INTRODUCTION
Main stream temperature of boilers at heatengine plant is an important parameter
of the thermal process, it affects the economical efficiency and security of
boiler operation. Low temperature affects the operating efficiency of the unit,
high temperature affects the operation security of turbines, superheaters and
other devices. The temperature deviation from set value should be less than
5°N (Wang et al., 1993). However, considering
the great inertia, longtime delay of the main stream temperature of boiler
and its parameters change with different situations, the control effect of traditional
cascadestage PID based on fixed model will not be ideal enough.
Wang et al. (1993) and Lv
(1995) combine the neural network and fuzzy control theory with cascadestage
PID control and adjust the parameters of PID control with the changes in output.
But it is still the PID control of varying parameters essentially and can not
overcome the impact of main stream temperature on control system, causing the
long debug time, lack of stability margin and even the shock of system. Thus,
the stability of the system will be influenced. Wang et
al. (2002) uses the predictive control to overcome the impact of great
inertia on control system but the prediction model is fixed. When it comes to
the change of operation duty of boiler, the model can not adapt to the change
of the model of main stream temperature, leading to the poor effect. The key
of the control of main stream temperature lies in the elimination of the effect
of great inertia, longtime delay and time varying at the meantime.
This study will solve this problem by combining predictive functional control
with multimodel switching. Predictive functional control is the third generation
model predictive control algorithm, it stresses the structure of controlled
variables, reduces the online calculation and leaves only several linear weighting
coefficients to calculate. Besides, it has fast tracking, high precision and
other characteristics. Using predictive functional control to predict the changes
of output variation can overcome the impact of great inertia, longtime delay
on control system; but the system performance of predictive functional control
will decline largely when the changes of parameters are too large (Kutze
et al., 1986; Richalet et al., 1987).
For this reason, establishing multiple main stream temperature models in advance
on different occasion, designing corresponding predictive functional control
and switching among the different models in line with the variation of working
condition can eliminate the impact on control system.
MULTIMODEL SWITCHING PREDICTIVE FUNCTIONAL CONTROL
Structure chart of multimodel switching predictive functional control of
mainstream: There are many factors that can affect the main stream temperature
of boilers: boiler load, gas temperature and flow rate, the temperaturedecreased
flux, the position of flame kernel, temperature of feed water and so on. To
overcome these disturbances and obtain more perfect control effect, the cascadestage
control structure combined with multimodel smooth switching predictive functional
control is used to design the control structure which is presented in Fig.
1. The controlled objection W2(s) in Fig. 1 is the transfer
function of leading segment, the regulating variable u of the valve of spray
water temperature reducing device is the input, the output is the stream temperature
θ_{1} of the exit of desuperheater; the controlled objection W_{1}(s)
is the transfer function of inert area, the input is θ_{1}, output
is the main stream temperature θ_{2}. Let’s take the vice
regulating loop and inert area as a whole and name the constitutive controlled
members after the generalized controlled members of main stream temperature.
G_{1}…G_{n} are m generalized controlled objects of main
stream temperature under typical working condition which equal with the oneorder
inertial combining delay component. PFC_{1}…PFC_{n} are
the predictive functional controls under every working condition.
The operating principal of control system is using the control signal of every
second in G_{1}…G_{n} and controlled process, then calculating
the output of model G_{1}…G_{n}, detecting the procedural
output and comparing the output of G_{1}…G_{n} with procedural
output to feed back to multimodel switching module and corresponding predictive
functional control PFC_{1}…PFC_{n}, switching to appropriate
control on the basis of multimodel switching tactics.
The control principle of multimodel switching predictive functional control:
Predictive Functional Control (PFC) shares three essential characteristics
with other predictive control algorithms: predictive model, receding horizon,
feedback compensation. What makes it different from the others is that it regards
the input structure of control as the key in affecting control system.
The typical system in industrial control is oneorder inertial combining delay
component which is used to approximate the common control process. In the main
stream temperature control, generalized controlled objects constituted by every
link in the box of Fig. 1 can be used in oneorder inertial
combining delay component to approximate (Wang et al.,
2002), so the predictive model of predictive functional control can be:
As for oneorder inertial combining delay component, its output is obtained
by the principal of predictive functional control:

Fig. 1: 
Structure chart of multimodel switching predictive functional
control of main steam, PFC_{i } (i = 1, 2,…, n) is the predictive
functional controller, PI is the proportional integral controller; W2(s)
is the transfer function of leading segment controlled object; W1(s) is
the transfer function of inert area; G_{i} (i = 1, 2,…, n)
are generalized controlled objects of main stream with the different working
condition 
In the lastwritten formula:
In formula 2 P is the length of predictive time domain and in formula 3, T_{s}
is sampling period; T_{r} is the lag coefficient of reference trajectories
of predictive function control. In formula 4, D = T_{m}/T_{s}
reflects the lag degree of oneorder inertial combining delay component comparing
sampling period; y_{m}(k) is the output of k.
Formula 2 is the output controlled variable of control at k, u(k) can make
the difference between procedural output and controlled reference value reach
the smallest one at k+P. The detailed derivation process in can be acquired
by Richalet et al. (1987).
The approach to oneorder inertial combining delay component of main steam
generalized controlled object: Once the predictive function control algorithm
of oneorder inertial combining delay component in the previous section is obtained,
next oneorder inertial combining delay component of main steam generalized
controlled object is demanded when the main stream temperature is controlled
by PFC.
Now a boiler with 30% workload is regarded as an example, oneorder inertial
combining delay component of main steam generalized controlled object of this
boiler can be approximated. The transfer function of leading segment is 8.07/(24s+1)^{2},
that of inertial area is 1.48/(46.6s+1)^{4}. As shown in Fig.
2, cascadestage method is used to control system and PI control to adjust
in inner loop, δ = 0.0694, T_{i} = 12, the transfer function which
equals oneorder inertial combining delay component is obtained by simulation:
The comparison curve of them is shown in the Fig. 2. The
two curves shown in Fig. 2 are so close that they can be used
to replace generalized controlled objects approximately with oneorder inertial
combining delay component.
The five given typical transfer functions of leading segment and inertia area
at working load point of this boiler after simulation experiment (Han
et al., 2003) in which the inner loops use the same PI control and
the parameter of control is δ = 0.0694, T_{i} = 12.

Fig. 2: 
Response of main steam generalized controlled object of 30%
load and oneorder inertial combining delay component 
Multimodel switching strategy: The disturbances which affect the main
stream temperature model are mainly: the temperature and pressure and flux of
main stream. The changes in temperature have the smallest effect on the parameters
of model, the effect of pressure is middle and the effect of flux is the biggest.
Comparing with the latter, the effect of temperature may be neglected in the
theory analysis. Main stream pressure and flux are coupling and the changes
in flux can cause the changes in pressure (Fan et al.,1997),
so the reasons for the changes in main stream temperature model is the changes
in operating load of boiler.
When the operating load of boiler changes, if the initial model is used still
as the effect of predictive control, the effect will be worse, even can trigger
the instability of control system. So the models under different working condition
ought to be adopted and design the corresponding PFC control and use the multimodel
switching tactics to switch predictive control model to control which is closest
to the practical model to ensure the best control effect.
The index of multimodel is:
e_{i}(k)=y(k)–y_{i}(k) also known as e_{i}(k)
is the difference between procedural output and output of model i at, α,
β are weight and represents the impact of current and past difference between
procedural output and model on switching index respectively, N represents the
number of the model, L represents the length of error which effects the switching
of index, ρ represents memory effect, J_{i} represents the degree
of difference between control procedure and ith model, the smaller the difference
is, the distance between process and model is closer.
To avoid the instability from switching randomly, the hysteretic switching
algorithm is used which is presented by Middleton et
al. (1988). Suppose that it is control i in the control system which
is controlling, every time after sampling procedural output, formula 6 can be
got:
Find the model number j which has the smallest switching index, if j≠i,
the switching tactics are used to judge the necessity of switching, if:
Then switch to the jth control or still use the ith control, in which ρ
is delay factor.
SIMULATION EXPERIMENTS
The comparison between singlemodel predictive function control and traditional
PID control: First, the traditional PID and PFC control algorithm are applied
to simulate the main stream temperature model and compare the results. The two
algorithms are both cascadestage control and PI control for inner loop, the
parameter of its control is δ = 0.0694, T_{i} = 12. The control
parameter of PID adopts critical proportion band (Guo and
Wang, 2009) to get the parameters in the three stages of the proportional
differential and integration; the oneorder inertial combining delay component
in Table 1 (it is the option table for control model of predictive
function) which equals the generalized predictive object is predictive model.
Table 2 gives the proportions, differentials, integrations
of the parameters of PID control and the parameters of PFC control under different
loads. Figure 35 show optimum control effect
by changing T_{s}, T_{r} and P of predictive function control
under every load. The impact of these three parameters on predictive function
control can be seen in formula 24.
From the simulation curves above, It conclude that the difference of control
effect between PID control and PFC control and the overshoot of PFC are both
small and when the boiler is operated under low load and small effect of inertia;
the inertia of (Table 2) PID control and PFC control parameters
of different main stream temperature is obvious when the boiler is under overload,
this is because that predictive function can percept the variation trend of
output in advance by predictive model and the control can make regulation in
advance.
Table 1: 
Oneorder inertial combining delay component of main steam
generalized controlled object 


Fig. 3(ab): 
Control effect of, (a) 30% and (b\) 44% load 

Fig. 4(ab): 
Control effect of, (a) 62% and (b) 88% load 

Fig. 5: 
Control effect of 100% load 
Table 2: 
PID and PFC control parameters of different load 

PID is the proportional integral derivative controller, PFC
is the predictive functional controller, δ is proportion band, T_{i}
is differential time, T_{d} is integration time, T_{s} is
sampling period; T_{r} is the lag coefficient of reference trajectories
of predictive function control, p is the length of predictive time domain 
Then, the control effect of PFC is much better than PID. Thus, in this study,
the predictive function control algorithm is chosen as the algorithm for main
control in cascadestage control.

Fig. 6: 
Robustness analysis of predictive functional control 
Robustness analysis of singlemodel predictive function: The predictive
function control algorithm is applied into real control which demands the knowledge
of the precise or approximate model of controlled objects. For main stream temperature
control system, when the control parameters under the specific load are known,
the parameters of corresponding control vary with the loads or the control effect
will be worse. Now take the boiler of 88% load as an example, the control parameters
of PFC of optimum control effect can be obtained, the same control parameters
are used to adjust the boiler model into other four known loads and then analyze
the robustness of the system.
Based on the simulation results above, for singlemodel predictive function,
by observing Fig. 5 and 6, the two conclusion
are obtained: one is the output of the system will shock when the load goes
up; the other is the response speed of control will slow down sharply when the
boiler is under load.

Fig. 7: 
Simulation analysis of multimodel predictive functional control 
Therefore, the predictive function control of singlemodel can not deal with
the largerange variation of boiler.
The simulation result of multimodel switching predictive function control:
Since the singlemodel predictive function control can not overcome the impact
of changes in load on main stream temperature, the multimodel switching tactics
are adopted in this study to solve this problem. The control structure is presented
in Fig. 1 and formula 2 for predictive function control, formula
3 for multimodel switching tactics, Fig. 7 for simulation
curve.
From the simulation result above, it conclude that the multimodel switching
predictive function control can still obtain preferable dynamic performance
when the load of boiler changes. Therefore, the control scheme of multimodel
switching predictive function can solve the puzzle in the main stream temperature
of boiler.
CONCLUSION
These study combines predictive function control with multimodel switching
which presents the multimodel switching predictive function control, provides
the switching tactics and then apply it into the control of main stream temperature.
Plenty of simulation experiments show that the main stream temperature control
based on multimodel switching has preferable dynamic performance, strong robustness
and easy algorithm. It can be implemented easily in engineering, so it has certain
engineering practical value.