aide温度800

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)cx, sR, cR, xR

and choose uniform velocity convergence law as the following form:

signs, (0, Rm) s

1, s0

where signs

1, s0

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) xRn, uRm, tR x

Designing sliding mode controller is confirming switching function vector

s(x), sR,

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 lims0;

s0dt

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:

dT1cm1dtk1u11(T1T2)F1

cm

dT2

2

dt

2(T1T2)F2ck2u2(T2T0)

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(T1T2)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(T1T2)F2 is the absorbed heat

flow of water in the external tube through the outside wall

of the internal tube, and ck2u2(T2T0), a nonlinear

one of this system, is the heat flow taken away by the

water overflowing from the external tube. Let us define

a1F1,1

b1F1,a2F22,2F2,

cm11cm1cmb2

2cm2

dk1

,cmd2

k2(T2T0). 11m2

The system is given by the state equation T1a1 b1T1

d1 0u1 （1） T

2

aT

2 b220 d2u2

Measure and calculation through the experiment, we can determine parameters value as follows:

c4.183kJ/(kg

C); m14.97kg; m25.45kg;

F0.4m2;F2

2120.36m; 17800W/(mK);

2

27600W/(mK); k11kJ/(smA);

k2

20.009m/(smA);T0

025C

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

xt

1

e1

dt

or x2e1r1T1

x3

t

e2

dt

or x4e2r2T2

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



1x2 （2） x2

a1T1b1T2d1u1x



3x4 x4

a （3） 2T1b2T2d2u2From above in (2) and(3), choose the following switching function respectively:

s1c1x1x2 s2c2x3x4

The following condition is satisfied when the system enter

siding mode:

s1c1x1x2x

1c1x10 s2c2x3x4x3c2x30 Solving for x1 and x3, the roots are

xt

1tx10e

c1 x3tx30e

c2t

Obviously, only when c1>0，c2>0, the variable structure

control system is steady [2]—[3]. And then