Estimation of precursor density of a power reactor using uniform second order sliding mode observer Safdar Hussain a,⇑ , Aamer Iqbal Bhatti a , Abdus Samee b , S. Hameed Qaiser c a Mohammad Ali Jinnah University, Islamabad, Pakistan b Chashma Center for Nuclear Training, Mianwali, Pakistan c Nuclear Engineering Division, Pakistan Institute of Nuclear Science and Technology, P.O. Nilore, Islamabad, Pakistan article info Article history: Received 19 July 2012 Received in revised form 18 November 2012 Accepted 20 November 2012 Available online 23 December 2012 Keywords: Reactivity Precursor density USOSMO (Uniform Second Order Sliding Mode Observer) abstract In this paper a uniform second order sliding mode observer is used to estimate the precursor density of a pressurized water reactor (PWR). Precursors produce delayed neutrons which are most important in con- trol of nuclear reactor, but cannot be measured directly. This estimation is done under varying load con- ditions and taking into account the effects of reactivity feedback due to temperature. For the proposed estimation scheme the measurement data of Chashma Nuclear Power Plant Unit-1, Pakistan is used. These measurements include neutron density, coolant temperature and control rod position. Before the estimation a model of 998 MW (thermal) pressurized water nuclear power reactor is validated with experimental data because the mathematical model of plant should be accurate and precise for param- eter estimation as well as controller design. Measured neutron density and modeled neutron density are compared and found close to each other. Further more measured and modeled coolant temperatures are also compared. The response of mathematical model coincides with actual plant with minor error. This error may be due to uncertainties and unmodeled dynamics. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Nuclear power plants are very complex, nonlinear and time varying systems. Their characteristics change with fuel burn up and operating power level. Therefore, for designing a controller to regulate output power of a nuclear power plant and to estimate some immeasurable parameters, an accurate and precise mathe- matical model of the plant is required. Edwards Robert et al. (1990) developed a five state model of a nuclear power reactor with single delayed neutron group and proposed state feedback as- sisted classical control. They simulated the controller with step change in input. However, they did not consider the transients sit- uations. Gabor et al. (2009) identified a model for VVER-type pres- surized water reactor with temperature effects and xenon poisoning. They validated the model under varying load condi- tions. They also estimated some parameters of the plant with known data of some parameters like neutron density and coolant temperature. Pomerantz et al. (2002) validated a theoretical model with experimental data with the technique of flux mapping. This method was tested on CANDU-600 type reactor having seven reac- tivity device configurations. Lathouwers et al. (2003) presented a dynamics modeling and stability of a fluidized bed nuclear reactor. A theoretical model describing coupling behavior of the neutronics, thermal hydraulics and fluidization in a fluidized bed reactor were considered. The model was linearized around equilibrium points and stability was proved by root locus analysis. Sliding mode observers are extensively used in recent research. For example: (Wang et al., 2001; Butt and Bhatti, 2008; Qadeer and Bhatti, 2011; Qaiser et al., 2009a,b). Wang et al. (2001) estimated the external reactivity and Xenon concentration of nuclear reactor using first order sliding mode observer. They used point kinetic model of nuclear reactor for reactivity estimation and Chernick’s model for estimation of xenon concentration. They used a low pass filter to remove the chattering effect which is induced by first order sliding mode. Butt and Bhatti (2008) used higher order sliding mode for parameter estimation of gasoline engine. They used sin- gle dynamical equation of nonlinear model to estimate more than one parameters. In their work sliding mode technique based on real twisting algorithm was used. They estimated throttle body discharge coefficient, indicated torque and load torque as a func- tion of inlet manifold pressure. Qadeer and Bhatti (2011) estimated automotive engine parameters and efficiencies by second order sliding mode observer based on super twisting algorithm. The esti- mated parameters were volumetric efficiency, combustion effi- ciency, frictional torque and throttle discharge coefficient. Qaiser et al. (2009a,b) validated the model of Pakistan Research Reactor- 1 with experimental data. They also used second order sliding mode observer Qaiser et al. (2009a,b) for estimating the delayed 0306-4549/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2012.11.017 ⇑ Corresponding author. Tel.: +92 3335072515. E-mail address: safdar478@gmail.com (S. Hussain). Annals of Nuclear Energy 54 (2013) 233–239 Contents lists available at SciVerse ScienceDirect Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene