【 – 字数作文】
aide温度800(一)
1
INTRODUCTION
Variable structure control is a synthesis method which belongs to the nonlinear control theory on the basis of phase-plane. Its basis thought is that systematic state variables reaches some switching surface firstly, then in this surface they slide to the origin more and more. When this movement of sliding has good quality, the purpose of control is finished [1]. The main characteristic of this kind of control is extremely strong robust. That is, to the model error, system parameter variation and external disturbance, it is insensitive.
Therefore, main tasks of designing sliding mode controller are confirming switching surface and designing control law. Above all, the structure of variable structure controller or the figure of switching surfaces and the form of switching functions should be confirmed.
Generally, we choose linear switching functions, whose figure means the control variables count, i.e. ,
s(x)cx, sR, cR, xR
and choose uniform velocity convergence law as the following form:
signs, (0, Rm) s
1, s0
where signs
1, s0
Obviously, for a VSC system, the existence and the
0 . reaching conditions are stated as ss
mmxnn
2 SLIDING MODE CONTROLLER
For the general control system, the equation is given as
f(x,u,t) xRn, uRm, tR x
Designing sliding mode controller is confirming switching function vector
s(x), sR,
and seeking variable structure control
u(x), s(x)0
u(x)u(x) u(x)
u(x), s(x)0
m
3
DESIGN OF SLIDING MODE
CONTROLLER FOR TEMPERATURE SYSTEM
3.1 System Model
such that
sliding
This paper uses PCT-III process control systems experimental device produced by Zhejiang Qiushi Co, Ltd.
mode exists, that is, satisfies This device imitates the boiler and carries out experiments. ds
The heater for internal tube uses the electricity heat silk of lims0;
s0dt
2KW, which uses controllable silicon phase-move and
satisfies the reaching condition, and the touch off unit, whose input control signal adopts 4-20mA phase-contour beyond the switching surface s will standard electric current signal. Its phase-move and touch reach switching surface in limit time; off angle is proportional to the input control electric switching surface is sliding mode region, whose current. In order to control water temperature T1 of the sliding movement is steady more and more, and internal tube, We can control the end voltage of the heater
by controlling alternating voltage. When the input current the system has good dynamic quality.
is 4mA, the end voltage of the heater is 0V, and 20mA current corresponds to 220V voltage. Water temperature T-This work is supported by National Nature Science Foundation under 2 of the external tube depends on heat transferred from the
Grant 60177024
internal tube and taken away by water overflowed from the external tube. When T1 is low, the output voltage of the controllable silicon voltage regulator increases. Then T1 rises, the external tube water temperature T2 rises. When T2 is higher than the setting value, the inflowing water valve of the external tube must open big so that more water overflows from the external tube and takes heat away. It is obvious, the controllable silicon voltage regulator and the outflowing water regulating valve influence each other. Temperature T1 and T2 control system are systems of mutual compiling.
For the sake of it, we set up the following mathematical model:
dT1cm1dtk1u11(T1T2)F1
cm
dT2
2
dt
2(T1T2)F2ck2u2(T2T0)
Where c is the specific heat of water, m1 is the mass of water in the internal tube, m2 is the mass of water in the external tube, F1 is heat transfer area of the internal tube, F2 is heat transfer area of the external tube, 1 is heat transfer coefficient of the external tube to the internal tube, 2 is heat transfer coefficient of the internal tube to the external tube, k1 is the coefficient of the heat that the electricity silk produces to the input signal of voltage regulator, k2 is the coefficient of the open degree of regulating valve to the inflowing water, u1 is a input signal 0-1000 of the controllable silicon voltage regulator corresponding to 4-20mA, u2 is the opening degree of the outflowing water regulating valve whose value is
0-1000, T0 is the ambient temperature, cmdT1
1is the dtincreased heat flow of water in the internal tube, k1u1 is the absorbed heat flow from the heater of water in the internal tube, 1(T1T2)F1 is heat flow of water released
from the internal tube through the inside wall of the internal tube, cmdT22 is the increased heat flow of water dt
in the external tube, 2(T1T2)F2 is the absorbed heat
flow of water in the external tube through the outside wall
of the internal tube, and ck2u2(T2T0), a nonlinear
one of this system, is the heat flow taken away by the
water overflowing from the external tube. Let us define
a1F1,1
b1F1,a2F22,2F2,
cm11cm1cmb2
2cm2
dk1
,cmd2
k2(T2T0). 11m2
The system is given by the state equation T1a1 b1T1
d1 0u1 （1） T
2
aT
2 b220 d2u2
Measure and calculation through the experiment, we can determine parameters value as follows:
c4.183kJ/(kg
C); m14.97kg; m25.45kg;
F0.4m2;F2
2120.36m; 17800W/(mK);
2
27600W/(mK); k11kJ/(smA);
k2
20.009m/(smA);T0
025C
Then, we get
a1＝－0.15; b1＝0.15; a2＝0.12; b2＝－0.12; d1＝0.05
3.2 Sliding Mode Structure of Controller
For the system, let us define
xt
1
e1
dt
or x2e1r1T1
x3
t
e2
dt
or x4e2r2T2
where r1= temperature establishing value of the
internal tube
e1= temperature error of the internal tube
r2= temperature establishing value of the
external tube
e2= temperature error of the external tube
Thus, the state equation of the multi-input-multi-output system is converted into the following first-order equations:
x
1x2 （2） x2
a1T1b1T2d1u1x
3x4 x4
a （3） 2T1b2T2d2u2From above in (2) and(3), choose the following switching function respectively:
s1c1x1x2 s2c2x3x4
The following condition is satisfied when the system enter
siding mode:
s1c1x1x2x
1c1x10 s2c2x3x4x3c2x30 Solving for x1 and x3, the roots are
xt
1tx10e
c1 x3tx30e
c2t
Obviously, only when c1>0，c2>0, the variable structure
control system is steady [2]—[3]. And then