Comparison of Mixed H 2 /H∞ with Regional Pole Placement Control and H 2 Optimal Control for the Design of Steam Condenser

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.


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 steam-based 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.

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.

 
While the temperature and pressure is approximated linearly as  Table 1 and Table 2 respectively.

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.

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.

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.

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.

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.

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.

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.  Table 3 below.  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.

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.