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Abstract:In order to control the two inputs nonlinear temperature system, this paper establishes the mathematical model of the diesel engine fuel temperature system. And the model is regarded as one imitative nonlinear system. Appling the sliding mode variable structure control theory, a sliding mode variable structure controller for imitative nonlinear system of two inputs is designed which controls the temperature of two-inputs-two-outputs nonlinear coupling system.
Key Words:nonlinear temperature systemimitativesliding mode variable structure control
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 switchingsurface 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. 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.
2.SLIDING MODE CONTROLLER
For the general control system, the equation is given as
Designing sliding mode controller is confirming switching function vector
s(x),s∈Rm
and seeking variable structure control
such that
· sliding mode exists, that is, satisfies
· satisfies the reaching condition, and the phase-contour beyond the switching surface s will reach switching surface in limit time.
· switching surface is sliding mode region, whose sliding movement is steady more and more, and the system has good dynamic quality.
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∈Rm,c∈Rmxn,x∈Rn
and choose uniform velocity convergence law as the following form:
Obviously, for a VSC system, the existence and the
reaching conditions are stated as.
3.DESIGN OF SLIDING MODE CONTROLLER FOR FUEL TEMPERATURE SYSTEM
3.1 System Model
Fuel temperature control of the ship diesel engine is the most important factor to guarantee a suitable viscosity of fuel and entire burn. As shown in Fig. 1, the oil that comes out from the oil cupboard enters the diesel engine and burnt after heating by the steam of the heating. So oil temperature should be controlled effectively that passes in and out the heat exchanger.
The cold oil whose beginning temperature is θ3and flow amount is M2 comes out from the oil divided machine and enters the mix oil cupboard. At the same time, warm oil whose temperature is θ1 and flow amount is (G1-G0) that the main engine has not consume up enters the mix oil cupboard too. After two kinds of oil are mixed together, its temperature is T2 and flow amount is G2. Finally, it enters the heat exchanger. Since its temperature is far lower than the demand output one, it is heated by steam and flows out ,then enters the main engine at last whose flow amount is G1 and temperature is θ1. The main engine consumes hot oil whose flow amount is G0 according to the variation, and the remaining flows back to the mix oil cupboard, then go round and begin again like this. Among the whole course, oil temperature θ1 and θ2 are variable outputting. Steam flow M1 and hot oil consumed by the main engine G0 are variable input. Others are constants. As shown in fig 1.
So we set up the following mathematical model:
The original system equation is:
Write as
a1=-1,b1=1,a2=G1/G2,b2=-(M2+G1)/G2
d1=λ/cG1,d2=-(θ1-θ2)/G2,z=M2θ3/G2,u1=M1,u2=G0
3.2 Sliding Mode Structure of Controller
For formula ①, select state variable as:
Where r1 is fixed temperature value; e1 is a temperature deviation.
Where r2 is fixed temperature value;e2is a temperature deviation.
So the state equation of the original system is written as:
Then original double input double output system resolves into two single output system.
Because described above system ② and ③ belong to the linear brief type system:
Its sliding model movement equation is:
There variable structure controls are:
Consider the system ② has the same structural form as the system ③, the system ③ could be writtenas the linear and brief type form as:
So
,,
α(x)=-a2θ1-b2θ2+z
Where,
u2=G0,θ1=r1-x2,θ2=r2-x4
z=M2θ3/G3,d=-1/G2
Select he following functions of switching over:
then
At last, we can get the sliding mode controller as:
u1 is the same as u2.
(作者单位:江苏省苏州市城区地方海事处)
Key Words:nonlinear temperature systemimitativesliding mode variable structure control
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 switchingsurface 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. 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.
2.SLIDING MODE CONTROLLER
For the general control system, the equation is given as
Designing sliding mode controller is confirming switching function vector
s(x),s∈Rm
and seeking variable structure control
such that
· sliding mode exists, that is, satisfies
· satisfies the reaching condition, and the phase-contour beyond the switching surface s will reach switching surface in limit time.
· switching surface is sliding mode region, whose sliding movement is steady more and more, and the system has good dynamic quality.
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∈Rm,c∈Rmxn,x∈Rn
and choose uniform velocity convergence law as the following form:
Obviously, for a VSC system, the existence and the
reaching conditions are stated as.
3.DESIGN OF SLIDING MODE CONTROLLER FOR FUEL TEMPERATURE SYSTEM
3.1 System Model
Fuel temperature control of the ship diesel engine is the most important factor to guarantee a suitable viscosity of fuel and entire burn. As shown in Fig. 1, the oil that comes out from the oil cupboard enters the diesel engine and burnt after heating by the steam of the heating. So oil temperature should be controlled effectively that passes in and out the heat exchanger.
The cold oil whose beginning temperature is θ3and flow amount is M2 comes out from the oil divided machine and enters the mix oil cupboard. At the same time, warm oil whose temperature is θ1 and flow amount is (G1-G0) that the main engine has not consume up enters the mix oil cupboard too. After two kinds of oil are mixed together, its temperature is T2 and flow amount is G2. Finally, it enters the heat exchanger. Since its temperature is far lower than the demand output one, it is heated by steam and flows out ,then enters the main engine at last whose flow amount is G1 and temperature is θ1. The main engine consumes hot oil whose flow amount is G0 according to the variation, and the remaining flows back to the mix oil cupboard, then go round and begin again like this. Among the whole course, oil temperature θ1 and θ2 are variable outputting. Steam flow M1 and hot oil consumed by the main engine G0 are variable input. Others are constants. As shown in fig 1.
So we set up the following mathematical model:
The original system equation is:
Write as
a1=-1,b1=1,a2=G1/G2,b2=-(M2+G1)/G2
d1=λ/cG1,d2=-(θ1-θ2)/G2,z=M2θ3/G2,u1=M1,u2=G0
3.2 Sliding Mode Structure of Controller
For formula ①, select state variable as:
Where r1 is fixed temperature value; e1 is a temperature deviation.
Where r2 is fixed temperature value;e2is a temperature deviation.
So the state equation of the original system is written as:
Then original double input double output system resolves into two single output system.
Because described above system ② and ③ belong to the linear brief type system:
Its sliding model movement equation is:
There variable structure controls are:
Consider the system ② has the same structural form as the system ③, the system ③ could be writtenas the linear and brief type form as:
So
,,
α(x)=-a2θ1-b2θ2+z
Where,
u2=G0,θ1=r1-x2,θ2=r2-x4
z=M2θ3/G3,d=-1/G2
Select he following functions of switching over:
then
At last, we can get the sliding mode controller as:
u1 is the same as u2.
(作者单位:江苏省苏州市城区地方海事处)