5. SYNTESIS OF THE ONСE-THROUGH BOILER CONTROL SYSTEM
5.11. Application of the PID-controller to the great system
The system with the PIDD-controller provides the best quality of transient processes (the least setting time and zero-overshoot). However, the system has the unacceptable shape of manipulated variable.
The system with the PID-controller based on the localization method is the only system, which fulfilled all requirements and provides the acceptable result for the all tests.
The system with the PID-controller based on the root locus method and the system with the robust controller also have the acceptable result, but the manipulated variable has oscillation nature.
The PID-controller based on the localization method was chosen to test on the great non-linear model, which was developed in the Technical University of Liberec [19, 20]. This controller was chosen because it is the only controller, which fulfills all requirements.
5.11. Application of the PID-controller to the great system
This model is closer to the real system than the linear model. The obtained controller from subchapter 5.2 was used without any changing.
Figure 5.23 shows the modelling result with the PID-controller.
Figure 5.44: Modelling result
Constant power level, the step response The modelling results are shown in figures 5.35 – 5.38.
0 200 400 600 800 1000
470 480 490 500 510 520 530 540 550 560
Q=50%
T [°C]
t [s]
1. input 2. output
3. output of pre-filter
68 Figure 5.45: Modelling result (the power level
is equal 50%)
Figure 5.46: Modelling result (the power level is equal 70%)
Figure 5.47: Modelling result (the power level is equal 90%)
Figure 5.48: Modelling result (the power level is equal 100%)
3. output of pre-filter
1. error
3. output of pre-filter
1. error
3. output of pre-filter
1. error
3. output of pre-filter
1. error
1. current v
69 The obtained results are similar to the results from subchapter 5.3.1. The setting time is smaller; the overshoot is equal zero.
Constant power level, the disturbance reaction The modelling results are shown in figures 5.49 – 5.52.
Figure 5.49: Modelling result (the power level is equal 50%)
Figure 5.50: Modelling result (the power level is equal 70%)
3. output of pre-filter
1. error
3. output of pre-filter
1. error 2. current dTout
1. current v
70 Figure 5.51: Modelling result (the power level
is equal 90%)
Figure 5.52: Modelling result (the power level is equal 100%)
The obtained results are similar to the results from subchapter 5.3.2. The time of disturbance reaction is smaller.
Changing power level, step response The modelling results are shown in figure 5.53.
0 200 400 600 800 1000
3. output of pre-filter
1. error
3. output of pre-filter
1. error 2. current dTout
1. current v
71 Figure 5.53: Modelling result
The PID-controller is able to keep the output steam temperature in the desired level with changing power level. All results show that the PID-controller based on the localization method solves the given task; all requirements are fulfilled.
0 200 400 600 800 1000
496 498 500 502
T [°C]
0 200 400 600 800 1000
-2 0 2 4
T [°C]
0 200 400 600 800 1000
40 60 80 100
T [°C]
0 200 400 600 800 1000
100 150 200 250
V [%]
t [s]
1. input 2. output
3. output of pre-filter
1. error
1. current v
1. power
72
CONCLUSION
The following contributions were done during the work:
1. The method of PID-controller calculation, based on the localization method, was developed. This method provides possibility to control system with linear and non-stationary plant.
2. This obtained method was implemented to assigned problems, which include Real Rotation speed control with an elastic clutch and temperature control of a non-linear PowerStation.
3. The robust control method and the root locus method were also implemented in the same systems for comparison with developed method.
4. The results were obtained by making experiments in laboratory on the real control process and the numerical simulation with linear and non-linear model of the once-through boiler.
Evaluation of achieved results is based on numerical experiments and measurements in the laboratory. The achieved results can be summarized as follows:
1. The results of the PIDD-controller, based on the localization method, show that this method enables to design and parameterize a PIDD-controller. The measurement and simulation show that there is a good quality of the transient processes and performance with different power level. However, the shape of manipulated variable makes it to be impossible to implement this controller to the real system.
2. The results of PID-controller, based on the localization method, enable to design and parameterize a PID-controller. The system with such controller works slower, but it fulfills the requirements of the control system.
3. The results obtained by using other considered methods (the Root locus method, the robust control method) show that these methods can solve only some part of the task.
4. The obtained algorithm of PID-controller calculation is respectively simple and independent from type of control object. I suppose, it can be used as for control of simple linear plant as for control of great non-linear plant. Of course there must be fulfilled a number of restriction and limitation given by the controlled plant. It is a classical trial error method.
5. In addition, the method was tested in the real system of speed control and on the great non-linear model of the once-through boiler. These results show that method can be implement in practice.
73
REFERENCE
[1] PID-controller [online], 2014 [01.03.14] http://ru.wikipedia.org/wiki/ПИД-регулятор [2] Vostrikov А.S., Frantsuzova G.A. Theory of automatic control. Novosibirsk: NSTU, 2003.
[3] Nikulin Е.F. Basics of automatic control theory. Frequency methods of analysis and synthesis systems. Manual for high schools. Saint Petersburg: BHV - Petersburg,2004.
[4] PID-controller on practical examples [online], 2013 [10.12.13]
http://pidcontrollers.narod.ru/
[5] Encyclopedia of APCS [online], 2014 [01.03.14] http://www.bookasutp.ru/
[6] Dorf Richard C., Bishop Robert H. Modern control system. Prentice Hall, Upper Saddle River, NJ, 11th edition, 2008, 1034p. (or in Russian: Moscow: Laboratory of Basic Knowledge, 2002, 832p.).
[7] Robust control [online], 2014 [02.03.14]
http://ru.wikipedia.org/wiki/Робастное_управление
[8] Prof. Proske. Automatic Control Theory. Course of lectures. Zittau: Hochschule Zittau/Görlitz, 2013. 290p.
[9] Boiler [online], 2014 [21.03.14] http://ru.wikipedia.org/wiki/Паровой_котел
[10] Vostrikov А.S. The problem of controller synthesis for automatic system: state prospects.
AUTOMETRIYA, 2010 T.46, №2
[11] T. Nahlovsky, O. Modrlak, “The Fuzzy Approach to the Temperature Control of Superheated Steam” System Theory, Control and Computing (ICSTCC), 2013 17th International Conference
[12] Opalka, J.; Nahlovsky, T., "Continuously switched linearized models of the nonlinear once-through boiler model," Process Control (PC), 2013 International Conference on , vol., no., pp.263,267, 18-21 June 2013 doi: 10.1109/PC.2013.6581420
[13] Steam turbine [online], 2014 [28.03.14] http://ru.wikipedia.org/wiki/Паровая_турбина [14] Zemtsov N.S. Analysis of typical controller parameters calculations for linear system
Novosibirsk: NSTU, 2012, 52p.
[15] Prof. Modrlák, Ing. Hubka. ROBUST AND FUZZY CONTROL. Course of lectures.
Liberec: TECHNICKÁ UNIVERZITA V LIBERCI, 2014. 216p.
[16] Hilbert Space [online], 2014 [02.04.14]
http://ru.wikipedia.org/wiki/Гильбертово_пространсво
[17] H-infinity methods in control theory [online], 2014 [02.04.14]
http://ru.wikipedia.org/wiki/H∞-синтез_(теория_управления)
[18] L. Hubka, P. Školník, S. Gärtner. Rotation Speed Control with Flexible Binding. Liberec, 2013.
[19] Hubka, L.; Modrlak, O., "The practical possibilities of steam temperature dynamic models application," Carpathian Control Conference (ICCC), 2012 13th International , vol., no., pp.237,242, 28-31 May 2012 doi: 10.1109/CarpathianCC.2012.6228646
74 [20] Hubka, L: Temperature dynamics of heat exchangers in boiler, "Eurosim 2010 -7th EUROSIM Congress on Modelling and Simulation" Praha. CTU, 2010. ISBN 978-80-01-04589-3
75
ATTACHMENT
A.1. Identification program identific.m:
clear all; clc; close all;
load('PID_mestdesyu without controller_1.mat');
plot(t, u, t, y, 'LineWidth',2);
title(strcat('Input Data To Identification, Step #',num2str(i)));
grid on; xlabel('Time [s]'); ylabel('\Deltau, \Deltay [1]');
legend('Input \Deltau', 'Output \Deltay', 0);
%% initial guess and structure definition T=[1 2 1];
K=1.3;
%% run the parameters estimation process F=idKTi_func(t,u,y,K,T)
% x - vector of parameters to optimize x=[K T];
lB=length(K);
%% optimization via 'fminsearch'
OPTIONS=optimset('LargeScale','off','MaxIter',500,'Display','off','TolFun',1e -9);
figure;
x = fminsearch('critIdKTi',x,OPTIONS);
close;
%% postprocessing
% reconstruction of the A, B polynomials from x vector K=x(1:lB); A=[x(lB+1:end) 1];
% system transfer function definition G=tf(K,A);
%% plot results [yi,ti]=lsim(G,u,t);
figure;
plot(t,u,t,y,'LineWidth',2);hold on;plot(t,yi,'r','LineWidth',2);hold off;
grid on; xlabel('t [s]'); ylabel('\Deltau, \Deltay, y_{model}');
string_TF=evalc('G');
title(strcat('Model and measure, T=[',num2str(T),'],',10,' Model TF:', string_TF));
legend('Input - u','Measure output - y','Model output - ym',0);
76 critIdKTi.m:
%% criterium function for N different time constant transfer function structure
function f=critIdKTi(x) global t u y lB
%% reading of 'x' vector
K=x(1:lB); A=[x(lB+1:end) 1];
sys=tf(K,A);
[yi,ti]=lsim(sys,u,t);
f_sum=sum((yi-y).*(yi-y));
plot(t,y,t,yi,'LineWidth',2);grid on;
title(strcat('Criterion = ',num2str(f_sum)));
pause(0.01)
%% criterium calculation (LQ) f=f_sum;
77