industry because of deregulation. One consequence of this is that the demands for rapid changes in power generation is increasing. This leads to more stringent requirements on the control systems for the processes. It is required to keep the processes operating well for large changes in the operating conditions. One way to achieve this is to incorporate more process knowledge into the systems. The goal is to develop moderately complex nonlinear models that capture the key dynamical properties over a wide operating range. The models are based on physical principles and have a small number of parameters; most of which are determined from construction data. Particular attention has been devoted to model drum level dynamics well. Drum level control is an important problem for nuclear as well as conventional plants. In Parry, Petetrot and Vivien (1995) it is stated that about 30% of the emergency shutdowns in French PWR plants are caused by poor level control of the steam water level. One reason is that the control problem is difficult because of the complicated shrink and swell dynamics. This creates a nonminimum phase behaviour which changes significantly with the operating conditions. Since boilers are so common there are many modelling efforts. There are complicated models in the form of large simulation codes which are based on finite element approximations to partial differential equations. Although such models are important for plant design, simulators, and commissioning, they are of little interest for control design because of their complexity. The model presented here is adapted from K.J Astrom and R.D. Bell (1998). A nonlinear dynamic model for natural circulation drum-boilers is adapted. The model describes the complicated dynamics of the drum, downcomer, and riser components. It is derived from first principles, and is characterized by a few physical parameters. A strong effort has been made to strike a balance between fidelity and simplicity. Since the model is derived from first principles it can describe the system for a wide operating range. Simulation of the model is done using MATLAB R2010a and results have been verified with plant data presented in K.J Astrom and R.D. Bell (1998). The conventional PID controller is applied when the boiler is operating at medium load for both servo and regulatory problems. Advanced controllers such as Fuzzy logic controllers(FLC) and Neural Network(NN) predictive controllers have been also tried with satisfactory results. The details of these controllers are discussed in the report within. The drum boiler is a simple boiler which consist of a drum, downcomer and riser components. A simple schematic of the drum boiler have been shown in Figure 1. The heat Q, supplied to the risers causes boiling. Gravity forces the saturated steam to rise causing a circulation in the riser-drum-downcomer loop. Feedwater q f , is supplied to the drum and saturated steam, q s , is taken from the drum to the superheaters and turbine. The presence of steam below the liquid level in the drum causes the shrink-and-swell phenomenon which makes level control difficult. In reality the system is much more complicated than shown in the figure. The system has a complicated geometry and there are many downcomer and riser tubes. The outflow from the risers passes through a separator to separate the steam from the water. In spite of the complexity of the system it turns out that its gross behaviour is well captured by global mass and energy balances.
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8/19/2019 Modeling,simulation and control of a drum boiler
There are dramatic changes in the power industry because of deregulation. One consequenceof this is that the demands for rapid changes in power generation is increasing. This leads to
more stringent requirements on the control systems for the processes. It is required to keep
the processes operating well for large changes in the operating conditions. One way to
achieve this is to incorporate more process knowledge into the systems. The goal is to
develop moderately complex nonlinear models that capture the key dynamical properties over
a wide operating range. The models are based on physical principles and have a small number
of parameters; most of which are determined from construction data. Particular attention has
been devoted to model drum level dynamics well. Drum level control is an important
problem for nuclear as well as conventional plants. In Parry, Petetrot and Vivien (1995) it is
stated that about 30% of the emergency shutdowns in French PWR plants are caused by poor
level control of the steam water level. One reason is that the control problem is difficult because of the complicated shrink and swell dynamics. This creates a nonminimum phase
behaviour which changes significantly with the operating conditions. Since boilers are so
common there are many modelling efforts. There are complicated models in the form of large
simulation codes which are based on finite element approximations to partial differential
equations. Although such models are important for plant design, simulators, and
commissioning, they are of little interest for control design because of their complexity. The
model presented here is adapted from K.J Astrom and R.D. Bell (1998). A nonlinear dynamic
model for natural circulation drum-boilers is adapted. The model describes the complicated
dynamics of the drum, downcomer, and riser components. It is derived from first principles,
and is characterized by a few physical parameters. A strong effort has been made to strike a
balance between fidelity and simplicity. Since the model is derived from first principles it can
describe the system for a wide operating range.
Simulation of the model is done using MATLAB R2010a and results have been verified with
plant data presented in K.J Astrom and R.D. Bell (1998). The conventional PID controller is
applied when the boiler is operating at medium load for both servo and regulatory problems.
Advanced controllers such as Fuzzy logic controllers(FLC) and Neural Network(NN)
predictive controllers have been also tried with satisfactory results. The details of these
controllers are discussed in the report within.
The drum boiler is a simple boiler which consist of a drum, downcomer and riser
components. A simple schematic of the drum boiler have been shown in Figure 1. The heat
Q, supplied to the risers causes boiling. Gravity forces the saturated steam to rise causing acirculation in the riser-drum-downcomer loop. Feedwater qf , is supplied to the drum and
saturated steam, qs, is taken from the drum to the superheaters and turbine. The presence of
steam below the liquid level in the drum causes the shrink-and-swell phenomenon which
makes level control difficult. In reality the system is much more complicated than shown in
the figure. The system has a complicated geometry and there are many downcomer and riser
tubes. The outflow from the risers passes through a separator to separate the steam from the
water. In spite of the complexity of the system it turns out that its gross behaviour is well
captured by global mass and energy balances.
8/19/2019 Modeling,simulation and control of a drum boiler
The shrink and swell phenomena in a drum boiler makes the level control very
difficult. Under boiling conditions, steam supporting field products such as bubbles
exist below the water/steam level interface. These bubbles have volume and therefore
displace water to create a misrepresentation of the true water level in the drum.
Another effect upon drum level is pressure in the drum. Because steam bubbles
compress under pressure the steam bubbles expand or contract respective to these
pressure changes. A higher steam demand will cause the drum pressure to drop, andthe steam bubbles to expand to give the appearance of a water level higher than it
truly is.This fictitious higher water level causes the feedwater input to be shut down at
a time when more water is really required.
A surge in water level as a result of the
drum pressure decreasing is called 'swell'. A water level decrease due to drum
pressure increase is called 'shrink'.
8/19/2019 Modeling,simulation and control of a drum boiler
flowrate we observe a decrease in the outlet steam flow rate .These flow rates equalize
almost after 30 seconds. The condensation flow changes in an almost step like manner. A
combination of water and steam dynamics are responsible for the response in drum level
indication and is somewhat complicated .The initial increase in the water level is due to the
rapid initial response of steam. The response in level is a combination of two competingmechanisms. The water volume in the drum increases due to increased condensation caused
by increasing pressure. The volume of steam in the drum first increases a little and then it
decreases because of the increasing pressure.
Fig 2: Response due to step change in fuel flow at medium load.
Steam flow changes at medium load
8/19/2019 Modeling,simulation and control of a drum boiler
starts to oscillate. For a “quarter amplitude decay” type response the K P value should
be set as half of the value at which the response starts to oscillate. Next we have to
increase K I until the offset is eliminated in sufficient time of the process and at last
increase K D, if required until loop is quick to reach its reference after a load
disturbance. But, too much increase in K D can cause excessive response andovershoot. A fast PID loop usually overshoots a little bit to reach its response
reference point more quickly; however in some system overshoot is not acceptable, in
which case we require an overdamped response.
Parameter Rise time Overshoot Settling
time
Steady-
state error
Stability
K p Decrease Increase Small
change
Decrease Degrade
K I Decrease Increase Increase Eliminate Degrade
K D Minor
change
Decrease Decrease No effect in
theory
Improve in
K d small
Table 2: Effects of increasing a parameter independently(14).
In our process we will try the manual tuning method only to tune the PID controller.
Fig 5: Simulink model to control the level in feedback control scheme using the PID
controller.
8/19/2019 Modeling,simulation and control of a drum boiler
The basic and key concept of fuzziness is that it allows a gradual and continuous
transition rather than a sudden and abrupt change in values. For example in a fuzzy seta member does not either or neither belongs to a group. Each and every member have
some membership in that group whereas in a normal set it either belongs to a group or
it neither belongs to a group[ either 0 or 1]. In fuzzy logic a member can take any
value between 0 to 1 depending on its membership of the group i.e. how much it
belongs to the group.The membership function of a set maps each element to its
degree i.e. it gives the degree of membership for each element under consideration.
Fuzzy control is a control technique based on fuzzy logic. The basic idea of fuzzy
control is to apply fuzzy inference to control problems. In fuzzy control, the control
box includes fuzzification, fuzzy inference using fuzzy if-then rules, anddefuzzification procedures. Fuzzy rules can include human descriptive judgements.
Commonly used fuzzy variables and their membership functionsWe define fuzzy variables that can represent values of the input and output variables.
A commonly used set of seven fuzzy variables follows:
NB = Negative Big
NM = Negative Medium
NS = Negative Small
ZO = Zero
PS = Positive Small
PM = Positive MediumPB = Positive Big
Or, the two mediums, NM and PM, may be omitted, resulting in the following set of
five fuzzy variables. This smaller set of fuzzy variables is simpler, but it would result
less fine or delicate control. For simplicity, we will use this five fuzzy variable
version hereafter.
NB = Negative Big
NS = Negative Small
ZO = Zero
PS = Positive Small
PB = Positive Big
The next step is to define membership functions for these fuzzy variables. Defining amembership function is up to us, and the selection of membership
functions affects the control performance. What membership function we choose
depends on many factors, such as the type of application, how much fine control is
required, how fast the control must be performed, and so on. A rule of thumb is that
simpler membership function causes lesser computation time but reduces fine control.
There are two categories of membership functions. One is continuous and the other
discrete
8/19/2019 Modeling,simulation and control of a drum boiler
Fig 6: Graphical representations of continuous triangular membership functions for seven
fuzzy variables.
The membership functions can be of various shapes such as triangular, trapezoidal
Gaussian etc.
Typical fuzzy control setup
At each time interval our fuzzy control system receives specific values for two inputs,
E and ∆E and yields one output, W.
Where En = ln-lsp : the level difference at time period n
∆E = En – En-1 : changing rate of E at time period n
Just as E is the difference between the current and target values, rather than the
current control value itself, W is a deviation from the current output value. Forexample, suppose that level is controlled by a feedwater flow rate, and the amount of
feedwater at time period n is qfn; then
qf n+1 = qf n +W.
Fuzzy if-then rules that derive W from E and ∆E
The fuzzy if then rules described for our system for level control is
Rule 1: If E is ZO and ∆E is NB then W is PB.
Rule 2: If E is ZO and ∆E is NS then W is PS
.
.
.
.
Rule 25: If E is PB and ∆E is PB then W is NB.
8/19/2019 Modeling,simulation and control of a drum boiler
The first stage of model predictive control is to train a neural network to represent the
forward dynamics of the plant. The prediction error between the plant output and the neuralnetwork output is used as the neural network training signal. The process is represented by
Figure 17.
One standard model that has been used for nonlinear identification is the Nonlinear
Autoregressive-Moving Average (NARMA) model:
..(31)
where u(k) is the system input , y(k) is the system output and d is the system delay (we will
use a delay of 1 for the predictive controller).
Fig 17: Plant Identification[7].
For the identification phase, we train a neural network to approximate the nonlinear function .
The structure of the neural network plant model is given in Figure 14, where the blocks
labelled TDL are tapped delay lines that store previous values of the input signal.
8/19/2019 Modeling,simulation and control of a drum boiler
Fig 23 : Changes in feed water flow rate to control the level.
The changes in the feed water flow rate at the beginning drops to almost 40 kg/s and
then rises to almost 65 kg/s and after about 200 s it settles to a constant value of 59kg/s. The water level increases at last to compensate to the losses in steam due to
increase in steam flow rate.
4.1.2 Servo problem
In the servo problem we are giving a step change of 0.1 m in the level set point.
The PID parameters obtained by manual tuning are
K C = 700
τI = 3 , τD = 1.
The response of the system can be seen as follows
8/19/2019 Modeling,simulation and control of a drum boiler
As we see from the response that in fuzzy control the response obtained is more
steady as obtained in PID controller. The response rises a peak of about 0.1 m aboveset point and then eventually decreases to the set point. The response obtained after 90
seconds.
Fig 29: response of FLC due to step change in fuel flow rate.
Fig 30: changes in feedwater flow rate to control the level for FLC for a step in fuel
flow.
8/19/2019 Modeling,simulation and control of a drum boiler