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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 4/4

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