Kai Li,Dewei Li*,,Yugeng Xi,Debin Yin2Department of Automation,Shanghai Jiao Tong University,Key Laboratory ofSystem Control and Information Processing,Ministry of Education,Shanghai200240,China

2Shanghai Xinhua Control Technology(Group)Co.,Ltd,Shanghai200241,China

Model Predictive Control with Feed forward Strategy for Gas Collectors of Coke Ovens☆

Kai Li1,Dewei Li*,1,Yugeng Xi1,Debin Yin21Department of Automation,Shanghai Jiao Tong University,Key Laboratory ofSystem Control and Information Processing,Ministry of Education,Shanghai200240,China

2Shanghai Xinhua Control Technology(Group)Co.,Ltd,Shanghai200241,China

A R T I c L E IN F o

Article history:

Received 6 May 2013

Received in revised form 14 July 2013 Accepted 24October 2013

Available on line 18 June 2014

In coking process,the production quality,equipment life,energy consumption,and process safety are all influenced by the pressure in gas collector pipe of coke oven,which is frequently influenced by disturbances. The main control objectives for the gas collector pressure system are keeping the pressures in collector pipes at appropriate operating point.In this paper,model predictive control(MPC)strategy is introduced to control the collector pressure system due to its ability to handle constraint and good control performance.Based on a method proposed to simplify the system model,an extended state space model predictive control is designed, which combines the feed forward strategy to eliminate the disturbance.The simulation results in a system with two coke ovens show the feasibility and effectiveness of the control scheme.

?2014 Chemical Industry and Engineering Society of China,and Chemical Industry Press.All rights reserved.

1.Introduction

Coking industry is an important part in metallurgical industry.The pressure of gas collector in coke oven is an important parameter in coking process.Its stability influences the service time of coke oven, quality of coke,process safety and energy consumption.If the pressure is too high,the raw gas will leak out and even catch fire sometimes, shortening the service time of coke oven,causing air pollution and wasting energy.If the pressure is too low,air will enter coke oven chambers,deteriorating coke quality and eroding the construction material of oven by chemical reaction with air.Extremely low pressure will endanger the b last blower.Norm ally,the pressure should be kept within a range of±20 Pa[1]around the set point.

The multiple gas collector pressure system is a constrained multivariable nonlinear system with strong-coup ling characteristics.The systemsuffers considerable disturbances such as flow rate of raw gas generated in coking process,suction power of b last b lowers,temperature and flow rate of cycling ammonia water.Since it is difficult for conventional PID control strategy to deal with complicated systems such as the gas collector pressure system,new control methods are proposed,such as decoupling control method[2-4],intelligent control strategies and hybrid intelligent strategies.Fuzzy method,neural network theory,expert control,particle swarm optimization algorithm, and multi-agent system technology have been applied to the research of gas collector pressure systems[5-8],but these methods cannot handle the constraint and coupling properly.

Model predictive control(MPC)is an optimization control algorithm generated from industrial practice and has shown its good control performance in complicated industrial systems owing to its ability in constraint hand ling,decoupling and robustness[9-14].In recent years, the research on MPC achieves great development.For some applications, if the disturbance can be measured or calculated,the control performance will be greatly improved with feed forward strategy combined to MPC[15-18].As the front suction of blast blower is measurable,we introduce the feed forward strategy in to MPC for the control of gas collector pressure system.The feed forward strategy is used to eliminate the influence from the varying front suction of the blast blower.

For safety,direct testing is not permitted for coke ovens,so common identification method is not available.We can obtain the control model by simplifying the mechanism model and adjusting it with process data. For convenience in model adjusting,a simple model form available,i.e. ARMA model,is adopted and a method is presented to simplify the system model.Then,an ex tended state space based model predictive control is developed.

The simulation results of the proposed algorithm are compared to the performance with norm a lMPC and PID control.

2.Process Analysis

Fig.1 shows the structure of multiple gas collector pressure system coupled and distributed asymmetrically.The raw gas generated in coke ovens flow s in to collector pipes after cooling by cycling ammonia water.Then the gas flow s in to the transportation pipes through butterfly valves and suction pipes.After being cooled again by primary coolers,the raw gas is transmitted to next working procedure by blast blowers [19].The control objective is keeping the pressures in collector pipes at appropriate operating point by tuning butterfly valves.The main disturbances are the variation of pressures in coke ovens and the front suction of blast blowers.

Fig.1.Structure of the gas collector system.

2.1.System modeling

Because of immeasurable pressures in coke ovens and large time delay of front suctions of blast b lowers to pressures in collector pipes, it is unadvisable to get system model with disturbance model by implementing step test to the system.Identification method is not available either due to coup ling characteristics of the system.On the other hand,the mechanism model of the system can be constructed because the physical structures of each link in the system are simple.We can obtain the initial ARMA model by simplifying the mechanism model.Then the ARMA model is adjusted by process data.

We first construct the mechanism model.Modeling for gas collector pressure system is based on the fluid equilibrium[20].For simplicity,we consider a system with two coke ovens and one blast blower.The main characteristics of gas collector pressure system,especially coup ling and asymmetrical distribution,can be presented sufficiently with this system.

Fig.2 shows the structure of the system.Qi(i=1,2)(m3·s?1)is the raw gas flow rate generated in coke oven i,Pi(Pa)is the pressure in collector pipe,Pi′is the pressure after butterfly valve,Pbis the front suction of the blast blower,Psiis the gas pressure in the cokeoven,R1and R2(kg·m?4·s?1)are resistance coefficients of collector pipes,defined as d P/d Q,R12and R23are the resistance coefficients of transportation pipes determined by physical parameters of pipes,C(m4·s2·kg?1)is the capacity coefficient,definedasd V/d P and determined by the nature of raw gas,and V is the gas volume.We consider that the relationship between the resistance coefficient of collector pipe and the opening of butterfly valve is bijection.

Fig.2.Diagram of dynamic pressure characteristics of the system.

According to material balance,the system as shown in Fig.2 satisfies the following dynamic equations

From the relationship between flow rate and pressure,we have

where k1and k2(m7/2·kg?1/2)are coefficients determined by the diameter of bridge pipes,the nature of gas and other factors.

In this mechanism model for the system,P1and P2are controlled variables(output variables),R1and R2are manipulated variables (input variables),Ps1,Ps2and Pbare disturbances.

For Eqs.(1)-(4),if we set 1/Rias the input variables,the nonlinear characteristic of the system is the square-root parts,i.e.Eqs.(5)and (6).Through applying Taylor expansion to the nonlinear part,we find that the coefficients of the term s with the order of magnitude larger than 1 are very small since Psiis commonly much larger than Pi.Thus the gas collector pressure system is a weakly nonlinear system.We shall focus on the coupled and constrained characteristics of the system. 2.2.Model simplification and transformation

As the nonlinear characteristic of system is weak,we develop a model simplification method,which will be used as the control model in this study.

Since the system mainly runs in a neighborhood of equilibrium point,the system is simplified to a first-order system by matching the step response curves at the equilibrium point.The reasons for choosing this method are as follows.Firstly,most of the step responses between input and output,disturbance and output are similar to those of firstorder system.Fig.3 shows the unit step responses of the mechanism model.“Ri→Pj”means the step response between input Riand output Pj,and“Pb→Pj”means the step response between disturbance Pband output Pj.Vertical axis“Δ Pi”denotes the deviation from the equilibrium point.Secondly,the model accuracy requirement is not high for MPC. Only an appropriate variation trend is needed.Thus the proposed method can also be applied to“R1→P2”and“R2→P1”.Thirdly,the simple first-order model brings convenience to model adjusting with process data,since the number of parameters is reduced.

For first-order system y(s)/u(s)=K/(Ts+1),the unit step response is y(t)=K(1?e?t/T).We denote the sampled unit step response of the mechanism model as[y(1),…,y(k),…,y(N)], where y(N)is close to the steady state value,with the sampling period of Tp.We consider that the mechanism system and simplified system have a same steady state value,which means K=y(N).Atime constant T=kTpis obtained to minimize J=∑i=1→N|y(i)?K(1?e?i/k)|,where J indicates the error between the mechanism system and simplified system.Then the simplified transfer function is obtained as y(N)/(kTp·s+1).

Fig.3.Unit step response of the gas collector pressure system.——mechanism model;----simplified model.

Using this method,we obtain the simplified model of two coke ovens system.

where yi=ΔPi,ui=ΔRi,v=ΔPb,Gijand Gdiare the continuous transfer functions.Fig.3 also shows the feasibility of the simplification method by comparing the step responses of the mechanism model and simplified model.

The transfer functions are discretized by a same sampling time,

Accordingly,the initial ARMA model of the system can be obtained [14]

3.Model Predictive Control Design

In term s of the characteristics of the gas collector pressure system and the form of system model,ex tended state space based MPC is a better choice for control strategy.The front suction of the b last b lower can be measured and the model between it and the output can be obtained.Thus it is appropriate to add the feed forward strategy to the MPC algorithm,which is illustrated as follows.

3.1.Prediction model

To eliminate the steady-state errors of the closed-loop system,we apply u(k)=u(k?1)+Δu(k),v(k)=v(k?1)+Δv(k)in Eq.(9), where u(k)=[u1(k),u2(k)]Tand Δu(k)=[Δu1(k),Δu2(k)]T.The ARMA model can be obtained as

where v is the front suction of the blast blower,θ can be obtained from h, g,hd,and gdin Eq.(8).The disturbance is included by the model for feed forward compensation.Then,we can easily obtain the extended state space based prediction model

where matrices A,B,and E can be obtained from Eq.(10),and

With prediction horizon P and control horizon M,the resulted prediction model is

Due to the unknown future disturbance,we assume that Δv(k+i)= 0(i＞0),i.e.v will not change.Then,with

the output prediction model becomes

3.2.Formulation of optimization problem

At time k,the control objective is that the predictive output in predictive horizon approaches the expected output as close as possible and the manipulated variables do not change drastically.At the same time,the pressure in the gas collector must be controlled in a range of the set value for safety production and economic consideration.There are some other physical constraints in real systems.The valve opening can only change from 0°to 90°(norm ally 15°to 75°for controller), and the increm en t of valve opening is restricted in a specific range.

We formulate the optimization problem as

where ω(k)is the reference vector,and uM(k)=uM(k?1)+ΔuM(k).

Fig.4 shows the control structure of the method,where vmis the measurable disturbance and vimis the immeasurable disturbance.

4.Simulation Results

We take a real gas collector pressure system with two coke ovens as an example,whose physical structure is similar to that in Fig.2. The values of the expected operating point are R10=20,R20=20, P10=110,P20=100,P10′=70,P20′=60,Ps10=210,Ps20=200, and Pb0=0.Other physical parameters are R12=5,R23=15,C1= C2=10,C12=8,C23=4,and k1=k2=0.2.

Fig.4.The control structure of the proposed algorithm.

To consider both rapidity and vibration prevention,we choose M=1, P=8 and weighting matrices Q=diag(1,1,…,1)and R=diag(2,2,…, 2).The physical constraints include:Rimust be within[0.2,200]due to the restriction of butterfly valve opening in[15°,80°],the increment of Riis within[?5,5],and the pressure in the gas collector should be within [?15,15]around the expected operating point.If disturbances are drastic and large,the algorithm proposed can relax the restrictions on pressure to make the problem feasible.The sampling period is Ts=20 s.

Fig.5 shows the control result of the proposed MPC when we steer the operating point from P10=110 and P20=100 to P10=105 and P20=105.The traditional PID control is also employed for comparison. For the control performance of the system,including rapidity and overshoot,the proposed MPC method has advantages over the traditional PID control.

Com pared with the normal MPC and PID control,Fig.6 shows the disturbance rejection capability of the proposed method,i.e.model predictive control with feed forward strategy(MPC-FF).It is obvious that with the disturbance in Fig.7,the proposed method is better.

Fig.5.The control performance in changing operating point.

Fig.6.The control performance.

Fig.7.The disturbances.

5.Conclusions

The gas collector pressure system with external disturbances is a strongly coupled multi-variable system with nonlinear characteristics. An extended state space model predictive control with feed forward strategy is developed.The simulation results show that the proposed algorithm satisfies the control requirements.The future work is to implement the proposed method in to industrial applications,including the adjustment of the control model and parameters of controller with process data.

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☆Supported by the State Key Laboratory of Synthetical Automation for Process Industries,the National Natural Science Foundation of China(61374110,61333009, 61104078,61221003)and the Minhang Technology Project of Shanghai(2012MH211).

*Corresponding author.

E-mailaddress:dw li@sjtu.edu.cn(D.Li).

Gas collector pressure system Model predictive control

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