Data‐driven control for combustion process of circulating fluidised bed boiler

Owing to the advantages of burning low-quality coal (coal slime and coal gangue), furnace desulfurisation, low N O x emission and deep load adjustment, the circulating fluidised bed (CFB) combustion technology becomes one of the few fossil fuel utilisation technologies funded continuously by the Chinese government. However, compared with the pulverised coal boiler, the combustion process of CFB boiler is more complicated because of the larger time delay, significant uncertainty and more coupled variables. In this study, a data-driven proportional–integral-derivative (DD-PID) control strategy is presented for the combustion control of CFB boiler to improve the operating performance under full operating conditions. By analysing the running mechanism of combustion process, an inverse decoupler is introduced to transfer the combustion object to the generalised controlled object, which has relatively independent input–output relationship. After that, a normative procedure of DD-PID, including PID-parameter database establishment, information-vector neighbourhood selection, active PID-parameter determination, database update, and redundant vector deletion, is given. Finally, a series of case study, including numerical tests applied to the proposed combustion model and application test employed on 330 MW CFB simulation platform proves the feasibility of DD-PID control strategy.


Nomenclature
χ v proportion of volatile in fuel μ valve opening of the control valve of the turbine τ i (i = 1, . . . , 4) transmission delay in a certain process θ b bed temperature C specific heat capacity of bed material C a1 specific heat capacity of primary air C a2 specific heat capacity of air leaving the densephase zone C i specific heat capacity of materials entering the dense-phase zone C o specific heat capacity of materials leaving the dense-phase zone D q effective heat-absorbing of boiler

Introduction
Facing the deep adjustment of the energy structure and the increasingly severe constraints from climate and environment, as the world's largest energy producer and consumer, China will increase the proportion of installed capacity of non-fossil power generation from 35 to 39%, while decrease the proportion of installed capacity of coal-fired power generation from 59 to 55% by 2020 according to 'The 13th Five-Year Plan of Electric Power Development (2016-2020)' [1]. To achieve this goal, the Chinese government has stopped or postponed the construction of traditional coal-fired power plants in a planned way and has demolished a large number of the small coal-fired generation units with high energy consumption and high pollution emissions since 2016. It seems that the winter of coal-fired power generation is coming. However, circulating fluidised bed (CFB) power units, which also belong to the coal-fired power generation, became more and more popular in recent years in China, and are regarded as the representative of clean and efficient utilisation of traditional fossil fuels. More than eight supercritical CFB units, distributed in several provinces, have already been put into operation only for one year in 2018.
A typical structure and dynamic responses of a CFB boiler are shown in Fig. 1. The most distinctive equipment is a 'bed' at the bottom of the boiler furnace. The bed is a place where the coal or fuel spreads. High-pressure air is supplied from under the bed to With the aid of bed, the CFB boiler can burn all types of coal and a wide range of other fuels efficiently, which includes lowgrade and difficult-to-burn fuels [2]. The combustion temperature of CFB boiler is controlled between 850 − 950 o C to reduce emissions of NO x . With the limestone injected into the furnace, majority of the formed SO 2 during coal combustion can also be captured [3].
However, the wide operation range, strong fuel adaptability and complex combustion equipments of CFB boilers make it difficult for the traditional control systems to work normally, and to maintain good performance [4,5]. More and more application examples show that the reason for restricting the further popularisation of CFB boilers is not equipment manufacturing technology, but operation control technology. In recent years, many researchers focused on the modelling, control and optimisation of CFB boilers. Based on real operation data, Lv et al. [6] built a dynamic model for predicting the bed temperature of a 300 MW CFB boiler by adopting least squares support vector machine method. Hu et al. [7] combined the advantages of zone method and Aspen Plus to develop a detailed radiation model coupled process simulation of fluidised beds. Gao et al. [8] designed a doublefeedforward self-balance feed water instruction for a 350 MW CFB boiler, which can accelerate the control action of water feeding and speedup the tuning process. Liu and Wang [9] proposed a technical route for CFB boiler unit control by combining with non-linear function approximation of BP neural network, predictive control and real-time feedback revision. Niva et al. [10] presented a selfoptimising control structure, which decouples fluidisation and oxygen-carrying tasks and introduces new degrees of freedom and alternatives for control. From the control point of view, fixedparameter PID controllers are simple and easy to implement, but the load adaptability is poor, it is hard to meet the requirements of variable operating conditions. Neural network control has some intelligent characteristics, but it is difficult to complete the experiential learning process in practical applications. Predictive control requires low accuracy of the model and can handle all kinds of constraints, but the calculation of the optimal value of the objective function is relatively large. Therefore, effective use of mass real data and appropriate complexity of the control algorithm are the two key factors to improve the control performance of CFB boilers.
At present, the data-driven (DD) control has been a hot topic in control theory and applications. Kusiak et al. [11] developed a DD approach to minimise energy consumption of a heating, ventilating, and air conditioning (HVAC) system while maintaining the thermal comfort of a building with uncertain occupancy level. Lautenschlager and Lichtenberg [12] introduced DD iterative learning into model predictive control and approved its applicability by simulations of a heating system. Renani et al. [13] investigated and compared two different approaches in wind power forecasting which are indirect and direct prediction methods using DD method. DD control is also used in a class of non-affine nonlinear systems with output saturation only depending on the control input data and the saturated output data [14]. An adaptive dynamic programming problem for non-linear affine systems based on the DD control is identified in [15], which is solved by adopting the alternating direction method of multipliers. A hybrid optimisation algorithm is proposed to solve non-linear or non-convex DD models involved in DD predictive control [16]. The remarkable advantage of DD control is that it has active adaptability to the change of working conditions, and the design process has low requirement for the accuracy of the model. With the gradual deepening and enrichment of DD control research, it is possible to introduce it into the CFB boiler control, and the improvement of the operation performance will be worthy of expectation.
In this paper, a DD control strategy applied to the CFB combustion process has been established for the first time. The core of the control strategy is to automatically generate and renew PID parameters online with the change of working condition, and to obtain good tracking performance, variable load adaptability and anti-disturbance ability. The main contributions consist of the following aspects: • Coupling model of CFB unit combustion system is established. • A normative procedure of DD PID controller is designed, including PID-parameter database establishment, informationvector neighbourhood selection, active PID-parameter determination, database update, and redundant vector deletion. • The control strategy based on the DD technique is used for the CFB combustion process. And numerical and application tests are applied to the established CFB combustion model and a 330 MW CFB simulation platform of the Ningdong Power Plant, respectively.
The rest of the paper is organised as follows. The coupling relationship, dynamic mathematical model and control task of CFB combustion process are summarised in Section 2. The control structure and detailed design steps of DD-PID are presented for the CFB combustion control in Section 3. Comprehensive performance of the proposed control system is tested systematically in Section 4, and the conclusion of this work is listed in Section 5.

Characteristics of combustion system
A CFB unit is a kind of controlled plant with parameter coupling, as shown in Table 1. If we regard the weak coupling relationship between the variables as an independent system, a CFB boiler can be divided into three relatively independent parts: the superheat steam temperature sub-system, the water supply sub-system and the combustion sub-system. The control-system design of the first two sub-systems is similar to that of the pulverised coal boilers. However, there are some significant differences between combustion sub-systems of the CFB boiler and the pulverised coal boiler. So the design of combustion control system will be the key problem. According to the interaction relationship shown in Table 1, there are four tasks that must be done: (i) keep the energy balance of supply of boiler and demand of turbine by stabilising the steam pressure, (ii) control the discharge of pollutants reaching the standard by tuning the bed temperature within limitation, (iii) guarantee the safety of combustion process by keeping the hearth negative pressure, (iv) realise economic combustion by controlling oxygen content in optimal value. Generally, the hearth negative pressure, which is influenced by the changes in fuel and air supply, can be regulated by induced air. The economic combustion depends on the air-coal ratio which can be optimised by tuning the secondary air. Therefore, the latter two tasks are relatively independent and can be completed by two control loops separately. However, the main steam pressure and the bed temperature, which are two strong coupling parameters, are influenced by both the fuel and the primary air.

Core coupling model of combustion system
Before modelling, we make the following reasonable assumptions: • Dense phase zone and dilute phase zone of the CFB are all homogeneous, and the temperature and density of each point are the same. • Boiler is completely insulated with outside, there is no air leakage, and volatile matter in the dense phase zone is completely burned. • Specific heats of bed materials, fuel and gas are constants in a certain temperature range. • Desulfurisation reaction is not considered. • The temperature of the returned material system is close to bed temperature.
The nomenclature of CFB combustion system is shown in Table 1.

Bed temperature to fuel model:
Under the disturbance of the coal feed, F c , entering the furnace, according to the law of energy conservation in the dense phase zone [17], we have The heat release process of the fuel combustion can be described as The heat release process of volatile combustion is fast, so it can be formulated as Combining (1)- (3), the transfer function of bed temperature influenced by fuel flow yields Bed temperature to primary air model: Taking the primary air as input variable, and utilising the law of energy conservation in dense phase zone, we can obtain The primary air is mainly used for the fluidisation of materials in furnace. It changes in proportion to the fuel flow and accelerates the heat release of fuel. This relation can be expressed as Combining (5) and (6), and in order to better express a negative correlation between the primary air and bed temperature, the transfer function of bed temperature to primary air is written as where Main steam pressure to fuel model: The combustion and heat transfer process in the furnace can be simplified to a secondorder system [18], whose transfer function is Taking into account the energy storage of the boiler drum and steam pipes [19], the energy balance equation can be written as The non-linear characteristics of the dynamic process in boiler are mainly reflected in two parts: • The pressure drop from the drum pressure, P b , to the main steam pressure, P t , has a square root relationship with the main steam flow rate, D t . C d is coefficient of thermal storage in the steam drum. • D t is proportional to the product of the opening of the turbine control valve, μ, and the main steam pressure, P t .
The above two processes can be described as Suppose the combustion process is in an equilibrium state with a stable operating point P b *, P t *, D t *, μ* . Then a small range linear approximation for (10) and (11) can be obtained where ΔP b , ΔP t and ΔD t are small deviations from the stable operating point, and χ = 2k 4 D t *.
Combining (8), (9), (12) and (13), and considering the value of T cf is much smaller than those of other inertia times, the transfer function of main steam pressure to fuel can be deduced as where Main steam pressure to primary air model: The heat transfer process under the disturbance of primary air in the furnace can be simplified as Combining (8), (14) and (15), the transfer function of main steam pressure to primary air can be obtained where K p4 = k 6 /(k 4 μ). (4)-(16), we can see that the CFB combustion process is a two-input and two-output process. Let u 1 = F c and u 2 = V 1 be the inputs, and y 1 = θ b and y 2 = P t be the outputs, then the controlled object of the CFB boiler combustion process can be expressed as

Overall core coupling model: From
with

DD control of the core coupling part for CFB boiler combustion system
In this section, in order to show the design process of the DD control strategy, a practical system of 300 MW CFB unit in Sichuan Province with the structure of (17) is employed. And the parameters, which are derived under the condition of 50, 75 and 100% load, are given in Table 2.

Decoupling of core coupling model
Before designing a controller, the coupled degree of a coupling system should be introduced first. The Bristol [20] first defined a relative gain matrix to measure the coupling properties of multivariable systems. The information reflected by the relative gain matrix [21] can be summed up as follows (i) When the relative gain of a channel is less than or close to 0, it indicates that the input variable of this channel is not or weakly related to the output variable, and this channel should not be chosen as a control channel. (ii) When the relative gain of the channel is close to 1, it indicates that other channels have less correlation on the channel, and do not need to take any decoupling measure. (iii) When the relative gain of the channel is <0.8 or >1.2, it indicates that there is a serious coupling relationship between input and output variables.
For the core coupling model (17) of CFB boiler, the relative gain matrix can be deduced as where λ 11 , λ 12 , λ 21 and λ 22 refer to relative gains of θ b − F c channel, According to (18), we notice that λ 11 = λ 22 , λ 11 + λ 12 = 1 and λ 22 + λ 21 = 1. Then, using values shown in Table 2, relative gains under three typical working conditions are calculated and listed in Table 3. It is obvious that channel θ b − F c and channel P t − V 1 should be selected as control channels, and the coupling relationships of channel θ b − V 1 and channel P t − F c should be further weakened by decoupler. Hence an inverse decoupling method proposed by Shinskey [22] is adopted here. The superiorities of inverse decoupling method are the simple formulation, the clear structure, and the convenience for application.
Let c 1 and c 2 be the input of the inverse decoupler, the block diagram of the inverse decoupling structure is shown in Fig. 2 [23,24]. And the transfer function of the inverse decoupler, D(s), is Select 75% load as nominal working condition, according to (19) and Table 2, we can get the quantitative inverse decoupler D(s), which contains a prediction item e 30s . Taking into account the physical realisability, a compensator matrix, N r (s) = diag 1, e −30s , with time delay is selected to counteract the prediction item. Let D′(s) = D(s) ⋅ N r (s), the compensated inverse decoupler is obtained (see (20)) . The decoupled relative gain Λ of the CFB core coupling combustion process under three typical working loads are re-calculated, respectively, and the value of each item is enriched into Table 3. It can be seen that the decoupled λ 11 and λ 22 are all close to 1, which means that the decoupler (20) works well.

Design of DD-PID controller
With the rapid development of computing power, data storage capacity and transmission speed, the basic quality of industrial control system is greatly improved. It makes high control performance based on real-time data possible. DD PID (DD-PID) control is a real-time parameter adjustment control technology [25]. The key to this technology is that, whether a large number of real-time operating data and system states' information can be effectively used or not. As shown in Fig. 3, the DD-PID controller can be divided into two parts: adjustable PID controller (which is used to realise the closed-loop control directly) and the DD-PID parameter modifier [26].
In the database, a group of information vectors, which include typical I/O data (the reference input y r , the control signal for the generalised object c and the system output y) and corresponding PID parameters K under some typical working conditions, is stored. At each sample time, the current I/O data is inputted, and the parameter selector is used to calculate the distance between the current and the stored I/O data, then by selecting the nearest neighbours of the new input to get the current PID parameters K sel and put them into PID controller. Furthermore, to fit the change of object's dynamic features and avoid the unlimited expansion of the stored data, the real output y and the reference output ŷ are sent to parameter renewer to generalise the new PID parameters K ren and replace the old one stored in the database.
For the decoupled CFB core combustion process, DD-PID controller 1 is designed to let the bed temperature, y 1 , tracking its reference, y r1 , and DD-PID controller 2 is used to make the main steam pressure, y 2 , following its set-point value, y r2 .
Because the design procedures of DD-PID controller i i = 1, 2 are the same, we only discuss the first one. The DD-PID Controller 1 in Fig. 4 is designed for g 11 (s), so according to Table 2 and (17), the discretised g 11 (z) under 75% load can be deduced as then we get y 1 (t) = 1.856y 1 (t − 1) + 0.8613y 1 (t − 2) + 0.2817c 1 (t − 12) +0.01312c 1 (t − 13) − 0.2509c 1 (t − 14) To make the system have good dynamic performance, the reference model is designed as The PID controller 1 is described as  where Δy 1 (t) = y 1 (t) − y 1 (t − 1), K P1 sel , K I1 sel and K D1 sel are the proportional coefficient, the integral coefficient and the differential coefficient.
The design procedure of DD-PID controller 1 is shown as follows: Step 1: Establishing initial database It is necessary to build a database based on the historical data collected from the generalised control object before the system starts running.
The initial database Φ 1 ( j) is defined as where N(0) is the number of information vectors stored in the initial database, here we set N(0) = 6; the information vector φ 1 ( j) is selected as (see (26)) , and the initial PID controller parameter array K 1 (1) is defined as where the initial values of K P1 , K I1 and K D1 are obtained by the tune function of Simulink in MATLAB. If a set of fixed PID parameters is selected as the initial value, then all PID parameters in the initial database are equal. The initial PID parameters are expressed as Step 2: Calculating distance and choose neighbours The L-norm with weight is used to determine the distance between the input at time t, φ 1 (t), and the information vector φ 1 ( j). For j = 1, 2, …, N(t), the specific formula is defined as follows where φ l1 ( j) is the lth element of the jth information vector, and φ l1 (t) is the lth element of the input at time t; max φ l1 ( j) is the largest lth element in the database, where all information vector is stored; similarly, min φ l1 ( j) is the smallest element; N(t) is the number of information variables stored in the database at the moment t. Six pieces with the smallest distances of all vectors are selected as the neighbours φ 1 ( j) j = 1, 2, …, 6 .
Step 3: Calculating K 1 sel Based on the neighbours selected in step 2, a set of PID parameters, which corresponds to the neighbourhood of input, is calculated by linear-weighted average method.
Suppose ω j is the weight of the jth information vector φ 1 ( j) in the selected neighbours and is derived as follows: The unitary processing is carried out to achieve ∑ j = 1 6 ω j = 1. The K 1 sel (t) can be obtained as Then the parameter vector of the adjustable PID controller 1 is updated by K 1 sel (t).
Step 4: Updating K 1 ren In order to obtain better control performance, the steepest descent method is adopted to adjust the PID parameters so that the control error is reduced. The newly acquired PID parameters will be updated as And K 1 ren (t) is stored in the database as a set of K 1 . In (32), the learning rate η 1 := diag{η P1 , η I1 , η D1 }, the error criterion J 1 (t) := 0.5ϵ 1 2 (t) and ϵ 1 (t) = ŷ 1 (t) − y 1 (t).
Step 5: Deleting redundant data From the database, extract the information vectors with short distance to the query φ (t), which meets the condition and remove the PID parameters that meet the following condition: where ε 1 and ε 2 are the suppression coefficients of the deleted data chosen from the redundant data, and K l (i)(l = 1 − 3) mean K P1 , K I1 and K D1 , respectively. Finally, to prevent the system from crashing as a result of excessive data storage, we set a threshold N max . When the amount of data is greater than N max , the first data vector in the database will be deleted. In the actual system, ε 1 and ε 2 should be set between 0.1 and 1. The specific value needs to be set based on the performance and running time of system.

Case study
To evaluate the effectiveness of the proposed DD control strategy, the established 2 × 2 CFB combustion model in Section 2 and a 330 MW CFB simulation platform of Ningdong Power Plant are introduced for the numerical and application tests. In a wide load range, the comparison of performances of the DD-PID controller and the traditional PID controller will be discussed here.

Tracking test
For the purpose of test the tracking ability, at t = 300 s, it is supposed that the set-point value of the main steam pressure keeps constant, while the set-point value of the bed temperature is changed from 800 to 850°C. At t = 3000 s, the set point of the main steam pressure steps from 10 to 11 MPa. For the above two cases, the time responses of the system under the DD-PID control strategy and PID control strategy are shown in Fig. 5, where trajectories of PID parameters of the DD-PID controllers are also given. It should be noted that the traditional PID parameters are fixed under 75% while the PID values of DD-PID controllers are changing. Hence, we can get different initial PID values under these three loads (50, 75, 100%), which are shown in Table 4. (iii) The settling times θ b and the overshoots of the system outputs P t derived by DD-PID controllers are less than those obtained by traditional PID controllers.
(iv) The variation ranges of the control variables F c and V 1 derived by DD-PID controllers are smaller than those obtained by traditional PID controllers.

Robustness test
In order to show the effectiveness of the proposed new control strategy, the comparison of the performance index by using the DD-PID control strategy in this paper with the ones in [28] will be given in the following part. It is assumed that all parameters of the CFBB model vary from −20% to + 20% of the nominal value, and a unit step is added in the main steam pressure loop and bed temperature loop of each generated object, respectively. Based on the data carried out of the experiments of 1000 Monte Carlo, the settling times t s , overshoots σ%, and the mean value of t s and σ% are summarised in Table 5. It can be seen that the mean value of each index driven by DD-PID controller is much smaller than that of the traditional PID controller, which indicates that the system with DD-PID controller has better dynamic performance.  Moreover, the performance index of the main steam pressure loop and the bed temperature loop are shown in Fig. 8. It can be seen that the overshoot is larger and settling time is longer by using traditional PID control strategy, which indicates that the DD-PID control strategy can provide much better performance than the traditional PID control strategy. Furthermore, Fig. 9 shows the end value of DD-PID for bed temperature loop and main steam pressure loop.

Anti-disturbance test
Next, for the purpose of investigating the robustness to the external disturbances of output signals, 10°C step disturbance of θ b at t = 300 s and a 0.2 MPa step disturbance of P t at t = 3000 s are added to the system output position, respectively. The control results and trajectories of PID parameters are shown in Fig. 10. From Fig. 10 it is apparent that the system outputs go back to their initial stable values quickly and accurately. DD-PID controller is better than the traditional PID controller from the point view of the variation ranges of the control variables.
Then, add a 10t/h step disturbance of F c at t = 300 s and a 2 × 10 4 m 3 /s step disturbance of V 1 at t = 3000 s, the control results and trajectories of PID parameters are shown in Fig. 11, which means that the system outputs go back to their initial stable values quickly and accurately. And, DD-PID controller is better than the traditional PID controller from the point view of the maximum offset.
The above simulation results are obtained on a laptop computer with an 8 GB RAM and an Intel Core i5-3230M processor at a base speed 2.6 GHz. Comparing with the computing period (10 ms) of the traditional PID controller, the period (135 ms) of DD-PID controller increased significantly. For the process control of power generation unit, the qualification computing period of distributed control system is usually ≤250 ms, so the DD-PID can meet the requirement of field operation. In the DD-PID, redundant redundancy is an important step to reduce the computing load. In the examples above, due to the application of redundant redundancy, the average utilisation of the process control unit was reduced around 8.18%.

Application test
Finally, the DD-PID control strategy is applied to the simulation platform of the 330 MW subcritical CFB unit of Guohua Ningdong thermal power plant. Due to the inability to ensure the correctness and stability of the commissioning system, and consuming a lot of manpower and resources, many advanced control methods and strategies cannot be applied. Therefore, based on the real operation data of Ningdong Power Plant, a 330 MW CFB simulation platform with a simulation accuracy of 94% was developed. Based on this platform, various thermal adjustment processes can be debugged and optimised. The boiler of this unit is a subcritical, primary reheat, natural circulation drum boiler made by Dong Fang Boiler Work. It adopts close-fitting, semi-balanced ventilation, light metal roof and all-steel suspension structure. The tail of the boiler is separated by the enclosure wall to form a double flue structure in the depth direction of the boiler. A low-temperature superheater is arranged in the front flue, and a high-temperature   superheater and a low-temperature superheater are arranged in the rear flue from top to bottom. Table 6 shows the main design parameters of the boiler under B-MCR condition. The coal burning in Ningdong Power Plant is mainly bituminous coal. The calorific value of the coal burning is generally 3800-4200 kcal/kg, the dry ashless base volatile content is 30%, the base ash content (Aar) is 35.47%, and the base sulfur content (Sar) is 0.73%. Based on the real historical data of the load of the Ningdong Power Plant, a typical day is selected according to the longstanding practice of the local power grid, as shown in Fig. 12. It can be seen that there are two large load lifting and load reduction during the day. The DD-PID control algorithm is used to make the main steam pressure and the bed temperature move rapidly, and the load demand is satisfied more quickly.
Further, by calculating the integrated time absolute error (ITAE) performance indicators of the two control strategies (as shown in Table 7), the quantisation performance of DD-PID control is superior to the traditional PID control. In this process, the amount of coal is significantly reduced, which can save 517 t coal per day. According to the 'First National Pollution Sources Survey of Industrial Pollution Sources and Sewage Coefficients' in China, the detailed specifications are shown in Table 8. It can be known that the DD-PID algorithm can reduce dust productions/emissions by 28.4 t/25.85 kg and industrial waste gas by 5 × 10 6 m 3 per day. It can be estimated that using this technique can save 188705 t coal, reducing 10366 t/9435.25 kg dust productions/emissions, 1.825 × 10 9 m 3 industrial waste gas per year.

Conclusion
Data has become an important resource for modern industries. The effective use of data can improve the control and operation performance of power generation units. In this paper, a DD-PID control strategy is presented for the combustion control of the CFB boiler to improve the operating performance under full operating conditions.
(i) The core competence of DD-PID is to automatically generate and renew PID parameters online with the change of working condition. Surrounding the use of production data, a normative procedure that includes PID-parameter database establishment, information-vector neighbourhood selection, active PID-parameter determination, database update, and redundant vector deletion, is given.
(ii) The effectiveness, dynamic performance and disturbance rejection capability of the proposed strategy were verified by a set of real CFB boiler combustion models which came from real operation data identification. Besides, DD-PID control strategy is   tested on a 330MW CFB simulation platform of the Ningdong Power Plant to further prove its validity.
(iii) For general computer systems, there is no technical barrier to the implementation of the DD-PID. Unfortunately, considering the safety and reliability, the application modes of most power plant control systems are strict and conservative, few user-defined complex control algorithm can be applied freely. Therefore, the practical research and engineering test of the proposed control strategy will be the focus of our work in the near future.