A Robust Temperature Controller Design for an Innovative

Hyperthermic Intraperitoneal Chemotherapy Equipment

Iulia Clitan

, Corneliu Lungoci

, Vlad Muresan

, Daniel Moga

and Valentin Sita

Department of Automation, Technical University of Cluj-Napoca, 26-28 Baritiu Street, Cluj-Napoca, Romania

Department of Surgery, “Iuliu Hatieganu” University of Medicine and Pharmacy, 8 Victor Babes Street,

Cluj-Napoca, Romania

Keywords: Cytoreductive Surgery, Regional Chemotherapy, Hyperthermic Intraperitioneal Chemotherapy (HIPEC)

Equipment, Temperature Control, Strejc Identification Method, Robust Control, H

∞

Controller.

Abstract: This paper presents an advanced control structure for controlling the heating process of cytostatic solution

used in regional chemotherapy. The solution temperature control is an individual control structure which is

desired to be implemented on hyperthermic intraperitioneal chemotherapy (HIPEC) innovative device.

Cytoreductive surgery followed by HIPEC represents a therapeutic solution for patients suffering from

peritoneal carcinomatosis, an abdominal cancer. An H

∞

robust control structure is designed since the heating

process model’s parameters depend on the solution’s delivery flow. It is considered that the heating process

gain can vary from a nominal value to a maximum value, which represents an increase by up to 100% from

the nominal value. The responses to a step input signal for the nominal case, and the cases when the gain

varies by 50% or 100%, are simulated. The control structure is compared against a PID feasible controller

by means of overall performances. It resulted that the robust controller generates the best performance set

for the nominal gain and also for the case when the heating process gain varies.

1 INTRODUCTION

Peritoneal Carcinomatosis (PC), together with the

hepatic metastases was related in the past to the final

stage of cancer, being considered a surgically

incurable pathological state (Koppe et al, 2006). The

standard treatment, the systemic chemotherapy, for

this stage of the disease was not an efficient solution

because of the high tumor volume and the biological

exhaustion of the organism (Gleben et al, 2010). The

excess of mortality and morbidity due to cancers is a

reality that motivates consistent research and

development efforts aimed at solving these issues.

Cytoreductive surgery and regional chemotherapy:

the intensification of the cytostatic drugs effect

through the association of hyperthermia (delivered at

a high temperature of 41-43˚C), makes hyperthermic

intraperitioneal chemotherapy (HIPEC) a technique

that allows approaching PC in a therapeutic manner

(Levine et al, 2012; Sugarbaker and Clarke, 2006).

In the last years this radical therapeutic approach

for selected PC patients, through cytoreductive

surgery followed by HIPEC represents a standard

treatment (Sugarbaker, 2012). The procedures are

still in a more or less experimental phase, mainly

due to cost and technical limitations of the current

equipment and lack of appropriate monitoring. There

are few HIPEC devices commercially available, for

the delivering of the cytostatic drugs at the required

temperature, like ThermoChem HT-2000, Cavitherm

EFS 0685, SunChip or Anti-Meta. The HIPEC

devices based on the accepted Spratt model basic

architecture consists in peristaltic pump, heat

exchanger, temperature, pressure and flow sensors

and a storage reservoir (Spratt et al, 1980;

Sugarbaker, 2005). Some of the technical limitations

of the commercially available equipment are the

absence of a distributed temperature monitoring

system (able to provide comprehensive information

regarding the intraperitoneal temperature

distribution), the decreased number of delivery

channels (two inflow lines), or the absence of

advanced control algorithms (classical control

structures are used in order to ensure a homogenous

temperature in the peritoneal cavity at a constant

flow rate).

The authors are developing a HIPEC equipment

that offers: a complex solution distribution system

Clitan I., Lungoci C., Muresan V., Moga D. and Sita V..

A Robust Temperature Controller Design for an Innovative Hyperthermic Intraperitoneal Chemotherapy Equipment.

DOI: 10.5220/0005543800840091

In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2015), pages 84-91

ISBN: 978-989-758-123-6

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

with multiple nozzles; a multipoint temperature

measurement system; smart control algorithms for

localized flow and temperature control. In the social

and economic context, an affordable equipment for

HIPEC has a real implementation potential in all

cancer treatment centers, thus the cost of the

equipment is the main focus of the authors. The

pourpose is to create a functional and innovative

equipment that overcomes the previously stated

limitations of the HIPEC equipments.

The most suitable architecture for the proposed

HIPEC equipment was presented in (Lungoci et al,

2014; Stroia et al, 2014), and some of the essential

components of the equipments architecture are

indicated in figure 1, where:

 FC – represents the flow controller, used in

order to maintain a constant delivery flow of

the solution since the delivery flow varies

between 0.1 – 0.2 liters/minute;

 HC – represents the individual heating

controller used in order to maintain the

temperature of the solution in the range of 41-

43˚C;

 TS – represent temperature sensors that

measure the temperature of the solution at the

output of the preheating tank, and also the

temperature of the solution after the heating

element;

 FRS – represents the flow rate sensors;

 Storage tank – used in order to store and to

preheat the cytostatic solution at a temperature

of 38˚C;

 Supply and return pump – ensure the

circulation of the solution from the storage tank

to the patient cavity, and back;

 Individual heater – a heating resistance

constructed as windings on the exterior wall of a

cylindrical tube trough which the solution is

circulated (see figure 2), that works on the

principle of a heat exchanger;

The temperature sensors used for the

implementation of the HIPEC equipment’s

temperature monitoring system are PT 1000, such a

sensor is presented in figure 3.

The equipment architecture presented in figure 1

contains only one delivery channel. On the final

HIPEC equipment the authors are going to use a

number of up to eight delivery channels that are

going to have the same individual elements

presented above. The number of channels was

chosen by the authors in terms of delivery and

optimal homogenization of the solution inside the

peritoneal cavity (Lungoci et al, 2014; Stroia et al,

2014).

In this paper the authors present the design of an

advanced automatic temperature control structure

capable of maintaining the required temperature for

the cytostatic solution.

Figure 1: The HIPEC equipment components.

Figure 2: The individual heater.

Figure 3: The PT 1000 temperature sensor.

The case where a H

∞

robust controller is used in

order to control the solution’s temperature is studied.

The robust control is selected since the heating

A Robust Temperature Controller Design for an Innovative Hyperthermic Intraperitoneal Chemotherapy Equipment

process model’s parameters depend on the cytostatic

solution’s flow rate.

2 MATHEMATICAL MODEL OF

THE HEATING PROCESS

2.1 The Transfer Function Model

The mathematical model of the heating process is

obtained by using a graphical fitting method on a set

of experimental data. The experimental data plotted

in figure 4 represents the solution’s temperature at

the output of the heating element, measured at a step

type input signal and at a constant solution flow of

0.1 litres/ minute. The heating process input signal is

represented by the electric power used to heat the

heating element. The step response for the heating

system was achieved by applying a constant electric

power of 15.5 watts to the heating element, without

the pre-heater associated to the storage tank. This

means that the initial temperature of the solution, for

the experimental data from figure 4, is the

temperature of 15˚C instead of 38˚C.

In order to obtain a transfer function model the

Strejc identification method was applied, on the

basis of the shape of the experimental data set. The

method was explained in detail in a related work

(Clitan, 2015). The identification method consists in

approximating the heating system through a transfer

function of the following form:

()

(1 )





(1)

where n is the order of the process, k

represents

the heating system gain, and T

represents the

heating system time constant.

The order of the process and the heating system

time constant are obtained based on the correlation

between a series of calculated ratios and the Strejc

identification table (Mikleš and Fikar, 2007). The

corresponding ratios are calculated based on some

time periods determined graphically, in respect to a

tangent line drawn in the experimental signal’s

inflection point.

Following the identification method, a third

order transfer function with a time constant equal to

17 seconds results as the mathematical model for the

heating process.

The heating process gain (k

) is determined

using the steady state temperature value (t

) of

19.2˚C and the offset temperature value (t

) of 15˚C

(see figure 4).

Figure 4: The temperature experimental data.

19.2 15

0.271

15.5 0



  



ss o

(2)

The value of the heating process gain will be the

same regardless of the temperature offset, since if

that value changes than the steady state temperature

value will also change accordingly, as long as a

constant solution flow rate and electric power is

supplied.

The heating process mathematical model is

obtained as the transfer function given below in (3).

The model validation is presented in figure 5 where

the simulated model’s step response is plotted in

respect to the experimental data set.

0.271

()

(1 17 )





(3)

The heating process gain depends on the

solution’s flow value, since the output temperature

value varies with the flow. If the solution’s delivery

flow doubles in value (the maximum value of the

flow rate is 0.2 liters/minute) then the system gain

also doubles.

Figure 5: The heating process model validation.

ICINCO 2015 - 12th International Conference on Informatics in Control, Automation and Robotics

The control signal for the supplied electrical power

is applied using Pulse-width modulation (PWM).

The PWM transfer function has a gain equal to 30.

This gain needs to be added to the heating process

transfer function (H

) and the resulted fixed part

transfer function (H

) is given in (4).

3 3 2

30 0.271 8.13

()

(17 1) 4913 867 51 1





   

s s s s

(4)

2.2 The State Space Representation of

the Model

The heating process fixed part model can also be

represented by using the state space representation

given in (5).

1 1 2

( ) 0.1765 ( ) 0.01038 ( )

0.0002035 ( ) ( )

( ) ( )

( ) 0.001654 ( )





  





















x t x t x t

x t v t

x t x t

z t x t

(5)

where x

(t) represent the state variables, z(t)

represent the output temperature and v(t) represent

the input.

The state matrix, the input matrix, the output

matrix and the feedthrough matrix are presented

below in (6), (7), (8) and (9) correspondingly.

0.1765 0.01038 0.0002035

1 0 0

0 1 0

  











(6)











(7)

 

0 0 0.0061 0.271C

(8)

0D

(9)

3 ROBUST CONTROLLER

DESIGN

3.1 The H

∞

Robust Control

The main goal of a robust control is to design a

controller that stabilizes the process not only for its

nominal parameters values but also for the case in

which the parameters vary within a certain range

(Szelitzky et al, 2011). Such a control structure

ensures robust performance in response to parameter

uncertainty (Doyle et al, 1989). When using a robust

control structure the controlled process will have the

following requirements: low overshoot, short

settling time and disturbance rejection (Inoan, 2011).

Thus an H

∞

robust control is used for the

temperature control of the HIPEC equipment heating

process.

The H

∞

robust control design consists in finding

a controller that minimizes the lower linear

fractional transformation for the heating process

fixed part (Damen and Weinland, 2002).

In order to design an H

∞

robust controller the

augmented plant mathematical model (G) described

in (10) has to be constructed. This matrix form is

obtained from the state space representation which

includes the exogenous inputs and the error signals

(Inoan, 2011).

1 11 12

2 21 22











A B B

G C D D

C D D

(10)

3.2 The Robust Controller for the

Heating Process

The H

∞

controller design for the heating process

begins with the state-space representation of the

fixed part described in (5). Figure 6 shows the block

schematic representation of the fixed part state space

representation.

The heating process model’s parameters, namely

the process gain, depend on the cytostatic solution’s

flow rate since the heating process of the solution

depends on the amount and speed of the solution.

These values are set through the flow generated by

the supply pump.

As stated before the gain of the heating process

is influenced by the amount of solution flow. The

solution flow can vary between 0.1 – 0.2

liters/minute, thus the gain value can vary between

0.271 (considered to be the nominal value) and

0.542, which means that the parameters k

varies

by +100%.

The parameter k

may be represented as a lower

linear fractional transformation using the relative

variation





[0,1] and the matrix M

given in (11).













(11)

were p

is the maximum relative uncertainty (in this

A Robust Temperature Controller Design for an Innovative Hyperthermic Intraperitoneal Chemotherapy Equipment

case equal to 1), and k

is the nominal value of the

heating process gain.

Figure 6: The block schematic representation of the fixed

part state space model.

Using the lower linear fractional transformation the

uncertain parameter block k

from figure 6 is going

to be replaced with the group of blocks presented in

figure 7.

Figure 7: The heating process model validation.

The equations corresponding to the block

representation given in figure 7 are:





k k N

z k v

z p v k v

(12)

were v

represents the exogenous input and z

represents the error signal.

The dynamic behaviour of the heating process

with the uncertain parameters is described by the

system equations given in (13).

1 1 2

( ) 0.1765 ( ) 0.01038 ( )

0.0002035 ( ) ( )

( ) ( )

( ) 0.271 0.0061 ( )

( ) 0.001654 ( ) ( )





   



























x t x t x t

x t v t

x t x t

z t x t

z t x t p v t

(13)

In order to obtain the augmented plant mathematical

model matrix form, the state space representation

from (13) must be written as (14), having one

exogenous input and one error signal.

1 k 2

k 1 11 k 12

2 21 k 22

x(t) Ax(t) B v (t) B v(t)

z (t) C x(t) D v (t) D v(t)

v(t) C x(t) D v (t) D v(t)

  





  





  



(14)

The matrix form of the augmented plant model is

presented in (15).

The robust controller is designed in order to

minimize the error signal using the command

hinfsyn from MATLAB

and the augmented plant

model given in (15) (Gu et al, 2005).

0.1765 0.01038 0.0002035 0 1

1 0 0 0 0

0 1 0 0 0

0 0 0.001654 0 0

0 0 0.001654 1 0

  











(15)

In order to ensure good transient response the

following weighting functions were added (Gu et al,

2005).

5 10

0.3

2 0.0001

W 0.02









(16)

The H

∞

robust controller’s transfer function is

obtained from the matrix form by using the formula

given in (17) (Ogata, 2009). The resulted

controller’s fifth order transfer function is presented

in (18).

( ) ( )

H s C sI A B





(17)

4 3 2

1 2 3 4 5

5 4 3 2

1 2 3 4 5

()

   



    

n s n s n s n s n

s d s d s d s d s d

(18)

were

3.206 10

7.068 10

1.181 10

6814

132.3

1501

5211

5968

3081

0.154





(19)

0.0061 k =0.271

-0.1765

-0.01038

-0.0002035

ICINCO 2015 - 12th International Conference on Informatics in Control, Automation and Robotics

4 SIMULATION RESULTS

The temperature control structure previously

designed is analyzed based on its simulated step

response using MATLAB

Simulink, since the

experimental results will be obtained for a

forthcoming paper. A negative feedback control

structure is implemented using the controller’s

transfer function given in equation (17) and the

transfer function given in (4) for the PWM actuator

and the heating process to be controlled.

The H

∞

robust control structure is first simulated

using the nominal value for the heating process gain.

The step response for the nominal case is presented

in figure 8.

Figure 8: The H

∞

robust controller’s step response for the

nominal case.

The cytostatic solution’s heating process is

simulated over the temperature of 38˚C (the

preheated solution’s value) thus in order to heat the

solution to a temperature of 42˚C a temperature

reference signal of 4˚C is used in simulation. On the

step input signal a second order delayed element of

15 seconds is used.

The overall performances for the nominal case

are: zero steady state error, no overshoot and a

settling time of 49 seconds. In figure 9, along with

the step response for the nominal case, the step

responses for the cases when the gain’s value is

increased by 50% and by 100% are also plotted.

It can be observed that no steady state error and

no overshoot are obtained even if the value of the

gain varies. The settling time when the heating

process gain is increased by 50% is equal to 48

seconds, and the settling time when the gain is

increased by 100% is 47.5 seconds.

The robust controller is compared with a PID

controller designed using the Strejc design method

(Clitan, 2015). A first order filter was added to the

PID controller in order to have a feasible controller

and the PID controller’s transfer function is given in

(20). The two controllers are compared based on

their step responses for the nominal case and the

case when the system’s gain varies by 50% or by

100%, those step responses are presented in figure

10.

Figure 9: The H

∞

robust controller’s step responses for the

heating process gain nominal value, the case when the

gain is increased by 50% and also by 100%.

 

0.2844 1 0.6486

41.933

0.006486 1













PID

(20)

From the analysis of figure 10 it results that the

performances generated by the robust controller are

much better than those obtained when using the PID

controller, designed using Strejc method. With the

PID controller an underdamped step response is

obtained having a high overshoot of 38% and a

settling time of 270 seconds, for the nominal case.

Even if we adjust the PID parameters so as to obtain

better performances, the step responses would still

change if the process parameters vary from the

nominal values.

Since the robust controller is faster and has no

overshoot, meaning that the solution is heated only

at the desired temperature, this control structure is

chosen as the most suitable one for the temperature

control of the developed HIPEC equipment.

In figure 11 the control signals generated by the

robust controller in order to obtain the step

responses presented in figure 9 are depicted. The

negative values for the control signals are not a

problem since in order to ensure the initial

conditions a default level of electric power is

ensured.

The robust control law is going to be

implemented on a microcontroller by computing the

A Robust Temperature Controller Design for an Innovative Hyperthermic Intraperitoneal Chemotherapy Equipment

Figure 10: The graphical comparison between the H

∞

robust control structure and a PID control structure for the

nominal case and the case when the gain is increased by

50% and by 100%.

control signal according to the discrete-time

algorithm given below.

1 2 3

16 17

1 2 3

456

2.965 2.93 0.9653

2.22 10 5.551 10

0.1681 0.1681 1.319

1.301 0.1595 0.1595

  



  

   

    

   

  

k k k k

k k k

c c c c

e e e

(21)

where c

represents the current value of the control

signal that need to be computed, c

k-1

, c

k-2

, c

k-3

, c

k-4

, c

represent past values of the control signal and e

k-1

k-2

, e

k-3

k-4

k-5

k-6

represent past values of the

temperature error signal.

Figure 11: The control signals generated by the robust

controller for the nominal case, for the case when the gain

varies by 50% and by 100%.

The advantage of using the designed robust

controller is that it stabilizes and generates suitable

performances for the heating process not just for the

nominal value of the heating process gain, but also

for the case in which the gain varies. The gain

variation is due to the solution’s flow rate and it was

shown that this control structure generates similar

overall performances even if a constant solution’

flow is not provided.

This means that by using a robust temperature

controller the flow control structure is no longer

necessary, thus reducing the cost of the HIPEC

equipment since up to eight individual flow control

structures would be eliminated.

5 CONCLUSIONS

The authors design in this paper a temperature

control structure for the cytostatic solution heating

process, so as to obtain affordable HIPEC

equipment. A disadvantage of commercially

available HIPEC equipments is their high cost and

the fact that they do not have advanced control

structures.

A robust control structure is selected since the

heating process model’s parameters depend on the

cytostatic solution’s flow rate, namely the heating

process gain. A H

∞

controller is designed using

MATLAB. From simulation it was deducted that the

robust control structure generates similar overall

performances for the nominal case, and also for the

case when the heating process gain varies by +50%

or by +100%. A zero steady state error, no overshoot

and a settling time of about 50 seconds are obtained

for the cytostatic solution heating process even if the

solution’s flow varies.

The robust control structure was compared with

a PID control structure, obtained using Strejc design

method. Unlike the robust control the PID control

generates worst performances even for the nominal

case, in which we have a constant flow of 0.1 liters/

minute.

The advantage of using the designed H

∞

robust

controller is that it reduces the number of controllers

needed on the HIPEC device. A flow control

structure is no longer necessary since it was shown

that the robust controller maintains the required

temperature even if the solution flow is not constant.

This means that flow rate sensors are also no longer

necessary.

By implementing the robust controller designed

in this paper the cost of the HIPEC equipment is

reduced since up to eight individual flow control

structures would be eliminated.

ICINCO 2015 - 12th International Conference on Informatics in Control, Automation and Robotics

ACKNOWLEDGEMENTS

The research activity that helped the authors to

elaborate the paper is sponsored by the research

projects no. 30104/2014 and no. 30141/2014,

financed by the Technical University of Cluj-

Napoca.

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