A Multiobjective Particle Swarm Optimization (MOPSO) algorithm is proposed to finetune the baseline PI controller parameters of Alstom gasifier. The existing baseline PI controller is not able to meet the performance requirements of Alstom gasifier for sinusoidal pressure disturbance at 0% load. This is considered the major drawback of controller design. A best optimal solution for Alstom gasifier is obtained from a set of nondominated solutions using MOPSO algorithm. Performance of gasifier is investigated at all load conditions. The controller with optimized controller parameters meets all the performance requirements at 0%, 50%, and 100% load conditions. The investigations are also extended for variations in coal quality, which shows an improved stability of the gasifier over a wide range of coal quality variations.
Integrated Gasification Combined Cycle (IGCC) is an efficient method of clean power and energy generation. Here coal reacts with air and steam which is converted into producer gas (also called syngas) under controlled pressure and temperature. Purified producer gas is directed to gas turbine for generating power. The exhaust gas from the gas turbine enters Heat Recovery Steam Generator (HRSG) to produce steam which in turn runs the steam turbine, coupled with a generator. Coal gasifier is an important and primary element in IGCC. It involves many complicated chemical reactions with huge time constant, interactions among the control loop, and strong nonlinearity. The benchmark model of coal gasifier was developed in two stages at the Alstom Technology Centre, UK. The linear gasifier model at 0%, 50%, and 100% load conditions was issued in 1997. The details of this model, its specifications, and control techniques are discussed in the literature [
Researchers have attempted to design advanced control schemes and/or retune the baseline controller to meet the performance objectives at 0%, 50%, and 100% load conditions. This benchmark challenge II, which is a higher order state space model, is reduced to lower order model by different techniques [
Coal gasifier is a highly nonlinear, multivariable process, having five controllable inputs (char flow rate, air flow rate, coal flow rate, steam flow rate, and limestone flow rate), few noncontrol inputs (boundary conditions, pressure disturbance, and coal quality), and four outputs (fuel gas calorific value, bed mass, fuel gas pressure, and fuel gas temperature) with a high degree of crosscoupling between them. The process is a fourinput, fouroutput regulatory problem for the controller design with limestone flow rate at a constant value. Coal gasifier exhibits a complex dynamic behaviour with mixed, fast, and slow dynamics and it is difficult to control. The complete transfer function of coal gasifier is expressed as
The order of Alstom gasifier is found to be 25. The process is reduced to
Controller structure.
WCHR  WAIR  WCOL  WSTM  

CVGAS  0  PI  0  0 
MASS  P 
0  P 
0 
PGAS  0  0  0  PI 
TGAS  PI  0  0  0 
The structure of PI controller is given by
Input limits.
Input variable  Max. (kg/s)  Min. (kg/s)  Rate (kg/s^{2}) 

WCHR  3.5  0  0.2 
WAIR  20  0  1.0 
WCOL  10  0  0.2 
WSTM  6.0  0  1.0 
Gasifier outputs should be regulated within the limits for sink pressure (PSINK) disturbance test (Table
Output limits.
Output variable  Desirable  Limits 

CVGAS  ±10 kJ kg^{−1}  
MASS  Minimize  ±500 kg 
PGAS  fluctuations  ±0.1 bar 
TGAS  ±1 K 
Multiobjective optimization involves two or more objectives that are optimized simultaneously. The discussions about various multiobjective evolutionary approaches from analytical weighted aggression to population based approaches and Paretooptimality concepts are discussed by Fonseca and Fleming [
Mathematically,
minimize
subject to the constraints
Flow chart of Multiobjective Particle Swarm Optimization algorithm.
Nondominated vectors acquired in the primary population are compared with the elements of external repository which will be empty at the start of the search. An empty external archive accepts the current solution. If a new solution is dominated by an individual within the external archive, then such a solution is automatically rejected; otherwise such solution is stored in the external archive. At the end of the search, if the external population has achieved the specified capacity, the adaptive grid procedure is invoked. All the nondominated solutions are stored in external archive. Decision making problem is the process of finding best optimal solution from the existing alternatives. Many methods have been developed to solve Multiple Criteria Decision Making problem (MCDM). A prior knowledge of the relative importance of objectives is required in all MCDM methods.
Figure
MOPSO tuning objectives.
Sl. no.  Objectives 

1  MAE of CVGAS over 300 s 
2  MAE of MASS over 300 s 
3  MAE of PGAS over 300 s 
4  MAE of TGAS over 300 s 
5  IAE of CVGAS over 300 s 
6  IAE of MASS over 300 s 
7  IAE of PGAS over 300 s 
8  IAE of TGAS over 300 s 
Block diagram of optimization scheme.
Controller parameters of baseline PI controller are taken as decision variables. Input constraints are associated with Simulink model and they are not included in the desired specifications.
Coal gasifier has five manipulated inputs and four outputs. Setpoint to the gasifier is selected in accordance with 0% operating point. Disturbances such as pressure disturbance, load disturbance, and coal quality disturbance also affect the system performance. For this specific problem, a sinusoidal pressure disturbance of amplitude 0.2 bar and frequency of 0.04 Hz are applied. The measured outputs are compared with their corresponding setpoint that produces an error signal. MAE and IAE are calculated for 300 sec, which acts as the objective function for this optimization algorithm. MOPSO algorithm chooses the parameters of baseline PI controller, which takes necessary control action based on the error signal by manipulating the input variables. The controller should respond quickly enough so that the output variables do not deviate from the setpoint more than the specified constraints. Hence the sampling time is selected as 1 second. This procedure continues until the maximum number of iteration is reached. At the end, MOPSO algorithm provides a set nondominated solution for the controller parameters. From these nondominated solutions, optimal controller parameters are obtained so as to meet the inputoutput constraints at all load conditions and for all disturbances.
Table
Controller parameters.
Parameter  Baseline PI  Cuckoo PI  Bat PI  Simm A  MOPSO PI 

CV_Kp 





CV_Ki 





BM_Kp 





BM_Kf 





Pr_Kp 





Pr_Ki 





Tg_Kp 





Tg_Ki 





Cuckoo [
Following performance tests are conducted to verify the robustness of the system for the tuned values of baseline PI controller. Test results should satisfy the constraints for all performance tests. Using the tuned parameters, simulation is run for 300 sec at 0%, 50%, and 100% load conditions with sinusoidal and step pressure disturbance.
A step change in pressure disturbance of 0.2 bar and a sinusoidal pressure disturbance of amplitude 0.2 bar and frequency 0.04 Hz are applied to the Alstom gasifier at 0%, 50%, and 100% load conditions.
The dynamic response of Alstom gasifier for step and sinusoidal pressure disturbance at 0%, 50%, and 100% load is shown in Figures
Response to step disturbance at 0%, 50%, and 100% load.
Outputs and limits
Inputs and limits
Response to sinusoidal disturbance at 0%, 50%, and 100% load.
Outputs and limits
Inputs and limits
From Figure
(a) Summary of test output results—Maximum Absolute Error. (b) Summary of test output results—Integral of Absolute Error.
Test description  Outputs  Baseline PI  Cuckoo PI  Bat PI  Simm A  MOPSO PI 

100% load, 
CVGAS (KJ/kg)  4.8533  6.0736  6.5038  4.23649  1.0751 
MASS (kg)  6.9383  6.9382  6.9382  6.9407  7.4428  
PGAS (bar)  0.0499  0.040952  0.0410  0.05131  0.0561  
TGAS (K)  0.2395  0.27865  0.2941  0.22438  0.2698  


50% load, 
CVGAS (KJ/kg)  5.0310  6.7232  7.3247  4.45998  1.0659 
MASS (kg)  8.4548  8.4548  8.4548  8.4548  9.0476  
PGAS (bar)  0.0577  0.0496  0.0494  0.05918  0.0634  
TGAS (K)  0.2660  0.31869  0.3395  0.24766  0.2852  


0% load, 
CVGAS (KJ/kg)  5.8914  8.0184  9.8772  4.70603  1.0445 
MASS (kg)  11.053  11.053  11.053  11.0529  11.8115  
PGAS (bar)  0.0772  0.075986  0.0760  0.078547  0.0829  
TGAS (K)  0.3232  0.40339  0.4315  0.30182  0.3218  


100% load, sinusoidal disturbance  CVGAS (KJ/kg)  4.1025  3.7562  3.7838  2.4006  0.3603 
MASS (kg)  10.858  10.756  10.799  10.173  9.9925  
PGAS (bar)  0.0496  0.029062  0.0258  0.04049  0.0401  
TGAS (K)  0.3784  0.35226  0.3566  0.280606  0.2491  


50% load, sinusoidal disturbance  CVGAS (KJ/kg)  4.7122  4.3039  4.3730  2.7118  0.4094 
MASS (kg)  12.852  12.719  12.783  11.991  11.7817  
PGAS (bar)  0.0623  0.036325  0.0325  0.04949  0.0495  
TGAS (K)  0.4226  0.39123  0.3982  0.31069  0.2785  


0% load, sinusoidal disturbance  CVGAS (KJ/kg)  5.8585  6.8594  7.9930  3.4857  0.7028 
MASS (kg)  16.346  16.296  16.365  15.532  15.2117  
PGAS (bar) 

0.099138  0.0991  0.09041  0.0879  
TGAS (K)  0.4791  0.51445  0.5699  0.36566  0.3573 
Test description  Outputs  Baseline PI  Cuckoo PI  Bat PI  Simm A  MOPSO PI 

100% load, step disturbance  CVGAS (KJ/kg)  30.492  34.956  37.035  21.4567  4.1192 
MASS (kg)  795.29  766.03  768.72  770.167  845.6540  
PGAS (bar)  0.3883  0.71104  0.6365  0.66801  0.4134  
TGAS (K)  32.449  31.668  31.812  25.3313  28.0122  


50% load, step disturbance  CVGAS (KJ/kg)  32.224  37.329  38.920  23.588  4.3242 
MASS (kg)  421.53  442.03  437.36  905.62  1671.89  
PGAS (bar)  0.4669  0.96041  0.8552  0.8308  0.51978  
TGAS (K)  38.433  37.073  37.278  31.295  35.5484  


0% load, step disturbance  CVGAS (KJ/kg)  43.864  46.585  49.858  30.7476  5.65885 
MASS (kg)  667.9  573.95  580.91  834.466  1754.91  
PGAS (bar)  0.59493  2.2373  1.9707  0.86776  0.56538  
TGAS (K)  38.388  35.714  36.169  29.5588  32.109  


100% load, sinusoidal disturbance  CVGAS (KJ/kg)  773.94  703.34  709.01  450.358  68.077 
MASS (kg)  2076.5  2075  2073.8  2073.03  2191.29  
PGAS (bar)  9.2825  5.4295  4.8282  7.4122  7.452  
TGAS (K)  66.998  62.211  62.933  49.092  44.986  


50% load, sinusoidal disturbance  CVGAS (KJ/kg)  879.66  802.54  812.64  506.179  76.7957 
MASS (kg)  2522.2  2517.3  2515.5  2515.83  2655.36  
PGAS (bar)  11.506  6.7252  6.0099  9.125  9.1915  
TGAS (K)  74.717  69.129  70.358  54.105  50.16  


0% load, sinusoidal disturbance  CVGAS (KJ/kg)  1039.5  1061.7  1126.2  640.636  97.1409 
MASS (kg)  3007.2  3040.6  3018.1  3156.57  3336.64  
PGAS (bar)  19.145  13.123  12.702  14.4267  14.723  
TGAS (K)  79.541  82.098  85.674  64.371  60.749 
Table
Similarly Table
Performance indices show that the tuned MOPSO based PI controller provides better results and meets all the performance requirements without violating the constraints.
Stability of coal gasifier and controller function across the working range of the plant (0%, 50%, and 100% load) is investigated. The system is started at 50% load, allowed to reach the steady state, then ramped it to 100% over a period of 600 seconds (5% per min). The response is shown in Figure
Response to load increase from 50% to 100% load.
Response to ramped increase in load
Input response to load change
This procedure is repeated for 0% to 50% change in load. Similar type of response is obtained. It is clear from the results that MOPSOPI controller is able to track the changes in load.
The quality of syngas depends on various factors such as type of coal (calorific value of coal) and moisture content. Quality of coal greatly affects each output of the gasifier. In this test, the quality of coal that is fed to gasifier is increased and decreased by 18%; inputoutput responses for sinusoidal and step change in pressure disturbance are tabulated at 100%, 50%, and 0% load conditions.
For sinusoidal change in pressure disturbance, at 0% load, for −18% change in coal quality, PGAS reaches its upper limit. For the same pressure disturbance, at 100% load TGAS reaches it upper and lower limits for +18% and −18% change in coal quality, respectively. For the other entire scenario the outputs meet the performance requirements without violating the constraints. Figures
Response to sinusoidal disturbance at 0% load.
Outputs and limits
Inputs and limits
Response to sinusoidal disturbance at 50% load.
Outputs and limits
Inputs and limits
Response to sinusoidal disturbance at 100% load.
Outputs and limits
Inputs and limits
This procedure was repeated for step change in pressure disturbance along with coal quality variations. Figures
Response to step disturbance at 0% load.
Outputs and limits
Inputs and limits
Response to step disturbance at 50% load.
Outputs and limits
Inputs and limits
Response to step disturbance at 100% load.
Outputs and Limits
Inputs and Limits
Table
Violation variables under coal quality change (±18%) (
Load  100%  50%  0%  

Disturbance type  Sine  Step  Sine  Step  Sine  Step 
Coal quality  Char 
Char 
Char 
Within 
WStm 
Within 
increase (+18%)  T gas  


Coal quality  Coal 
Coal 
Within 
Coal 
Pgas 
Char 
decrease (−18%)  T gas 
WStm 
Table
Comparison of allowed coal quality variation (%).
Load  100%  50%  0%  

Disturbance  Sine  Step  Sine  Step  Sine  Step 
Baseline PI [ 
(−14,11)  (−18,18)  (−18,16)  (−18,18)  (0,0)  (−18,18) 
Simm A [ 
(−13,8)  (−5,14)  (−14,14)  (−12,18)  (0,5)  (−8,18) 
MOPI [ 
(−13,8)  (−5,14)  (−14,14)  (−12,18)  (−3,18)  (−8,18) 
SOPI [ 
(−13,8)  (−6,13)  (−14,14)  (−12,18)  (−4,18)  (−8,18) 
Cuckoo PI [ 
(−15,12)  (−18,18)  (−18,17)  (−18,18)  (0,6)  (−18,18) 
Bat PI [ 
(−15,12)  (−18,18)  (−18,17)  (−18,18)  (0,7)  (−18,18) 
Optimal PI [ 
(−17,13)  (−18,18)  (−18,18)  (−18,18)  (−7,18)  (−18,18) 
PADRC [ 
(−18,6)  (−17,14)  (−18,10)  (−12,18)  (−18,18)  (−8,18) 
MOPSO PI  (−16,13)  (−18,18)  (−18,18)  (−18,18)  (−9,18)  (−18,18) 
It is seen that MOPSO based baseline PI controller provides better response for wide range of coal quality variations as compared to the existing methods [
In this paper a Multiobjective Particle Swarm Optimization (MOPSO) algorithm is proposed to finetune the parameters of baseline PI controller of Alstom gasifier benchmark challenge II. MOPSO algorithm provides set of nondominated solutions for the baseline PI controller, among which a suitable set of PI parameters are selected. The performance tests such as pressure disturbance, load change, and coal quality variations are investigated. During pressure disturbance test, the controller with optimized settings meets all the performance requirements at 0%, 50%, and 100% load conditions. Load change test shows good results. During coal quality test, the gasifier along with optimized controller settings verifies its capability to handle wide range of coal quality variations.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to thank Dr. Roger Dixon, Director of Systems Engineering Doctorate Centre and Head of Control Systems Group, Loughborough University, UK, for useful communication through email, and the managements of St. Joseph’s College of Engineering, Chennai and Sri Krishna College of Engineering & Technology, Coimbatore for providing necessary assistance to complete the research work.