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Self-adaptive Generalized Predictive Controlnew

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					          The Application of the Self-adaptive Generalized Predictive Control in
                       Multi-functional Hyperthermia equipment

                                 Xiu-wu SUI, Yang LI, Yu-hong DU , Wang XIE
        Tianjin Key Laboratory of Advanced Mechatronics Equipment Technology, School of Machinery and
                        Electronics, Tianjin Polytechnic University , Tianjin 300160,China


                      ABSTRACT                                                               2. GPC ALGORITHM

In the hyperthermia, different microwave radiators,                  Process model
different treatment objects, different relative positions            The process model of generalized predictive control
of the temperature testing point and the radiator can                GPC is controlled auto-regressive integrated moving
influence the controlled object characteristic.                      average, CARIMA model, which can describe the
Traditional PID can not control the temperature stably               object with random disturbance, CARIMA model is in
and accurately. The paper presents the calculation                   Eq.(1).
equation of generalized predictive control algorithm,                 A( q− 1 ) y( k ) = B ( q −1 ) ∆u (k − 1) + C( q −1 )ξ ( k ) (1)
and realized the improved GPC combined with
self-adaptive control method in the multi-functional                        A( q− 1 ) = 1 + a1q− 1 + L + an q− na
hyperthermia equipment. The closed-loop control                            
                                                                           
                                                                                                            a


experiments show the algorithm control accuracy is 0.1               Here,  B( q ) = b0 + b1q + L + bnb q − nb
                                                                                 −1               −1
                                                                                                                                     (2)
                                                                           
                                                                            C (q ) =1 + c1q + L + cnc q
centigrade degrees, and it is suitable for the                                   −1             −1            − nc

multifunctional hyperthermia equipment.                                    
 Keywords: Microwave Hyperthermia, A lgorithm,
             Self-adaptive      Control,       Generalized
             Predictive Control, Temperature Control                 Target function
                                                                     The target function of the GPC is Eq.(3).
                 1. INTRODUCTION
                                                                     J ( N , N2 , Nu ) =
                                                                          1

                                                                        N2
                                                                       
                                                                                                           Nu
                                                                                                                                       (3)
                                                                                                                                      
Microwave hyperthermia is an effective means to cure                 E  ∑ [ y ( k + j) − y r (k + j )]2 + ∑ r( j )[∆ u( k + j − 1_]2 
human tumour, and it has been widely used. Human                        j =N 1
                                                                                                          j =1                       
                                                                                                                                      
body temperature usually is 36.5 centigrade degree,
when some given power microwave heating the body,                    Here, N1 is the minimum output length, N1 ≥ 1 , N 2 is
the normal tissue’ temperature with enough blood flow
                    s                                                the maximum output length, Nu is the control length,
will not increase so much as to be damaged, but the                   Nu ≤ N 2 ,and ∆ u( k + i − 1) = 0 ,( i > N u ), r(j) is the
                s
tumour tissue’ temperature will rise so much as to be
killed for lack of enough blood flow.                                control weight sequence and usually constant. yr ( j) is
                                                                     the reference output sequence.
In order to kill tumour, but not kill the normal tissue,
the temperature must be kept in a certain range. The
hyperthermia demands the temperature control is high                 Calculation of the control value
accuracy of 0.2 centigrade degrees.                                  In assumption of N1 = 1 , N1 = N , according to the target
                                                                     function 3, the current control value is calculated with
In the multifunctional hyperthermia process, many
                                                                     equation u (k ) = u( k − 1) + f ( yr − y1 )
                                                                                                             T
factors will influence the controlled object characteristic.                                                                          (4)
For example, as heaters, several microwave radiators                                     T
                                                                     In Eq. (4),     f       is the vector consisting of the elements
are ready for different treatment objects, such as
prostate, breast, abdomen and so on, in the heating                  in the first line of the matrix ( F T F + rI ) −1 F T , the
process, the distance between the temperature sensors                matrix F is defined as below.
and the radiators can change. Traditional PID algorithm
with constant or adjustable parameters can not control
the temperature stably and accurately. The paper
presents the method of self-adaptive generalized
predictive control algorithm, the closed-loop control
experiments show the control result is satisfactory and
the algorithm is suitable for the hyperthermia.


                                                               1/4
    f0               0           L    0                                                  A j ,i = Aj −1,i +1 + Aj −1,1 A1,i ,( i = 1,2, L na , j > 1)
    f                            L    0                                                 
                                                                                           B j ,i = B j −1,i +1 + A j −1,1 B1,i , (i = 0,1, L nb, j > 1)
                      f0
    1                                                                                                                                                       (7)
    f2                           L    M                                                 
                                                                                           C j ,i = C j −1,i +1 + Aj −1,1 C1,i , (i = 1,2, L nc , j > 1)
                      f1
F =                                                                         (5)
    M                f2          L    f0 
    M                M           L    M 
                                          
    f N −1
                 f N −2          L f N−Nu 
                                            N × Nu
                                                                                          Reference output

                                                                                             yr ( k + d ) = y m ( k + d )
Here, fi ( 0 ≤ i < N ) is step response sequence of the                                                                                                      (8)
                                                                                             yr ( k + d + j ) = α yr ( k + d + j −1) + (1 −α ) S
process,         yr = [ yr ( k + 1), yr (k + 2) L yr ( k + N )]T
                                                                                          Here, ym ( k + d ) is the next d step optimal prediction
is the reference output vector.
                                                                                          at time k, yr ( k + d + j ) is the next d + j step
y1 = [ y1 ( k + 1 | k ), y 1 (k + 2 | k ) L y1 ( k + N | k )]T is
                                                                                          reference output at time k, d is the delay time, α is the
predicted future output based on all the input and output                                 soft factor, S is the setting value.
before time k, and can be got by
C (q −1 ) y1 (k + j | k ) =
                                                                         ,                Control value calculation
G j (q− 1 ) y( k ) + Fj (q− 1) Vu(k + j − 1), j = 1,2,L , N                                                                                   % %
                                                                                          The target function is J = E{(Yr −Y )T (Yr − Y) + rU T U } ,
F j , G j can be got by the Diophantine equation,                                         r is the weight factor, the result of J by the least
                                                                                                             %
                                                                                          square method is U = (G T G + rI )− 1 G T (Yr − Ym ) , I is
C ( q−1 ) = A( q−1 ) Fj' (q −1 ) + q −1Gj ( q− 1) and                                     the identity matrix, the matrix G is
Fj' = F j ( q−1 ) / B (q −1 ) .                                                                 B1,0                  
                                                                                                                      
                                                                                                B2,0 B1,0             
                                                                                           G=                                              ,
                                                                                                 M                    
           3. IMPROVED GPC ALGORITHM
                                                                                               B N − d L         B1,0 
                                                                                                                       ( N − d ) ×( N −d )
Too much calculation in Diophantine equation needs
                                                                                                yr ( k + d + 1)          ym ( k + d + 1) 
too much time, so the GPC basic algorithm is not                                                y ( k + d + 2)           y ( k + d + 2) 
suitable for MCU. We improve the GPC algorithm to                                                                                        
                                                                                          Yr =  r                , Ym =  m               ,
reduce the calculation time.                                                                   M                        M                
                                                                                                yr ( k + N ) 
                                                                                                                         ym ( k + N ) 
                                                                                                                                           
Predicted output
For the model in equation 1, the predicted output based
                                                                                              ∆u( k )            
on the minimum variance is                                                                    ∆u( k + 1)         
                 na                              nb
                                                                                           % 
                                                                                          U =
                                                                                                                  
ym ( k + j) = ∑ Aj ,i y( k +1 − i) +∑ B j ,i ∆u(k − d − i ) +                                 M
                                                                                                                                                            (9),
                 i =1                           i =1                                                             
                  nc                             j −1
                                                                             (6)              ∆u( k + N − d − 1) 
                                                                                                                 
                 ∑C        j, i   e(k + 1 −i) + ∑B j −i ,0 ∆u( k − d + i )
                 i =1                           i=0                                       If g T is the vector consisting of the elements in the first
                     0, j ≥ 0                                                            line of the ( G TG + rI ) −1 G T .The control value is
Here ∆ u( k + j ) =                     , ∆u (k + j ) is the
                     ∆u( k + j ), j < 0                                                  u ( k ) = u( k − 1) + g T (Yr − Ym )                              (10).
control value increment, d is the delay time. A is the
matrix of N rows and na columns, B is the matrix of                                       Calculation procedure of GPC combined with self
N rows and nb + 1 columns, and C is the matrix of N                                       adaptive control

rows and nc columns. A, B, and C is defined as below,                                     The calculation procedure of modified GPC algorithm
                                                                                          combined with self adaptive control is as below.
      A1, i = ai , ( i = 1,2, L n a )
     
      B1, i = bi , ( i = 0,1, L nb ) ,                                                   First, identify the parameter in the model Eq. (1).
     
     C1,i = Ci ,( i = 1,2, L nc )                                                        Second, calculate the predicted output
                                                                                          sequence ym ( k + j ), j = 1,2, L N by Eq. (6)
                                                                                          Third, calculate the reference output yr ( k + j ) with



                                                                                    2/4
ym ( k+ j) and setting value S by Eq. (8).                               for the temperature signal.
                                                                                            Sample temperature
Fourth, calculate the matrix B by Eq. (7).
                                                                                             Digital filtering
                                                         T
Fifth, calculate the matrix G, and get the vector g          by
                                                                                          Parameter identification
Eq. (9)
                                                                                        Calculate the control value
Sixth, calculate current control value u( k ) by Eq. (10),
and then return to first step.                                                           Output the control value

                                                                                                 Return
         4. S ELF-ADAPTIVE GPC IN
     MULTIFUNCTIONAL HYPERTHERMIA                                                    Fig. 2 Interrupt programme flow chart
                 EQUIPMENT
                                                                         GPC parameters are defined as below, N1 is correlative
The structure of multifunctional hyperthermia                            with delay time d . When d is unknown,
equipment                                                                usually N1 = 1 , if d > N1 , the elements under main
The structure of multifunctional hyperthermia                            diagonal of F are zero, the information is not enough, so
equipment is in the figure 1.                                            as soon as d is known, we choose N1 = d . N 2
                             Temperature sensor       Human body
                                                                         must be more than the order of the polynomial B( q −1 ) ,
Host
                                                                         when it is approximately the rising time of the system,
Computer      C8051F021                                Microwave
                                   Control circuit
                                                        radiator         it is reasonable. In practice, take into account of the
              MCU
                                                                         calculation, we choose N 2 = 10 . Nu is very important in
Fig. 1 The structure of multifunctional hyperthermia equipment
                                                                         the algorithm, for a given system, Nu is great than the
The host computer gets the commands from the                             numbers of the unstable poles points and the little -damp
operator by human-machine interface, save the test
                                                                         zero points, our system is a open-loop stable system, we
result from MCU by RS232 interface, and makes some
                                                                         choose N u = 1 .Theory shows the range of r is
management and decision. The Micro control unit
C8051F021 is the control core of the system, it gets the                  0 < r < ∞ , but from equation 5, we see the control
temperature of the human body by temperature sensor,                     action decreases with r increases, and increases with r
calculate the control value u( k ) by the self adaptive                  decreases, the system is used for human body, no
                                                                         temperature sudden change is allowed, so, according to
GPC control algorithm, and then give the control value
                                                                         experience, we select the range of r is 3 < r < 5
to the control circuit, the control circuit convert the
control value to turn on time or cutoff time of the solid
state relay, SSR, thus the power of the microwave                                          5. EXPERIMENTS
generator is controlled. Microwave generator gives
915MHz microwave by the radiators to heat the body                       We carry out the self-adaptive GPC algorithm
tissue to increase its temperature. Temperature is                       simulation in MATLAB software, and on the two-order
measured by temperature sensor, which is our patent                      system made of resistances, capacitances and amplifiers.
consisting of four high resistance leads made of carbon                  The simulations show the control result of the GPC
fibre and a thermistor. The sensor can measurement the                   algorithm is very good.
temperature under high electromagnetic filed without
disturbance; the measurement accuracy is 0.1 centigrade                  We also carry out the experiment with multifunctional
degree. This is a closed-loop control system.                                                             ent
                                                                         microwave hyperthermia equipm on the different
                                                                         controlled objects, such as water, beef and human body.
The control algorithm                                                    In the experiments, we change the distance between the
The control algorithm is realized in C8051F021 time                      temperature testing point and the microwave radiator to
interrupt programme, the main programme initializes                      change the system parameter.
the sampling time interval is 0.5 seconds. The time
interrupt programme flow chart is as below.                              The table 1 shows the control result in the beef, d is the
                                                                         distance between the temperature testing point and the
The controlled system model is identified as a                           microwave radiator, tr. is the rising time form 36.5
two-order system and a delay system. According to the                    centigrade degree, the setting value is 43.5 centigrade
theory of Shannon, the sample frequency is at least                                  T
                                                                         degree, ¦¤ is the temperature variation in one hour
twice of the signal, and is usually 6~ 10 times in the                   after transition.
closed-loop control system. From experience, we decide
the sample time interval is 0.5 seconds, which is enough                               Table 1 Control data in the beef


                                                                   3/4
         d (mm)      Tr (s)          T(¡æ
                                    ¦¤ )
            10         55            0.1
            15         70            0.1
            20         80            0.1
            25         88            0.1
            30         93            0.1
            35         95            0.1

                  6. CONCLUSIONS
GPC is a novel computer control algorithm in recent
years, the theory and experiment show the algorithm is
robust and has high control quality.

The paper applies the self-adaptive GPC, which
combines the GPC algorithm and the parameter
identification, to control the multifunctional
hyperthermia equipment. The experiments in different
conditions show the system is stable, the control
accuracy is 0.1 centigrade degrees, and the self-adaptive
GPC is suitable for the multifunctional hyperthermia
equipment.

                   7. REFERENCE

[1] George M.hahn£¬    Biological Rationale for New
                     Proceedings of the 6th
    Clinical Trials £¬
    international Congress on Hyperthermia
    Oncology£¬   1992£® Vol.2. 79~81
[2] Guido Biffi, Gentili, et a1£¬Electromagnetic and
    Thermal Models of a water-cooled dipole
    Radiating in a Biological Tissue , IEEE Trans.
    On Biological Engineering, 1991, Vol. 38 (1),
    98~103.
[3] Li Qi-an, CHU Jian£¬   Improved algorithm for
    multivariable generalized predictive control of
    diagonal CARIMA model, Control Theory &
    Applications, Vol. 24 No. 3, 2007, 6, 423~426
[4] WANG Sh i-jie, SUI Xiu-wu, ZHANG Li-ru, et
    a1,The technical research on the temperature
    measurement and control for microwave
    hyperthermia equipment, Chinese journal of
    scientific instrument, 1997,Vol.18 (2),113-118.
[5] ZHANG Xiao-lan, GUO Bing-jing, ZHU Jian-min,
    et a1, The Fuzzy control system on the
    hyperthermia temperature based MCU and CPLD,
    Journal of Henan University of Science and
    Technology: Natural Science, 2007, Vol.
    28(4):24~27




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