Figure 1. Block diagram of SHS Temperature Control System
This paper explains the tuning of analog PID controller for Superheated Steam Temperature system of 500 MW boiler using Particle Swarm Optimisation Algorithm based on ITAE as the objective function. The analog controllers have large applications in industrial control. The fifth order model of Superheated Steam Temperature system of 500 MW boiler is taken for study. Most of the available tuning algorithms are based on FOPTD models which is given by G(s) = Ke –τs/(Ts+1). If the plant is not approximated well to good FOPTD model, good controllers may not be designed using existing algorithms. Genetic algorithm is a stochastic algorithm based on principles of natural selection and genetics. To tune the PID controllers using Particle Swarm Optimisation Algorithm , it does not require any FOPTD model. Hence the analog PID controller is tuned using Particle Swarm Optimisation algorithm for Superheated Steam Temperature system and the results are compared.
The analog PID controller has a wide range of applications in process industries. The choice of analog controllers like P,PI,PID depends upon the model of the process. Tuning is adjustment of controller gains to achieve desired response. The selection of the controller gains is essentially an optimization problem in which the designer of the control system attempts to satisfy some optimal criteria, the result of which is often referred to as good control. The typical criterion for good control is that the step response of the system should have minimum overshoot, one quarter–decay ratio, minimum rise time, and minimum settling time. The boiler has so many variables to be precisely controlled for efficiency and safety. Among those variables, superheated steam temperature of 500MW boiler is one of the important variable. The fifth order model of superheated steam temperature system of 500MW boiler is used for study [4].
The boiler system in a thermal power plant consists mainly of steam –water system and combustion system which produces a high pressure superheated system to drive a generator in order to produce power. Most operators of process know that they want in the form of a response to achieve a change in set point or load. In order to compare different responses that use different sets of controller parameters, a criterion that reduces the entire response to a single number, or a figure of merit is desirable. There are three such criteria. They are IAE, ISE and ITAE. Each of the three figures of merit has different purposes. The ISE will penalize the response that has large errors because the error is squared. The IAE will penalize the response for small errors. The ITAE will penalize the response, which has errors that persist for long time. The ITAE criterion will tune the controllers better because the presence of time amplifies the effect of even small errors in the value of integral. Figure 1 shows the SHS Temperature Control System.
Figure 1. Block diagram of SHS Temperature Control System
Superheated steam temperature is one of the important variables in boiler to be controlled precisely for efficiency and safety. Hence the control of this parameter has assumed paramount importance in boiler controls.
The Transfer function of superheated steam temperature system [[4], [7]].
Desuperheater reduces the steam temperature by spraying low temperature water from the boiler drum or economizer exit. The response of outlet temperature of desuperheater to the changes in spray water in the case of 500 MW boiler is instantaneous. Hence, there is no dynamics involved but the coefficient connecting the spray change to the change in outlet temperature of desuperheater at 100% load is 0.557.
The inlet temperature of the superheater is increased by a factor of 1.382 at 100% load for a 500 MW boiler because of heat input from the furnace. The dynamics of superheater is such that the response of outlet temperature to change in inlet temperature is characterized by a series of first order lags with time constants that vary inversely with steam flow rate. Fifth order transfer function model of superheater is used for study in the present research work.
The successful operation of any process control system depends in a very critical manner, on the precise measurement of the controlled output and uncorrupted transmission of the measurement to the controller. The transfer function of the measuring device in the case of SHS temperature control system for 500 MW boiler is unity.
The most common final control element is control valve. The overall steady state coefficient of control valve and desuperheater in the case of SHS temperature system for 500 MW boiler is 0.557.
From Figure 2 the mathematical expression of the PID controller is
Where u(t) is the input signal to the plant model, the error signal e(t) is defined as e(t) = r(t)−y(t), and r(t) is the reference input signal [12].
Actuator saturation limit:-10 to 10
Figure 2. Block diagram of PID controller
The objective function is required to evaluate the controller parameters for the superheated steam temperature system. An objective function could be created to find a controller that gives the smallest overshoot, fastest rise time or quickest settling time. Each chromosome in the population is passed into the objective function one at a time. The chromosome is then evaluated and assigned a number to represent its fitness, the bigger its number the better its fitness. The genetic algorithm uses the chromosome's fitness value to create a new population consisting of the fittest members. The cross over and mutation rate taken here is 0.8, 0.01 [2].
e. Go to step2 and repeat until termination condition.
The objective function is based on error criterion. The performance of the controller is evaluated in terms of error criteria.
Figure 3 and 4 show the Simulink diagrams .
Figure 3. Simulink diagram of SHS System
Figure 4. Simulink diagram of ITAE criteria
Using the mathematical model of superheated steam temperature system [equation 1] and using Genetic Algorithm and Particle Swarm optimisation algorithm responses are simulated in simulink of MATLAB. The step responses of PID controller for superheated steam temperature system using ITAE as the objective function of Genetic Algorithm are shown in Figure 5. The step responses of PID controller for superheated steam temperature system using ITAE as the objective function of Particle Swarm optimization Algorithm are shown in Figure 6 and 7. Table 1 shows genetic Algorithm parameters and controller parameters for superheated steam temperature system. Table 2 shows particle swarm optimization algorithm parameters and controller parameters for superheated steam temperature system.
Figure 5. Response of PID controller for superheated steam temperature system using ITAE as the objective function of Genetic algorithm
Table 1. Genetic Algorithm parameters and controller parameters for superheated steam temperature system using ITAE as the objective function
Figure 6. Screen shot of Tuning PID controller for Superheated steam temperature System using Particle Swarm optimization Algorithm
Figure 7. Response of PID controller for Superheated Steam Temperature system using ITAE as the objective function of Particle Swarm Optimization Algorithm
Table 2. Particle Swarm Optimisation Algorithm parameters and controller parameters for Superheated Steam Temperature system using ITAE as the objective function
The analog PID Controller tuned using ITAE as the objective function of Particle Swarm optimization Algorithm has least value of ITAE. Hence it can be concluded that the analog PID Controller tuned using ITAE as the objective function of Particle Swarm optimization algorithm is the best analog controller for superheated steam temperature system of 500MW boiler.