Journal of Science & Technology 101 (2014) 025-029 Grey-Box Identification of Steam Boiler Using Linear State-Space Model and Closed-Loop Data Trinh Thi Khanh Ly'-^, Hoang Minh Son '•* '" Hanoi University of Science and Technology, No I, Dai Co Viet Sir, Hai Ba Trung, Ha Noi, Viet Nam '^'Electric Power University Received March 03, 2014; accepted April 22, 2014 Abstract This paper presents a grey-box identification approach for developing a linear state-space model with the physical state variables of steam boilers The mam concept of this research is to combine theoretical modeling principles with the closed-loop identification technique The structure of the model was determined by theoretical analysis of the boiler dynamics The parameter estimation algorithm was derived based on the prediction error method and Gauss-Newton iterative method This method was applied to a steam boiler al Phu tAy Plant revealing its effectiveness in the closed-loop identification problem Keywords Grey-box identification, prediction error method, Gauss-Newton method, boiler modeling I Introduction Steam boiler is an important component found in many industrial processes Several dynamic models of the boiler system have been developed employing different methods such as theoreucal modeling {or physical modeling, modeling from the first principles) [1],[2], black-box idendfication [3],[4] and grey-box identification [5],[6] The models obtained from the first principles provide good insights into the system behavior but they are quite complex On the other hand, black-box models are built from experimental data and require no a prion knowledge However, the drawback of blackbox approach is the lost of physical interpretation, as in the case of state-space models where both system order and stale vanables may not associate with physical characteristics of the system Grey-box identificafion aims at combining theoretical modeling with experimental-based parameter estimation, thus provides a balance between fidelity and simplicity This technique is suitable to build dynamic models required for advanced control methods such as model-based predictive control For advanced process control, a state-space model is usually preferable to deal with high-order, multiple-mput multiple-output (MIMO) systems Thus, in this paper we aim al combining a closedloop idendfication technique based on prediction enor method [14] and Gauss-Newton iterative algorithm, and theorefical modeling to derive a linear MIMO state-space model with physical state variables of the steam boiler The physical model equations are utilized to determine the state-space model strucnire Then, the model parameters are estimated fi-om closed-loop data by employing the prediction enor method and Gauss-Newton iterative algorithm The obtained theoretical results are applied to develop a dynamical model of the steam boiler at Phu My plant [12] In this real boiler system, we focus on the master processes as shown in Fig 1, where the mam output vanables are temperamre and pressure of the superheated steam, and the inputs are tiie fuel flow rate, spray water flow rate and steam flow rate The Physical Model Equations and The Identiflcation Model Hitherto, several grey-box methods have been proposed for steam boilers using open-loop data [6][8] Yet in the practice, we are often interested in modeling of systems operating under closed-loop control, for which many conventional open-loop methods would fail Some closed-loop idenfificafion techniques have been applied for steam boiler as reported in [3],[4],[9]-[ll], However, for such a complicated system, they used black-box approaches In the following, we employ a linearized statespace model as published in [1], in which the material and the energy balance equations were derived with appropriate simplifications [[2],[5],[ 13]], AD,, = AD -I-AD (1) • Conesponding author: Tel.: (+84) 3869.2005 E-mail address, son.hoangminh@hust.edu -0,Cp,A7;;-(/(^3-A^]AO^,- -DCJ.^ +^Q,,,+[h,-h^^)AD^ (2) Journal of Science & Technology 101 (2014) 025-029 The noise e(k) represents uncertainties such as unknown disturbances, noises and mode! inaccuracy We model e(i)' as a white noise process with zero mean and stadstically independent of past input and output data, even in the case of closed-loop operation The covariance mafi-ix E[e{k)e^(k)] = R should be also estimated for use by different control design methods Simplified scheme of a drum-type steam APj -=Kj,AP^., +k^^ -^A From physical considerations, certain elements of the parameter matrices are zeros For a fix operating point, these matrices have constant (4) h (5) ^ ''9 ro o| c-\ [0 — t^, = — ( A D - A D , dt ^, ij Defme the parameter vector as: where Dj and D^i are steam mass flow rates &om the steam drum and the secondary superheater (kg/h), Ddi IS attemperator spray flow rate (kg/h), Df is fiiel flow rate (kg/h), Vst^Vsi are steam volumes m the primary and secondary superheater (m^); Aj, /ij;, hs2 and /ij^are specific enthalpies of the steam in the drum, the steam in the primary and secondary superheater, and the spray water (kj/kg), respecdvely; Qsh is heat supplied to the superheater from the ftimace, P j is drum pressure (bar), Ps2 is superheater steam pressme (bar), Tsi and T,,2 are steam temperatures at the outlet of the primary and the secondary superheater (°C); Kr IS pressure coefficient, the over-bar symbol ( * ) denotes the values at operating point = [a„ ,a,,i|,,.,,;>