Fault Tolerant Control of Multivariable Processes
Using Auto-Tuning PID Controller
IEEE TRANSACTIONS ON SYSTEMS, MAN, AND
CYBERNETICS—PART B: CYBERNETICS,VOL. 35, NO. 1,
FEBRUARY 2005
Ding-Li Yu ; Chang, T.K. ; Ding-Wen Yu
Professor: Ming-Shyan Wang
Student: Wei-Mei Laio
Outline
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Introduction
CONFIGURATION OF FTC SCHEME
ADAPTIVE NEURAL NETWORK MODEL
PID CONTROLLER AUTO-TUNING ALGORITHM
ADAPTIVE MODEL EVALUATION
APPLICATION TO THE CSTR PROCESS
CONCLUSION
REFERENCES
Abstract
Abstract—Fault tolerant control of dynamic processes is
inves-tigated in this paper using an auto-tuning PID
controller. A fault tolerant control scheme is proposed
composing an auto-tuning PID controller based on an
adaptive neural network model. The model is trained online
using the extended Kalman filter (EKF) algorithm to learn
system post-fault dynamics. Based on this model, the PID
controller adjusts its parameters to compensate the effects
of the faults, so that the control performance is recovered
from degradation. The auto-tuning algorithm for the PID
controller is derived with the Lyapunov method and
therefore, the model pre-dicted tracking error is guaranteed
to converge asymptotically. The method is applied to a
simulated two-input two-output continuous stirred tank
reactor (CSTR) with various faults, which demonstrate the
applicability of the developed scheme to industrial processes.
INTRODUCTION
WITH rapid increase in complexity of modern control systems, the importance of the fault tolerant control (FTC) concept
and technology has been realized and accepted by in-dustry.
Control system stability and reliability are not only crit-ical for
some projects where strict safety conditions apply, e.g., nuclear
power stations and passenger airplanes, but also essen-tial for
large-scale productions, since most of modern industrial plants are
complex and often include a number of subsystems which may
compensate for the effects of sensor faults and com-ponent
malfunction. This requires solutions that are very costly in both
hardware and development effort. Therefore, FTC is very important
from the viewpoint of safety, as well as reduced production costs.
FTC offers the capability to avoid inadvertent process shut downs
from simple faults, e.g. in instrumentation and control loops that
could develop into production stoppages or plant failures.
CONFIGURATION OF FTC SCHEME
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The main objective of the FTC is to obtain a control vari-able to drive the process to
track the desired trajectory when the process is not subject to any fault, while to maintain
the system stability and to recover from the performance degrada-tion as much and as
fast as possible when fault occurs in the process. Considering that chemical or biological
processes are complex and their mathematical models are usually unknown, an active fault
tolerant control approach is developed in this sec-tion. The control scheme includes two
parts, one is using a NN to model the process and the model is made adaptive to catch
the dynamics change caused by the fault, another is an auto-tuning PID controller based
on the model. When the model captures the post-fault dynamics, the PID controller is
adapted to compen-sate the degradation of system stability and performance. The
configuration of the FTC system is shown in Fig. 1.
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In Fig. 1 the MLP model is online adapted with the model prediction error using the EKF
algorithm. The adapted model is used to predict process output at next sample time. The
predic-tion is used by the auto-tuning algorithm to derive an optimal control variable. The
framed part in Fig. 1 is the PID controller. PID controller adapts its parameters in the way
that the produced control variable will drive the NN model output to track the de-sired
reference. A recursive auto-tuning algorithm derived using the Lyapunov method will
generate the optimal control that is guaranteed to minimize a squared tracking error. The
thick line between the model used for prediction and that to be adapted indicates that the
structure and weights are shared between the two models.
CONFIGURATION OF FTC SCHEME
ADAPTIVE NEURAL NETWORK MODEL
ADAPTIVE NEURAL NETWORK MODEL
ADAPTIVE NEURAL NETWORK MODEL
ADAPTIVE NEURAL NETWORK MODEL
ADAPTIVE NEURAL NETWORK MODEL
ADAPTIVE NEURAL NETWORK MODEL
ADAPTIVE NEURAL NETWORK MODEL
ADAPTIVE NEURAL NETWORK MODEL
ADAPTIVE NEURAL NETWORK MODEL
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Step 1) At sample
time
, obtain the desired trajectory , the
past process output and the past control variable to form the NN
model input vector
.
Step 2) Implement the PID auto-tuning algorithm given in (27), (34),
(36)–(38) and (26) in iterative form to predict the optimum PID
parameter vector
. The initial value is assigned to be the value
at the last sample time,.
Step 3)
Apply the obtained to the PID controller to calculate
the optimal control variable
in (29).
Step 4)
Apply the obtained to the NN model to calcu-late
the model output
in (11) and NN model tracking error,
in (27) at iteration step .
Step 5)
Repeat Step 1 to Step 4 until the NN model tracking
error, is less than a pre-specified threshold or a specified bound to
the iterative step is reached.
Step 6)
Set
to be equivalent to
, and then apply it
to the PID controller in the process.
ADAPTIVE MODEL EVALUATION
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To evaluate the learning performance of the developed adap-tive
network, the network is used to model a multivariable, non-linear
CSTR process.
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The CSTR process used in this research is a typical nonlinear
dynamic process used in chemical and biochemical industry. The
process will also be used to evaluate the developed FTC scheme. A
second order endothermic chemical reaction 2A B takes place in
the tank. The schematic diagram of the process is shown in Fig. 2.
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The process works in the following way. The reactant A with
constant concentration and variable temperature flows into the
tank with the flow rate . An endothermic chemical reaction takes
place in the tank, which is based on the temper-ature, and the
reaction absorbs heat energy. As a result, the re-action influences
the temperature and concentration of outflow liquid. The two
inputs and two outputs are chosen as follows:
CONCLUSION
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he proposed FTC scheme employs an auto-tuning PID controller to
compensate the fault effects. The auto-tuning algorithm is derived with
Lyapunov method to guarantee the convergence of the predicted tracking
error. The MLP model is made adaptive online with the EKF algorithm, the
post-fault dynamics can be modeled in time and thus, the degradation in
the process tracking performance and in system relative stability is quickly
recovered.
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The effectiveness of the method is demonstrated in the application to the
simulated CSTR process for different faults. Actuator and component faults
in abrupt and incipient modes with large amplitude can be tolerated with
the developed FTC scheme. The tracking error is compensated within
about 10 sample periods and the system stability is maintained. Table I
shows the process tracking error indices in the simulations under different
fault conditions.
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It should be noted that for the last two error indices the tracking errors
caused by the control variable bound are in-cluded. Therefore, the error
indices caused by the faults in the last two conditions should be in a similar
level to that in condition two and three, respectively.
CONCLUSION
It is noted that sensor faults are not included in evaluations.
In fact, sensor faults are not tolerable with the developed
method.
 This is because that the adaptive NN model is online trained
with measurement process input output data and
consequently, the effects of sensor faults will also be
modeled. This leads to a process tracking error of the size of
the occurred sensor fault. Sensor fault tolerance in processes
with unknown dynamics is the research being undertaken.
Due to lack of a test rig for which the fault simulation
mechanism is equipped, the devel-oped approach is evaluated
only by simulated process with the simulated faults. The
potential applications include different industrial processes
with multivariables, nonlinear dynamics, and a considerable
complexity, such as chemical or biological processes
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