Vol-6 Issue-2 2020 IJARIIE-ISSN(O)-2395-4396 11630 www.ijariie.com 773 Comparison of Mixed H 2 /H∞ with Regional Pole Placement Control and H 2 Optimal Control for the Design of Steam Condenser Mustefa Jibril*, Eliyas Alemayehu Tadese**, Messay Tadese*** *(School of Electrical & Computer Engineering, Dire Dawa Institute of Technology, Dire Dawa, Ethiopia ** (Faculty of Electrical & Computer Engineering, Jimma Institute of Technology, Jimma, Ethiopia ) *** (School of Electrical & Computer Engineering, Dire Dawa Institute of Technology, Dire Dawa, Ethiopia ) Abstract This paper investigates the comparison between mixed H 2 /H∞ with regional pole placement control and H 2 optimal control for the design of steam condenser. The comparison have been made for a step change in the steam condenser pressure set point for a step change of 10 & 23 seconds using MATLAB/Simulink environment for the steam condenser with mixed H 2 /H∞ with regional pole placement controller, steam condenser with H 2 optimal controller and steam condenser without controller. The steam condenser with mixed H 2 /H∞ with regional pole placement controller presented excellent and superior dynamic performance in response to the two step changes and an improvement in settling time. The overall simulation results demonstrated that the steam condenser with mixed H 2 /H∞ with regional pole placement controller can be an efficient alternative to the steam condenser with H 2 optimal controller for the steam condenser. Index Terms--Steam condenser, H 2 optimal control, mixed H 2 /H∞ with regional pole placement control 1 Introduction The condenser is one of the critical kinds of system in thermal electricity plant, nuclear electricity plants, and marine system plant. The reliability of condenser running at once impacts the protection and financial operation of the entire energy plant or power gadget. A steam condenser is a chunk of equipment that turns steam into water. Many steambased systems use a circuit of water to maximize their efficiency. Water is heated into steam, the steam offers motivation for a technique, a steam condenser turns it back into water, and the cycle begins again. The failure of the condenser may additionally cause the boiler or steam turbine unit to overheat, which endangers the safety of the whole producing unit or electricity plant. The condenser as a "lower source of heat" performs a special position in an energy plant, due to the fact the parameters of its work have a significant impact at the performance of the installation. Therefore, it's far critical to recognize the condenser operating parameters during both design and operation. For this purpose, mathematical models describing the paintings of the condenser in modified situations are created. Therefore, through the computer simulation experiments, the status quo of the dynamic version and knowledge the dynamic characteristics of the condenser have a wonderful significance on improving the protection and monetary operation degree of the steam condenser. Vol-6 Issue-2 2020 IJARIIE-ISSN(O)-2395-4396 11630 www.ijariie.com 774 2 MODELLING OF STEAM CONDENSER 2.1 Active Suspension System Mathematical Model The dynamic modelling of Steam Condenser (SC) shall be established using mass and energy balance condensation assumption. Therefore, according to the energy balance of the system, the heat of the steam will be equal to heat transferred to cooling water.  1hd mfrC R  Where, hdC = heat duty of the condenser in [KW], mfrR = flow rate of the mass in [kg/s], and  = latent heat of steam.  2 ln cwo icw hd tc cd icw cd cwo T T C Q T T T T            Where, tcQ =heat transfer coefficient (overall) /heat transfer area. cwoT = cooling water outlet temperature, cdT = condensation temperature, icwT =inlet temperature of cooling water. This yields to energy balance equation as    3cwfcwo hdicw cwo cwm cwm wh RdT C T T dt M M Q    cwoT =flow rate of cooling water [kg/s], cwmM = holdup (cooling water) [kg], whQ =cooling water heat capacity [KJ/kgK]. Based on the constant volume assumption, mass balance equation can be derived. The ideal gas equation is    4c c cd rs mfr c dP G T F R dt V   cP =condenser pressure [KPa], cG =gas constant cV = volume of condenser [m3], rsF = flow rate of steam [kg/s]. While the temperature and pressure is approximated linearly as CD cT P   Equation 3 and 4 are dynamic equations and system have 7 parameters and 8 variables. The variables and parameters with their values for a steam condenser are shown in Table 1 and Table 2 respectively. Table 1 Steam condenser variables Variable Value and unit rsF 7 kg/s mfrR 7 kg/s cwfR 127.1 kg/s cP 90 kPa cwoT 80 0C icwT 78 0C cdT 106 0C hdC 9862 kW Vol-6 Issue-2 2020 IJARIIE-ISSN(O)-2395-4396 11630 www.ijariie.com 775 Table 2 Steam condenser parameters Parameters Value and unit cG 0.3 kJ/(kgK) cV 8 m3  2455.65 kJ/kg tcQ 456 kW/K cwmM 8500 kg whQ 6.4 kJ/(kgK) 1 0.006 2 0.00045  0.86 K/kPa  78 0C 3 The Proposed Controller Design 3.1 H 2 Optimal Controller Design For Steam Condenser There are many ways in which feedback design problems can be cast as H 2 optimization problems. It is very useful therefore to have a standard problem formulation into which any particular problem may be manipulated. Such a general formulation is afforded by the general configuration shown in Figure 1. Figure 1 General control configuration The signals are: u the control variables, v the measured variables, w the exogenous signals such as disturbances w and commands r, and z the so-called "error" signals which are to be minimized in some sense to meet the control objectives. The steam condenser with H 2 optimal controller block diagram is shown in Figure 2. Figure 2 Steam condenser with H 2 optimal controller block diagram 3.2 Mixed H 2 /H∞ with Regional Pole Placement Controller design for steam condenser The mixed H 2 /H∞ control problem is to minimize the H 2 norm of overall state feedback gains k such that what also satisfies the H∞ norm constraint. Mixed H 2 /H ∞ synthesis with regional pole placement is one example of multi-objective design addressed by the LMI. The control problem is sketched in Figure 3. The output channel z is associated with the H ∞ performance while the channel z 2 is associated with the H 2 performance. Vol-6 Issue-2 2020 IJARIIE-ISSN(O)-2395-4396 11630 www.ijariie.com 776 Figure 3 Mixed H 2 /H∞ configuration The steam condenser with mixed H 2 /H∞ controller block diagram is shown in Figure 3 below. Figure 3 Steam condenser with mixed H 2 /H∞ controller block diagram The LMI regions for the pole placement is found using the command lmireg and we select the half plane region and the output region is 2.0000 1.0000 1.0000 0.0000an idi  And we use this region for the mixed H 2 /H∞ controller synthesis. 4 Result and Discussion The simulations of the steam condenser with the proposed controllers will present in this section. The Simulink model of the steam condenser with mixed H 2 /H∞ with regional pole placement controller, steam condenser with H 2 optimal controller and steam condenser without controller is shown in Figure 4. Figure 4 Simulink model of the steam condenser 4.1 Simulation of the cooling water outlet temperature for a step change of 10 & 23 seconds The Simulation output of the cooling water outlet temperature for a step change of 10 & 23 seconds for the steam condenser with mixed H 2 /H∞ with regional pole placement controller, steam condenser with H 2 optimal controller and steam condenser without controller is shown in Figure 5 and 6 respectively. Vol-6 Issue-2 2020 IJARIIE-ISSN(O)-2395-4396 11630 www.ijariie.com 777 Figure 5 Cooling water outlet temperature for a step change of 10 second Figure 6 Cooling water outlet temperature for a step change of 23 second 4.2 Simulation of the cooling water Flow Rate for a step change of 10 & 23 seconds The Simulation output of the cooling water flow rate for a step change of 10 & 23 seconds for the steam condenser with mixed H 2 /H∞ with regional pole placement controller, steam condenser with H 2 optimal controller and steam condenser without controller is shown in Figure 7 and 8 respectively. Figure 7 cooling water flow rate for a step change of 10 second Vol-6 Issue-2 2020 IJARIIE-ISSN(O)-2395-4396 11630 www.ijariie.com 778 Figure 8 cooling water flow rate for a step change of 23 second 4.3 Simulation of the Condenser Heat Duty for a step change of 10 & 23 seconds The Simulation output of the condenser heat duty for a step change of 10 & 23 seconds for the steam condenser with mixed H 2 /H∞ with regional pole placement controller, steam condenser with H 2 optimal controller and steam condenser without controller is shown in Figure 9 and 10 respectively. Figure 9 Condenser heat duty for a step change of 10 second Figure 10 Condenser heat duty for a step change of 23 second 4.4 Simulation of the Condenser Pressure for a step change of 10 & 23 seconds The Simulation output of the condenser pressure for a step change of 10 & 23 seconds for the steam condenser with mixed H 2 /H∞ with regional pole placement controller, steam condenser with H 2 optimal controller and steam condenser without controller is shown in Figure 11 and 12 respectively. Vol-6 Issue-2 2020 IJARIIE-ISSN(O)-2395-4396 11630 www.ijariie.com 779 Figure 11 Condenser pressure for a step change of 10 second Figure 12 Condenser pressure for a step change of 23 second 4.5 Numerical Value Comparison of the Proposed Controllers for Settling Time The Numerical Value Comparison of the Proposed Controllers for Settling Time is shown in Table 3 below. Table 3 Numerical Value Comparison of the Proposed Controllers for Settling Time No Control Target Without Contr mixed H 2 /H∞ H 2 optimal 1 cwoT SC 10 s 49 s 16 s 27 s cwoT SC 23 s 50 s 28 s 38 s 2 cwfR SC 10 s 49 17 27 cwfR SC 23 s 50 29 42 3 hdC SC 10 s 50 20 28 Vol-6 Issue-2 2020 IJARIIE-ISSN(O)-2395-4396 11630 www.ijariie.com 780 hdC SC 23 s 50+ 34 42 4 cP SC 10 s 48 18 26 cP SC 23 s 50+ 33 40 As a result from Table 3, the steam condenser with mixed H 2 /H∞ with regional pole placement controller settling time is small as compared to the steam condenser with H 2 optimal controller and steam condenser without controller. 6 Conclusion In this paper, the design of steam condenser, H2 optimal and mixed H 2 /H∞ with regional pole placement controllers have been done using Matlab/Simulink software successfully. Comparison of the steam condenser with H2 optimal controller, mixed H 2 /H∞ with regional pole placement controller and without controller for the control targets cooling water outlet temperature, cooling water flow rate, condenser heat duty and condenser pressure using a step change in the pressure set point. The simulation results prove that the steam condenser with mixed H 2 /H∞ with regional pole placement controller shows a good response in improving the response of the control targets effectively with best settling time than the steam condenser with H2 optimal controller and without controller. Finally the comparison and simulation results prove the effectiveness of the presented steam condenser with mixed H 2 /H∞ with regional pole placement controller. References [1]. Haozhi Bian et al. "Numerical Investigations on Steam Condensation in the Presence of Air on External Surfaces of 3x3 Tube Bundles" Progress in Nuclear Energy, Vol. 111, pp. 42-50, 2019. [2]. L.L. Tovazhnyanskyy et al. "Mathematical model of a plate heat exchanger for condensation of steam in the presence of non-condensing gas" Bulgarian Chemical Communications, Volume 50, Special Issue K (pp. 76 – 82) 2018. [3]. Maneesh Punetha et al. "a CFD Based Modelling Approach for Predicting Steam Condensation in the Presence of Non Condensable Gases" Nuclear Engineering and Design, Vol. 324, pp. 280-296, 2017. [4]. N. Shaukat et al. "Comparative Study of Control Methods for Steam Condenser" International Conference on Energy Conservation and Efficiency, Vol. 978, Issue. 1, 2017. [5]. Ying Liu et al. "Research Progress of Control of Condensate Depression for Condenser "Journal of Physics Conference Series, Vol. 887, Issue. 1:012026, 2017. [6]. Pooya Mirzabeygi et al. "Multi-Objective Optimization of a Steam Surface Condenser using the Territorial Particle Swarm Technique" Journal of Energy Resource and Technology, Vol. 138, Issue. 5, 052001 p 10 pages, 2016. [7]. Rafal Laskowski et al. "Cooperation of a steam Condenser with a Low Pressure Part of a Steam Turbine in OffDesign Conditions" American Journal of Energy Research, Vol. 3, Issue. 1, pp. 13-18, 2015.