HUNGARIAN JOURNAL OF INDUSTRIAL CHEMISTRY VESZPREM Vol. 30. pp. 181- 185 (2002) EQUIVALENT SYSTEM METHOD APPLIED TO MULTIVARIABLE CASCADE CONTROL OF INDUSTRIAL TUBULAR FURNACE A. G. ABILOV, 0. TUZUNALI', Z. TELA TAR and H. G. ILK (Department of Electronics Engineering, Faculty of Engineering, Ankara University, 06100-Tandogan, Ankara!I'URKEY) Received: July 3, 2002 The purpose of this paper is to apply and improve a multi variable advanced control structure on the basis of equivalent system teclmique for two-flow tubular furnace, which has widespread application in industrial fumace plants. After analyzing the dynamic properties of furnaces, it was concluded that these furnaces are symmetric MIMO processes, having two inputs and two outputs. There are a numerous reciprocal interactions between input and output variables. For this reason, equivalent system method was employed to investigate and develop advanced control structures for these furnaces. According to this method, symmetric MIMO system was divided into two equivalent separate systems. Finally, the equivalent model control design of combined feedback/feedforward multivariable cascade system is given and the results are presented. Keywords: industrial furnace plant, symmetric MlMO systems, combined feedback/feedforward control structure Introduction Furnaces are the basic and most important industrial units of petroleum refineries and petrochemical processes. The furnaces can have single or multiple flows according to their technological structures. They are made up from the regions of convection and radiation_ The heat exchange between chimney gasses and petroleum flows is realized in the regions of convection and radiation. Sufficient quantity of oxygen, required for the control of the burning process in these regions, is obtained from the air. In addition, an optimum amount of air is desired for the economical and ecological sound burning in furnaces. There appeared many studies in literature about controlling the burning process [l-7]. These studies have shown that furnaces are multivariable, distributed, complex dynamic control systems. In multiple flow furnaces, there are also large delays in their dynamic channels and cross relationships between the control parameters. In most applications, a linear model was used to present the dynamic behaviour of the process (impulse/step response function, transfer function, state- space model). Due of these complexities, it is necessary to investigate the more effective multivariable advanced control structures working on the basis of equivalent system technique [8]. The following steps are carried out in the study of the equivalent system method: Transformation of the system to the equivalent method. Constructing the control algorithms of the system according to equivalent model. Application of the control algorithms to separate systems working under different conditions. Performance evaluation. In this paper, an advanced multivariable cascade equivalent control system has been developed for two flow industrial petroleum refinery furnaces. The following sections present the proposed algorithm in detail. The simulation results are given. Finally, discussion and conclusion are presented. Process description In the industrial furnace plant, crude oil is passed through two spiral pipes and divided into two flows and then it enters into the burning chambers in the convection and radiation sections. Firstly, the petroleum Contact information: E-mail: abilov@science.ankara.edu.tr; tuzunalp@ science.ankara.edu.tr; telatar@science.ankara.edu.tr; iik@science.ankara.edu.tr 182 Fig.l Schematic diagram of tubular furnace. FC: The feed control, PC: Control of pressure, RC: Ratio control, TC1: Temperature control of the chimney gasses, TC2: The outlet temperature of the petroleum · flow is heated by chimney gasses, and then at the outlet, two flows are combined by the flame in the burning chamber. The unit operates between 700 and 900 °C intervals with a duty to bring the outlet crude oil to 320 °C, and to leave the stack gases at 750 °C. The outlet temperature of the petroleum in the left and right pipeline is obtained by supplying sufficient quantity of oxygen and natural gas to the right and the left fuel chambers. This creates reciprocal relations between these parallel transfer channels. When these properties of the furnace are considered, it is quite important to develop and apply new temperature control algorithms. In a burning process, the oxygen/fuel ratio must be OmmS:O~max· So, the complete combustion affecting the concentration in the chimney gases that pollute the environment is achieved by adjusting the vacuum required for the furnace. On the other hand, the complete combustion is evaluated by the concentration of the oxygen in the chimney gasse-s. Besides, the temperature of the combustion depends significantly on the quantity of the used air. The schematic diagram of an industrial petrol refinery furnace is illustrated in Fig.l. Transfer function of the process Our industrial research on the dynamic characteristics of furnaces reveal that furnaces consist of a MIMO system with two inputs and two outputs and that there are symmetric reciprocal interactions between the input- output ''ariables. A block diagram showing the dynamic channels is given in Fig.2. where x." x:;, Xr, y,.y,::. Y~tl and Yt~ are the consumption of natural gas. given to the left and light fuel chambers The consumption of the pettoleum flow given to furnace. the outlet temperatures of the pettoleum in the left and right sides and the temperature of the chimney gases which enter the left and right sections of the convection chamber, respectively. · The transfer function of the dynamic channels was determined from the reaction curve of the process Fig.2 Block diagram of the dynamic channels Fig.3 Block diagram of the symmetric control systems with two inputs-outputs obtained by ± step disturbances to the fuel inlet of the furnace. Since the furnace with two flows is a symmetric process, the transfer functions are as follows. W11 (s)=W22 (s), W12 (s)=W2/s), Kn(s)=K22 (s) (1) The Laplace domain transfer function of the symmetric multivariable system is: W. (s)"' 5 ·10 2 · e·180s 11 356·106 s3 +7.96·104 s 2 +4.71·102 s+l oc I % max. fuel consumption (2) "' ( ) - 4·102 -!80s rr 12 s e 8.74 ·106 s3 + 10.9 · Hr' s 2 + 5.31·102 s + 1 °C I% max. fuel consumption (3) 1.6·102 ·180s e 5.22·106 s3 +8.68·104 s 2 +4.88·10 2 s+ 1 "C I% max. fuel consumption (4) K ( ~- 10·102 ·30• u s, e 3680s 2 + 280s + 1 "C I% max. fuel consumption {5) Symmetric multivariable control system of the p:I:'OCess Block diagram of symmetric conttol system with two input.-output for two flow furnaces is given in Fig.3. x,(s) W,,,(s)= W<(s) ± Wl(s) Y•(•) + x,(-'-s)'---fVr_,...t-_w._:'',(.:..:s)_·_W._l(:.:._•)_±W----'-',(s)'-->..J-+~~~~y,(s) + Fig.4 Block diagram of control of the equivalent transfer function :xt(s) Y•qv(s) Fig.5 Block diagram of multi variable cascade equivalent seperate system The differential equations of this system can be formulated as follows. Here, W0 (s) is the transfer function of the main control channel; w; (s) is the transfer function of the inside cross dynamic channel and wA~ )is the transfer function of the petroleum flow as a disturbance. Since the system is symmetric. W0 (s)=Wu(s)=W22 (s) , W1(s)=W12 (s)=W21 (s) , Wft(s)=W1,(s) (8) Due to the symmetry of the system, the transfer function of the main and cross channels are identical and in accordance with the other. Differential equation of the controller system is: u1 (s) = WR(s) [XJ (s)- Y1 (s)J, uz (s)== WR(s) fxz (s)- Yz (s)] The form of transfer function matrices (9) Y(s) = [W0 (s)E+ w;(s)A]u(s)+WAs)E f(s) {10) where, A=jo II E=ll 0 I f(s)==lft(s)~ It 0 0 1 f2 (s~ 183 Fig.6 Combined feedforward/feedback equivalent separate system Equivalent decoupled control system Equivalent block diagram of the relevant control system is given in Fig.4. In this system, because the transfer function of the equivalent channels is symmetric, it is identified as, Equivalent multivariable cascade control system A block diagram of the multi variable cascade control of the equivalent system is shown in Fig.5. In this separated system, the object of the control was also divided into two stages. The transfer function of the internal chimney gas is K 11(s) and the transfer function of the equivalent channel is Weq(s). In this system, the same controller could be used for both of two control loops [l-4}. The main feature of the system is that the optimum parameters of the stabilizator and the regulator controller are found in two control loops with different frequencies. For this purpose, firstly the parameters of the stabilizator loop are calculated and then the parameters of the regulatpr are evaluated within the framework of the calculated optimum parameters. In this stage, for the evaluation of the parameters of the regulator loop, a transfer function is obtained by the combination of the transfer function of the closed loop stabilizator and the transfer function of the equivalent channel. So the transfer function of the controller Qbject can be written as follows; (l3) Combined feedback/feed forward control system in equivalent multivarlable cascade As known, these systems consist of two loops. One of them is open loop based on compensating the exterior effects {disturbances) and the other is dosed loop based U(s)= WR(s )Ef,x(s)- y(s)} (11) on the feedback control principle 18*101. Combined 184 Table I The optimum PI parameters of the control systems in furnace Control Loop of Loop of Loop of Systems Regulaton Stabilization Compensation Kx104 Tx104 Kxl04 Tx104 Kxl0 4 Tx104 ForWu(s) -5.85 0.05 For Weqv(s) 44 0.01 Multi variable Cascade 5.5 0.013 70 1.12 Control Combined multi variable 5.5 0.013 70 1.12 0.1 20 cascade open and closed loop multivariable cascade control structure of the furnace is given in Fig.6. u(s) = X1 (s)-WRI (s)u * (s); (14) (15) h(s) = wf (s )x/1 (s); (16) Yeqv(s)= Yeqv 1 (S)+h(s); (17) Ycgl (s) = K 11 (s )u(s); (18) The transfer function of the whole system between the inputs (xh Xn) and the output (y*eqv) are described as follows, * w.qvl(s) Y,qvl (s) 1 + w, 4 • 1 (s )vRI (s )wR 2 (y )+ WR 1 (s )K11 (s (• + (20) [ Wf,(s)+WR,(s)Kll(s)wf,(s) { 'ur f)~ + W () +WRII,SJY•,I_S Xfl(s) e-q~rl s From this statement, according to provision of the absolute invariant, the transfer function of the compensator is defined as follows. Wc(s) ==- [W.fl(s) + WRJ(s)Kn(s) Wil(s)] I (21) Mostly, in this type of systems, because the transfer function detennined by the principle of the absolute invariant consists of a higher degree of fraction, realization of this statement can be difficult. This feature can practically be expressed by showing the compensatory as a simplified differential block, Wc(s) = K{ Tsi(Ts+ 1)] (22} Naturally, the compensator block expressed in this way cannot completely compensate the external disturbances. But, by selecting the appropriate parameters of the K and T, the outlet value of y;tp·l 15.0 1-W 11 (s) 2-Weqv(s) 3-cascade control ~ 10.0 ofWeqv(s) ~- 4-K 11 (s)