A MPC based Fault Tolerant Control Strategy for Actuator FaultMd Raihan Mallick, Syed A. ImtiazFaculty of Engineering and Applied Science

Memorial University of NewfoundlandSt. John’s, NL, A1B 3X5, Canada

mrm171@mun.ca

simtiaz@mun.ca

Abstract—A Model Predictive Control (MPC) based fault tol-erant control application has been described. The controller wasapplied to control the concentration and level of a solid crystaldissolution tank. The system was frequently suffering processupset due to difficulty in solid discharge. The controller used anerror calculated from an intermittent signal as a feedforward tothe controller. The intermittent signal posed challenges in modeldevelopment and also for control. An iterative technique wasused to develop the model. The developed controller successfullyeliminated the operational problem.

Keywords: Solid Handling, Actuator Fault, Model PredictiveControl, Fault Tolerant Control

I. INTRODUCTION

Solid handling is often encountered in processing industries

ranging from chemical, materials and minerals to agricul-

tural, food and pharmaceutical. Examples include separation

of different petrochemicals and pharmaceutical products in

crystal form, Ni-Hydrometallurgey, oil sand processing etc.

These areas of manufacturing have a current value exceeding,

according to some estimates, two trillion dollars and a growth

factor of 5 to 10 over the next decade [1]. The vary nature

of solid makes it difficult to dispense and transport solid

between different units of the process. One common problem

is dispensing solid from storage in a controlled way. Solids are

typically stored in hoppers, which are circular or rectangular in

cross-section, with conical or tapering sections at the bottom.

Discharge from hopper takes place through an aperture at

the bottom of the cone. Due to factors such as, mechanical

interlocking, surface attraction, elctrostatic attraction, or pres-

ence of moisture, bridging of particles may take place which

leads to stable arches that impedes the smooth flow of solids.

Other known problems are rat-holing, shaft formation, arching,

piping etc [2]. If a stable arch is formed above the outlet,

difficulties commonly experienced are large fluctuation in flow

and in the extreme case no discharge at all from the hopper.

This often leads to operational problems in the downstream

processing units. Almost all of the solutions considered are

design changes in hopper, for example, changing the slope of

the conical section, different hopper geometry or attachment

of vibrators to the wall. Even after design change in many

cases the problem cannot be eliminated completely. Especially

the problem gets complicated when precise flow needs to be

maintained. It is important to manage this problem opera-

tionally as well. The motivation of this research comes from

0This work was financially supported by Research and DevelopmentCorporation (RDC).

a petrochemicals plant where solid crystals were dissolved

in a tank with water. The process used to run into frequent

operational problems when the crystals did not flow smoothly

from the hopper. In this paper we model the solid discharge

problem as an actuator problem propose a fault tolerant control

strategy that is able to deal with this problem. The proposed

fault tolerant strategy was implemented in the process which

effectively eliminated the problem.

A. Problem Description

A simplified process diagram for the system is shown in

Fig. 1. In this system solid crystals (for our purpose we will

call CRYSTAL-A) is dissolved in a tank with water. Water is

pumped into the tank under flow control. CRYSTAL-A is fed

to the dissolution tank from a hopper using a rotary feeder. The

feed rate of solid crystals to the mixing vessel is controlled

by the speed of the rotary feeder (RPM). The Water Level

in tank (LI) and the concentration of the liquid going out

of the tank (DI) are measured variables. The main control

objectives of the system are to prevent any overflow (maintain

the tank level) and maintain the concentration at desired value.

Under the existing control strategy, two PID controllers are

used to meet these objectives, the concentration of the outlet

stream is controlled by manipulating the rotary valve rpm,

while the flow controller under cascade control maintains the

tank level. However, the concentration at the outlet is subject

to frequent large disturbances when the operators have to take

control of the process and control the process manually during

this abnormal condition. The root cause of the disturbance

is the difficulty in solid dispensing. Occasionally because of

the variation in moisture content the solid gets lumped in

the rotary feeder. As a result solid does not dispense from

the feeder uniformly. After a while when the lump gets too

big it falls into the tank creating a big disturbance in the

concentration which causes further problem in the downstream

process. During these abnormal conditions the rotations of the

rotary feeder is not correlated with the solid discharge as a

result manipulating only rpm to control the concentration is

not effective. Under the existing control strategy this was a

frequent occurrence which caused severe operational problem.

Therefore it was important to design a controller that is able

to address this problem proactively. We designed a model

predictive controller based strategy to deal with operational

problem.

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Fig. 1. Process flow diagram with the existing control strategy

B. Why PID Failed?Given the overwhelming popularity of PID controller in

process industry, one relevant question is, why PID based

techniques were not used for managing the fault. Several

alternative PID control structures can be thought of which in

theory should have better success in rejecting the disturbance.

One possible control structure is to use a cascade control in

the solid feed. Instead of directly using the rpm to control

the density, in the slave layer rpm can be used to control

the solid flowrate, while the setpoint of the solid flowrate

can be cascaded to the concentration. This should allow early

rejection of the any disturbance in the solid flow. Another PID

based alternative structure can be to use the solid flowrate as a

feedforward to the controller. However, in practice these PID

control structures could not be used for several reasons. First,

there was no continuous measurement for the solid flowrate

to the tank. The solid flow rate is an intermittently calculated

signal from the ‘loss in weight’ of the hopper shown in Fig.

2. The hopper is mounted on a load cell which gives the

‘loss in weight’ of the hopper. Once the sensed weight reaches

the hopper refill level (low weight) the hopper is recharged,

during the recharge period the ‘loss in weight’ calculation is

not valid. Therefore the signal has missing periods of data for

the recharge events. The ‘mass flowrate’ signal after applying

‘zero order hold’ for each refilling periods is shown in Fig.

3. PID controller does not have a built in mechanism to deal

with this type of intermittent signal. Essentially during ‘zero

order hold’ period it is a constant signal and under cascade

control the controller will not take any action for the changesin density. Therefore the controller will be inactive for half of

the time. Secondly, prediction error of solid discharge could

constitute a good feedforward signal. However, PID controller

does not have the prediction capability therefore it requires

Fig. 2. Solid flow rate calculated from ‘loss in weight’ of the hopper

Fig. 3. Fault in the solid discharge under PID control

additional customization in the Distributed Control System

(DCS) to calculate dynamic prediction error. In addition to

that, the Single Input Single Output (SISO) nature of the PID

controller is also not ideal for rejecting the disturbance due

to actuator fault. Once the actuator (rotary control valve) is at

fault it has limited effectiveness. Therefore it is important to

use other handles which can quickly bring the concentration

within the limit. However, because of the SISO nature of PID

controller it cannot use other handles to reject the disturbance.

Therefore we used a model based controller, Dynamic Matrix

Controller (DMC) with additional fault handling capability to

manage this fault.

II. FAULT HANDLING IN DYNAMIC MATRIX CONTROL

There are several variants of DMC: ‘original’ DMC [3],

DMC with least squares satisfaction of input constraints

[4]. DMC with constrained linear programming optimization

(LDMC) [5], DMC with constrained quadratic programming

optimization (QDMC) [6], discrete state space version of

DMC [7]. A fault tolerant variant of DMC able to handle

sensor faults is proposed by [8]. These variants use different

optimizers and vary in terms of the structure of the prediction

models, however use the same prediction and minimization

of error concept. In our application we used Dynamic Matrix

Controller (DMC) and modified it for fault rejection. Dynamic

Matrix Control is a variant of Model Predictive Control that

uses a step response model to predict the future behavior of

the plant. Excellent reviews on MPC can be found in [9], [10].

The control input is calculated in a way that it minimizes the

error between the prediction and the desired set point. In this

application we used the following optimization at each time

step.

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Fig. 4. Step response model for DMC

minimize J(Δu) = (r− y)TQ(r− y) +ΔuTRΔu. (1)

y is the predicted value given by,

y = y∗ +A Δu. (2)

Minimization of the above objective function gives the

following control law,

Δu = (ATQA+R)−1ATQT (r − y∗). (3)

In the current application we modeled the solid discharge

problem as an actuator fault. In order to detect the fault

prediction error was calculated from the difference of the

predicted solid flow based on the rpm setpoint of the rotary

feeder and the solid flowrate calculated from ‘loss in weight’

of the hopper. Here we will give the modified DMC for

the error signal and defer the application problem due to

the intermittent nature of the error signal in the following

section. In this case, the uncontrolled output predictions have

an additional term of this disturbance,

y∗t+p = Zt+p +n∑

i=p+1

aiΔut+p−i + νt+p. (4)

The disturbance in this case is a multiple of input signal

that goes through the process,

νt+p =n∑

i=p+1

aiδt+p−i. (5)

where δt+p−i is the prediction error calculated from the

difference of predicted solid discharge and the calculated solid

flowrate.

III. CONTROLLER DESIGN AND MODELING

The core of the Dynamic Matrix Controller (DMC) design

is the 2×2 matrix with two Manipulated Variables (MVs) (i.e.,

Water Flowrate and RPM of rotary valve) and two Controlled

Variables (CVs) (i.e., Concentration and Tank Level). The

design philosophy for the controller is to manipulate Water

Flowrate setpoint as the primary handle for the level control. In

order to control concentration the RPM setpoint will be used as

the primary handle and Water Flowrate as a secondary handle.

The step response model for DMC is shown in Fig. 4. In an

ideal situation this structure should be sufficient for controlling

these two variables. However, the system frequently suffers

large disturbance in concentration due to the solid discharge

problem discussed in the previous section. This warrants

special fault tolerant configuration of the controller. The error

between the measured solid flowrate and the predicted solid

flowrate was used to early detect the fault in solid discharge.

The dynamic ‘Solid flow vs. RPM’ model was used to predict

the solid flow rate at anytime based on the RPM of the rotary

valve. Subsequently the predicted solid flowrate was subtracted

from the solid flow signal from the load cell, this gives the

δt+p−i in Equation 5. The calculated error signal was used

as a feedforward to the concentration control. As soon as the

fault initiates the error, signal magnitude (δi) keeps increasing,

the effect of the fault gets reflected on the concentration

prediction. The controller will first use the primary handle

(RPM) in order to keep the concentration within limit, if the

error keeps growing it will use the secondary handle (Water

Flowrate), which has a faster dynamics with respect to the

concentration.

A. Modeling using intermittent signalThe above fault tolerant formulation of the controller re-

quires two additional dynamic models ‘Solid Flow vs. RPM’

and ‘Concentration vs. Solid Flowrate’. However, these models

cannot be identified directly because of the intermittent nature

of the solid flow signal. The intermittent signal poses problem

in the modeling phase as well as in the control phase. We used

the following iterative technique to estimate the ‘Solid Flow

vs. RPM’ model parameters.

• Step 1 The solid flowrate signal is linearly interpolated

for the periods the signal values are missing; a model

between the rpm and the solid flowrate is estimated.

• Step 2 The model calculated from Step 1 is used to

predict solid flow. The missing values in the solid flow

signal are replaced by the predicted values.

• Step 3 Steps 1 and 2 are repeated until there is no

significant change in the model.

Subsequently the reconstructed ‘Solid Flowrate’ signal was

used to estimate the ‘Concentration vs. Solid Flowrate’ model.

The solid prediction error will have the same relationship with

concentration as the ‘Solid Flowrate’. The estimated model

was used to predict the disturbance in concentration for error

in the solid flowIV. RESULTS AND DISCUSSION

The controller was successfully implemented on the system.

The unique feature of the controller is the calculation of

the error in solid flow. However, the intermittent nature of

solid flow signal posed difficulty in online error calculation.

Under the current control strategy when the measurements are

unavailable, error value is frozen to its previous value. The

strategy worked well for the controller. The controller showed

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Fig. 5. Concentration control after the implementation of DMC

good performance in controlling the concentration and the

level. Since the implementation of the controller, operators

never had to intervene for the solid discharge problem. The

concentration signal under current control strategy is shown

in Fig. 5. Two instances when the solid flow was not smooth

are marked in the figure. In the first event the disturbance

is reflected in the concentration, however the controller was

able to keep it within the acceptable limit. In the second case,

the error was detected early and the controller took proactive

action. As a result of the proactive action the fault had very

little effect on the concentration.

V. CONCLUSIONS

The application of a DMC based fault tolerant control strat-

egy is described. The novelty of the controller is it is simple

to apply in process yet effective. The other contribution of the

research is the modeling and control strategy when a signal has

missing values. The proposed controller successfully managed

the actuator fault in a solid handling process.

VI. ACKNOWLEDGMENT

The authors would like to thank Research and Development

Corporation (RDC) for financial support.

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