Chinese Journal of Chemical Engineering 22 (2014) 769–773

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Chinese Journal of Chemical Engineering

j ourna l homepage: www.e lsev ie r .com/ locate /CJCHE

Process Control

Model Predictive Control with Feedforward Strategy for Gas Collectors ofCoke Ovens☆

Kai Li 1, Dewei Li ⁎,1, Yugeng Xi 1, Debin Yin 2

1 Department of Automation, Shanghai Jiao Tong University, Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai 200240, China2 Shanghai Xinhua Control Technology (Group) Co., Ltd, Shanghai 200241, China

☆ Supported by the State Key Laboratory of SyntheIndustries, the National Natural Science Foundation of61104078, 61221003) and the Minhang Technology Proje⁎ Corresponding author.

E-mail address: dwli@sjtu.edu.cn (D. Li).

http://dx.doi.org/10.1016/j.cjche.2014.05.0131004-9541/© 2014 Chemical Industry and Engineering So

a b s t r a c t

a r t i c l e i n f o

Article history:Received 6 May 2013Received in revised form 14 July 2013Accepted 24 October 2013Available online 18 June 2014

Keywords:Gas collector pressure systemModel predictive controlFeedforward

In coking process, the production quality, equipment life, energy consumption, and process safety are allinfluenced 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 pipesat appropriate operating point. In this paper, model predictive control (MPC) strategy is introduced to controlthe collector pressure system due to its ability to handle constraint and good control performance. Based on amethod proposed to simplify the system model, an extended state space model predictive control is designed,which combines the feedforward strategy to eliminate the disturbance. The simulation results in a system withtwo 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. Thepressure of gas collector in coke oven is an important parameter incoking process. Its stability influences the service time of coke oven,quality of coke, process safety and energy consumption. If the pressureis too high, the raw gas will leak out and even catch fire sometimes,shortening the service time of coke oven, causing air pollution andwasting energy. If the pressure is too low, air will enter coke ovenchambers, deteriorating coke quality and eroding the constructionmaterial of oven by chemical reaction with air. Extremely low pressurewill endanger the blast blower. Normally, the pressure should be keptwithin a range of ±20 Pa [1] around the set point.

The multiple gas collector pressure system is a constrained multi-variable nonlinear system with strong-coupling characteristics. Thesystem suffers considerable disturbances such as flow rate of raw gasgenerated in coking process, suction power of blast blowers, tempera-ture and flow rate of cycling ammonia water. Since it is difficult forconventional PID control strategy to deal with complicated systemssuch as the gas collector pressure system, new control methods are pro-posed, such as decoupling control method [2–4], intelligent controlstrategies and hybrid intelligent strategies. Fuzzy method, neuralnetwork theory, expert control, particle swarm optimization algorithm,andmulti-agent system technology have been applied to the research of

tical Automation for ProcessChina (61374110, 61333009,ct of Shanghai (2012MH211).

ciety of China, and Chemical Industr

gas collector pressure systems [5–8], but these methods cannot handlethe constraint and coupling properly.

Model predictive control (MPC) is an optimization control algorithmgenerated from industrial practice and has shown its good controlperformance in complicated industrial systems owing to its ability inconstraint handling, decoupling and robustness [9–14]. In recent years,the research onMPC achieves great development. For some applications,if the disturbance can be measured or calculated, the control perfor-mance will be greatly improved with feedforward strategycombined toMPC [15–18]. As the front suction of blast blower ismeasur-able, we introduce the feedforward strategy into MPC for the control ofgas collector pressure system. The feedforward strategy is used to elimi-nate the influence from the varying front suction of the blast blower.

For safety, direct testing is not permitted for coke ovens, so commonidentification method is not available. We can obtain the control modelby simplifying themechanismmodel 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 thesystem model. Then, an extended state space based model predictivecontrol is developed.

The simulation results of the proposed algorithm are compared tothe performance with normal MPC and PID control.

2. Process Analysis

Fig. 1 shows the structure of multiple gas collector pressure systemcoupled and distributed asymmetrically. The raw gas generated incoke ovens flows into collector pipes after cooling by cycling ammoniawater. Then the gas flows into the transportation pipes through butter-fly valves and suction pipes. After being cooled again by primary coolers,

y Press. All rights reserved.

N

Cokeoven 1

Cokeoven 2

Cokeoven N

BVBV2BV1

Primarycooler 1

Blastblower 1

Primarycooler 2

Blastblower 2

Fig. 1. Structure of the gas collector system.

770 K. Li et al. / Chinese Journal of Chemical Engineering 22 (2014) 769–773

the raw gas is transmitted to next working procedure by blast blowers[19]. The control objective is keeping the pressures in collector pipesat appropriate operating point by tuning butterfly valves. The main dis-turbances are the variation of pressures in coke ovens and the front suc-tion of blast blowers.

2.1. System modeling

Because of immeasurable pressures in coke ovens and large timedelay of front suctions of blast blowers to pressures in collector pipes,it is unadvisable to get system model with disturbance model byimplementing step test to the system. Identificationmethod is not avail-able either due to coupling characteristics of the system. On the otherhand, the mechanism model of the system can be constructed becausethe physical structures of each link in the system are simple.We can ob-tain the initial ARMAmodel by simplifying themechanismmodel. Thenthe ARMA model is adjusted by process data.

We first construct the mechanismmodel. Modeling for gas collectorpressure system is based on thefluid equilibrium [20]. For simplicity,weconsider a system with two coke ovens and one blast blower. The maincharacteristics of gas collector pressure system, especially coupling andasymmetrical distribution, can be presented sufficiently with thissystem.

Fig. 2 shows the structure of the system.Qi (i=1, 2) (m3·s−1) is theraw gas flow rate generated in coke oven i, Pi (Pa) is the pressure incollector pipe, Pi′ is the pressure after butterfly valve, Pb is the front suc-tion of the blast blower, Psi is the gas pressure in the coke oven,R1 and R2(kg·m−4·s−1) are resistance coefficients of collector pipes, defined asdP/dQ, R12 and R23 are the resistance coefficients of transportationpipes determined by physical parameters of pipes, C (m4·s2·kg−1) isthe capacity coefficient, defined as dV/dP and determined by the natureof raw gas, and V is the gas volume. We consider that the relationship

1P 2P

1P2P

,Ps Q 2 2,P

bP

1R 2R

1C 2C

,R C

1 1 s Q

12 12 23 23,R C

1# 2#

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

between the resistance coefficient of collector pipe and the opening ofbutterfly valve is bijection.

According tomaterial balance, the system as shown in Fig. 2 satisfiesthe following dynamic equations

C1dP1

dt¼ Q1−

P1−P01

R1ð1Þ

C2dP2

dt¼ Q2−

P2−P02

R2ð2Þ

C12dP0

1

dt¼ P1−P0

1

R1− P0

1−P02

R12ð3Þ

C23dP0

2

dt¼ P2−P0

2

R2þ P0

1−P02

R12− P0

2−Pb

R23: ð4Þ

From the relationship between flow rate and pressure, we have

Q1 ¼ k1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPs1−P1

pð5Þ

Q2 ¼ k2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPs2−P2

pð6Þ

where k1 and k2 (m7/2·kg−1/2) are coefficients determined by the diam-eter of bridge pipes, the nature of gas and other factors.

In this mechanism model for the system, P1 and P2 are controlledvariables (output variables), R1 and R2 are manipulated variables(input variables), Ps1, Ps2 and Pb are disturbances.

For Eqs. (1)–(4), if we set 1/Ri as the input variables, the nonlinearcharacteristic of the system is the square-root parts, i.e. Eqs. (5) and(6). Through applying Taylor expansion to the nonlinear part, we findthat the coefficients of the terms with the order of magnitude largerthan 1 are very small since Psi is commonly much larger than Pi. Thusthe gas collector pressure system is a weakly nonlinear system. Weshall 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 amodel simplification method, which will be used as the control modelin this study.

Since the system mainly runs in a neighborhood of equilibriumpoint, the system is simplified to a first-order system by matching thestep response curves at the equilibrium point. The reasons for choosingthis method are as follows. Firstly, most of the step responses betweeninput and output, disturbance and output are similar to those of first-order system. Fig. 3 shows the unit step responses of the mechanismmodel. “Ri → Pj”means the step response between input Ri and outputPj, and “Pb → Pj” means the step response between disturbance Pb andoutput Pj. Vertical axis “ΔPi” denotes the deviation from the equilibriumpoint. Secondly, the model accuracy requirement is not high for MPC.Only an appropriate variation trend is needed. Thus the proposedmeth-od can also be applied to “R1 → P2” and “R2 → P1”. Thirdly, the simplefirst-order model brings convenience to model adjusting with processdata, since the number of parameters is reduced.

For first-order system y(s) / u(s) = K / (Ts + 1), the unit stepresponse is y(t) = K(1 − e− t/T). We denote the sampled unit stepresponse of the mechanism model as [y(1), …, y(k), …, y(N)],where y(N) is close to the steady state value, with the samplingperiod of Tp. We consider that the mechanism system and simplifiedsystem have a same steady state value, which means K = y(N). A

0 1000 2000 3000 4000 0 1000 2000 3000 4000

0 1000 2000 3000 4000 0 1000 2000 3000 4000

0 1000 2000 3000 4000 0 1000 2000 3000 4000

0

1

2

R1 P1

time/s

-0.4

-0.2

0

R1 P2

time/s

-0.4

-0.2

0

R2 P1

0

1

2

R2 P2

0

0.5

1

Pb P1

0

0.5

1

Pb P2

→

→

→

→

→

→

ΔP1/

Pa

ΔP2/

Pa

ΔP2/

Pa

ΔP1/

Pa

ΔP1/

Pa

ΔP2/

Pa

time/s time/s

time/s time/s

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

771K. Li et al. / Chinese Journal of Chemical Engineering 22 (2014) 769–773

time constant T = kTp is obtained to minimize J=∑i = 1 → N|y(i) −K(1 − e− i/k)|, where J indicates the error between the mechanismsystem and simplified system. Then the simplified transfer functionis obtained as y(N) / (kTp·s + 1).

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

y1 sð Þy2 sð Þ

� �¼ G11 sð Þ G12 sð Þ

G21 sð Þ G22 sð Þ� �

u1 sð Þu2 sð Þ

� �þ Gd1 sð Þ

Gd2 sð Þ� �

v sð Þ ð7Þ

where yi=ΔPi, ui=ΔRi, v=ΔPb, Gij andGdi are the continuous transferfunctions. Fig. 3 also shows the feasibility of the simplification methodby comparing the step responses of the mechanism model and simpli-fied model.

The transfer functions are discretized by a same sampling time,

y1 z−1� �

y2 z−1� �

0@

1A ¼

g11z−1

1−h11z−1

g12z−1

1−h12z−1

g21z−1

1−h21z−1

g22z−1

1−h22z−1

0BBB@

1CCCA

u1 z−1� �

u2 z−1� �

0@

1A

þgd1z

−1

1−hd1z−1

gd2z−1

1−hd2z−1

0BBB@

1CCCAv z−1

� �: ð8Þ

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

A z−1� � y1 kð Þ

y2 kð Þ� �

¼ B z−1� � u1 kð Þ

u2 kð Þ� �

þ E z−1� �

v kð Þ ð9Þ

where A(z−1) = I + ∑i = 1 → 3Aiz−i, B(z−1) = ∑i = 1 → 3Biz

−i, andE(z−1) = ∑i = 1 → 3Eiz−i. Based on Eq. (9), the ARMA model can beadjusted by process data.

3. Model Predictive Control Design

In terms of the characteristics of the gas collector pressure systemand the form of system model, extended state space based MPC is abetter choice for control strategy. The front suction of the blast blowercan be measured and the model between it and the output can beobtained. Thus it is appropriate to add the feedforward strategy to theMPC algorithm, which is illustrated as follows.

3.1. Prediction model

To eliminate the steady-state errors of the closed-loop system, weapply u(k) = u(k − 1) + Δu(k), v(k) = v(k − 1) + Δv(k) in Eq. (9),where u(k) = [u1(k),u2(k)]T and Δu(k) = [Δu1(k),Δu2(k)]T. The ARMAmodel can be obtained as

y1 kð Þ �� y2 kð Þ

� �¼ θ2�12 �

�y1 k−1ð Þ y1 k−2ð Þ y1 k−3ð Þ u1 k−2ð Þ u1 k−3ð Þy2 k−1ð Þ y2 k−2ð Þ y2 k−3ð Þ u1 k−2ð Þ u1 k−3ð Þ

u2 k−2ð Þ u2 k−3ð Þ v k−2ð Þ v k−3ð Þ Δu1 k−1ð Þ Δu2 k−1ð Þ Δv k−1ð Þu2 k−2ð Þ u2 k−3ð Þ v k−2ð Þ v k−3ð Þ Δu1 k−1ð Þ Δu2 k−1ð Þ Δv k−1ð Þ

�Tð10Þ

where v is the front suction of the blast blower, θ can be obtained from h,g, hd, and gd in Eq. (8). The disturbance is included by the model forfeedforward compensation. Then, we can easily obtain the extendedstate space based prediction model

eX kþ 1ð Þ ¼ AX kð Þ þ BΔu kð Þ þ EΔv kð Þ ð11Þ

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

X kð Þ ¼ y1 kð Þy1 k−1ð Þy1 k−2ð Þ u1 k−1ð Þ u1 k−2ð Þ½ jy2 kð Þ y2 k−1ð Þ y2 k−2ð Þ u2 k−1ð Þ u2 k−2ð Þj v k−1ð Þ v k−2ð Þ�T:

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

eXPM kð Þ ¼ eAX kð Þ þ eBΔuM kð Þ þ eEΔvP kð Þ ð12Þ

104

106

108

110

P1/

Pa

P2/

Pa

Setpoint

MPCPID

0 200 400 600 800 1000 1200 1400 1600 1800 2000100

102

104

106

time/s

0 200 400 600 800 1000 1200 1400 1600 1800 2000

time/s

Setpoint

MPCPID

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

772 K. Li et al. / Chinese Journal of Chemical Engineering 22 (2014) 769–773

where eXPM kð Þ ¼ ½ eX kþ 1ð ÞT ⋯ eX kþ Pð ÞT �T , ΔuM kð Þ ¼

Δu kð ÞT ⋯ Δu kþM−1ð ÞT� �T, ΔvP kð Þ ¼

Δv kð Þ⋮

Δv kþ P−1ð Þ

24

35, eA ¼

A⋮AP

24

35;

eB ¼

B⋮ ⋱

AM−1B ⋯ B⋮ ⋱ ⋮

AP−1B ⋯ AP−MB

266664

377775, and eE ¼

E 0 ⋯ 0AE E ⋱ ⋮⋮ ⋱ ⋱ 0

AP−1E AP−2E ⋯ E

2664

3775.

Due to the unknown future disturbance, we assume thatΔv(k+ i)=

0 (i N 0), i.e. v will not change. Then, with eE ¼ ET ETAT ⋯h

ET

AP−1� �T

�T and

eXPM kð Þ ¼ eAX kð Þ þ eBΔuM kð Þ þ eEΔv kð Þ ð13Þ

the output prediction model becomes

eYPM kð Þ ¼eleXPM kð Þ; ð14Þ

where eYPM kð Þ ¼ Y kþ 1ð Þ ⋯ Y kþ Pð Þ½ �T, Y kð Þ ¼ y1 kð Þ y2 kð Þ½ �T, el ¼diag l ⋯ lð Þ, and l¼ 1 0 0 0 0

0 0 0 0 0

� 0 0 0 0 01 0 0 0 0

0 00 0

�.

3.2. Formulation of optimization problem

At time k, the control objective is that the predictive output in pre-dictive horizon approaches the expected output as close as possibleand the manipulated variables do not change drastically. At the sametime, the pressure in the gas collector must be controlled in a range ofthe set value for safety production and economic consideration. Thereare some other physical constraints in real systems. The valve openingcan only change from 0° to 90° (normally 15° to 75° for controller),and the increment of valve opening is restricted in a specific range.

We formulate the optimization problem as

min ω kð Þ−eYPM kð Þ 2

Qþ ΔuM kð Þk k2R

s:t: eYPM kð Þ ¼ eleAX kð Þ þeleBΔuM kð Þ

þeleEΔv kð Þ Ymin≤ eYPM kð Þ≤Ymax; umin≤uM kð Þ≤umax;Δumin≤ΔuM kð Þ≤Δumax

ð15Þ

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 vm is the

measurable disturbance and vim is the immeasurable disturbance.

4. Simulation Results

We take a real gas collector pressure systemwith two coke ovensas 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.

1

z

z

yu

mv imv

uMPC Plantω Δ

−

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

To consider both rapidity and vibration prevention, we chooseM=1,P =8 andweightingmatrices Q= diag(1, 1,…, 1) and R= diag(2, 2,…,2). The physical constraints include: Rimust bewithin [0.2, 200] due to therestriction of butterfly valve opening in [15°, 80°], the increment of Ri iswithin [−5, 5], and the pressure in the gas collector should be within[−15, 15] around the expected operating point. If disturbances aredrastic and large, the algorithm proposed can relax the restrictions onpressure to make the problem feasible. The sampling period is Ts = 20 s.

Fig. 5 shows the control result of the proposed MPC when we steerthe operating point from P10 = 110 and P20 = 100 to P10 = 105 andP20 = 105. The traditional PID control is also employed for comparison.For the control performance of the system, including rapidity and over-shoot, the proposed MPC method has advantages over the traditionalPID control.

Compared with the normal MPC and PID control, Fig. 6 shows thedisturbance rejection capability of the proposed method, i.e. modelpredictive control with feedforward strategy (MPC–FF). It is obviousthat with the disturbance in Fig. 7, the proposed method is better.

Fig. 6. The control performance.

0 1000 2000 3000 4000 5000 6000-200

-100

0

100

200

300

400

time/s

P/P

a

Ps1

Ps2

Pb

Fig. 7. The disturbances.

773K. Li et al. / Chinese Journal of Chemical Engineering 22 (2014) 769–773

5. Conclusions

The gas collector pressure system with external disturbances is astrongly coupled multi-variable system with nonlinear characteristics.An extended state space model predictive control with feedforwardstrategy is developed. The simulation results show that the proposed al-gorithm satisfies the control requirements. The future work is to imple-ment the proposed method into industrial applications, including theadjustment of the control model and parameters of controller with pro-cess data.

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