B.T. Shingissov1, A.M.Kuanyshbayeva1, K.S. Ivanov2, N.T. Zhetenbaev2, Sh.M. Kurmanalieva3
HYDRAULIC ADAPTIVE CONTROL SYSTEM
1Academy of Logistics and Transport,
2Almaty University of Power Engineering and Telecommunication,
3Almaty Technological University E-mail: [email protected]
Abstract. The paper considers a mechanical system with two degrees of freedom and one input that has a force adaptation effect. A hydraulic system with two degrees of freedom and one input can be considered as a variant of mechanical system. The paper proves that a hydraulic system with two degrees of freedom, having one input and a differential coupling superimposed, also has the force adaptation effect.
Keywords. Mechanical system, hydraulic system, adaptation.
Introduction.
Adaptive system control consists of adapting the system to external parameters. An adaptive control system is, for example, a control system for the automatic transmission of a vehicle. This control system ensures that when the engine power is constant, the speed of the vehicle is variable, depending on the external load.
Materials and Methods.
The purpose of this paper is to analyse the theoretical regularities of a system with two degrees of freedom using a hydraulic system as an example, to prove the existence of an adaptation effect for such a system, and to define general principles for creating an adaptive control system.
The adaptation effect of the system can be formulated as follows: if the system content (e.g. power) is constant, one of the output variables (e.g. speed) is inversely proportional to the other variable (e.g. force). The research is based on the laws of mechanics and hydraulics. The adaptive hydraulic system is shown in Figure 1.
The system contains inlet reservoir A, outlet reservoir B, inlet piston 1, intermediate piston blocks 2-4 and 3-5 and outlet piston 6. The pistons 1, 2, 3 are placed in inlet tank A. Pistons 4, 5, 6 are placed in outlet reservoir B. Denote
S
ii = 1 ... 6
- priston area.V
ii = 1 ... 6
-speeds movements of the pistons.Figure 1- Adaptive hydraulic system
Piston blocks 2-4 and 3-5 together with reservoirs A and B create a control structure in the form of a closed hydraulic circuit placed between inlet piston 1 and outlet piston 6.
There is a driving force acting on the inlet piston F1. On the output piston there is a resistance force
F
6= p
6 S
6.During operation, the force F1 on inlet piston 1 creates in the inlet cylinder pressure
1 1 1
F / S
p =
and moves piston blocks 2-4 and 3-5. Pistons 4 and 5 create in output cylinder pressurep
6= F
6/ S
6and move the output piston 6.A closed hydraulic circuit ensures system adaptation.
Relationship of parameters.
Fluid flow rate in cylinders A and B
3 3 2 2 1
1
V S V S V
S + =
.2 4 6 6 3
5
V S V S V
S = +
.or
S
1 V
1= S
3 V
3− S
2 V
2. (1)2 4 3 5 6
6
V S V S V
S = −
Multiply equation (1) by
p
1 and equation (2) byp
6With pS =Fwe obtain
2 2 3 3 1
1
V F V F V
F = −
. (3)2 4 3 5 6
6
V F V F V
F = −
. (4)Subtract equation (4) from equation (3), obtaining
2 4 3 5 2 2 3 3 6 6 1
1
V F V F V F V F V F V
F − = − − +
. OrF6
1 A
3 5
B 6
2 4
F1
V1 V6
0
system is in equilibrium, then according to the principle of possible displacements, the sum of external force powers is zero. Consequently, the sum of the internal force powers is also zero.
Thus, the following pattern holds: If the hydraulic system is in closed circuit, the sum of the internal forces is equal to zero.
Equating the left-hand side of equation (5) to zero, we obtain
F
1 V
1= F
6 V
6. (6)Equation (6) allows you to determine the output speed from a given constant input power
1 1
1 F V
P = and a given variable output resistance force
V
6= F
1 V
1/ F
6. (7) Equation (7) defines an adaptive control operator for the hydraulic system. If one output parameter is set arbitrarily, the other output parameter automatically takes on the corresponding value.Equation (7) defines the relationship between the output kinematic parameter and the output force parameter. This relationship only occurs in a closed-loop hydraulic system. A hydraulic system with closed loop has never been considered before.
From equation (5) it follows that the sum of the internal force powers is zero
0 )
( )
( F
3− F
5 V
3− F
2− F
4 V
2=
. (8)Denote
F
35= F
3− F
5- total force on the piston 3 - 5, F24 =F2−F4- full force on the piston 2 - 4. Then we get
F
35 V
3= F
24 V
2. (9)Equation (9) is is the equation internal circulating energy. Internal forces
F
35, F
24generally speaking (atV
3 V
2) are not equal between themselves, but the equilibrium is performed according to the principle of possible displacements. Static equilibrium conditionF
35= F
24 isfulfilled in the particular case of
V
3= V
2, when there is no relative movement of pistons 3-5 and 2-4.Internal speeds
V
3, V
2 of pistons 3-5 and 2-4 we define by solving the system equations (1 3), (2 4) with known valuesV
1, V
6.From equation (6) it follows that
S
1 p
1 V
1− S
6 p
6 V
6= 0
. From this we obtain the relationship between the pressures in cylinders A and B6
1 1
6 6
1 p
V S
V
p S
= . (10)
Results and Discussion.
Interrelation of adaptive hydraulic system parameters.
Each element of the hydraulic system (piston) is characterised by two Parameters S
p
F = - force and V - speed of motion. Product of the parameters determines the content of the system element (transmitted power) P= FV.
The input state (status) of a system is characterised by constant input parameters, F1 and V1 . The output state of the system is characterised by the variables output parameters F2 and V2 . Power input P1 = F1V1. Power output
P
6= F
6 V
6. Power at inputs and outputs are the sameP
1= P
6. That is to say6 6 1
1
V F V
F =
. (3) Adaptive control the system provides hydraulic A closed loop hydraulic system ensures that external and internal fluid flow rates are interlinked.Interrelation of fluid flow rates in the inlet cylinder
3 3 2 2 1
1
V S V S V
S = +
. (4) Interrelation of fluid flow rates in the outlet cylinder3 5 2 4 6
6
V S V S V
S = +
. (5) Multiply equation (4) by p1 , and equation (5) byp
6 we get3 3 2 2 1
1
V F V F V
F = +
. (6)3 5 2 4 6
6
V F V F V
F = +
. (7) Subtract equation (7) from equation (6). Given equation (3) we obtain0 )
( )
( F
2− F
4 V
2+ F
3− F
5 V
3=
. (8) That is, the sum of the internal capacities on pistons 2-4 and 3-5 is zero.Equation (8) describes the existence of an additional coupling in a closed-loop system with two degrees of freedom. This additional coupling is the control function. For the existence of the control function, equation (8) should have determinability of all parameters. Let us prove the existence of determinability.
The areas of all pistons are set. The pressures in the cylinders are determined by external acting forces.
The speeds of all the pistons must also be found.
The system inlet content (liquid flow rate) is constant and set. The output parameters of the system are variable. Adaptation of the system consists in that by one given output parameter another output parameter is determined. From equation (3) follows
At known speeds inputs и output
V
1, V
6you can determine intermediate speeds as follows3 2
, V
V
. To do this, we present the system of equations (4), (5) in
V
1= S
2 V
2/ S
1+ S
3 V
3/ S
1. (10)V
6= S
4 V
2/ S
6+ S
5 V
3/ S
6. (11) Solving the system of equations (8), (9), determine the intermediate velocitiesV
2, V
3.Thus, equation (6) is determinable and characterises the existence of a control function. The control function is equation (7).
However, equation (7), as mentioned earlier, requires a design change in the output piston area. This can be avoided by using the cylinder pressure parameters
p
1, p
6.Multiply the equation (4) by p1, а equation (5) at
p
6. Considering 5, 4 , ,
3 , 2 ,
1 6
1S =F i = p S =F j=
p i i j j
p
6 S
6= R
6 get
F
1 V
1= F
2 V
2+ F
3 V
3. (12)R
6 V
6= F
4 V
4+ F
5 V
5. (13) The control function is equation (7). The control function of the adaptive hydraulic system can be formulated as follows: given constant input parameters of the system (input piston area S1and speed of movement inlet piston V1 ) speed output piston V6 is in inverse proportion to the output piston area.
Multiply equation (3) by the pressure p2. Taking into account
p
2s
1V
1= N
1 (where N1 - input power) we obtain the connection of the parameters according to the principle of possible displacements
N
1+ R
4V
4= F
3V
3. (14) Subtract equation (2) from equation (4) to obtain
N
1= R
6V
6. (15) From formula (5) it follows
V
6= N
1/ R
6. (16) This means that the output piston 6 moves at a speed inversely proportional to the drag force. In other words, there is a force adaptation of the hydraulic system to a variable output load at a constant input power. In other words, with a constant input power applied to the input piston, the output piston moves at a speed inversely proportional to the drag force.Conclusion.
Thus, the analysis of interaction of parameters of a hydraulic system with two degrees of freedom confirms the possibility of creating a differential coupling in it and the existence of a power adaptation effect in hydraulics. The found laws allow to create adaptive hydraulic
mechanisms. There is no doubt that hydraulic adaptive systems will find wide application in modern machinery.
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Beibit Shingissov, PhD, associate professor, Academy of logistics and transport, Almaty, Kazakhstan, [email protected]
Asela Kuanyshbayeva, мaster, teaching assistant, Academy of logistics and transport, Almaty, Kazakhstan, [email protected]
Konstantin Ivanov, doctor of technical sciences, professor, Almaty University of Power Engineering and Telecommunications named after G. Daukeyev, Almaty, Kazakhstan, [email protected]
Nursultan Zhetenbaev, doctoral student, teaching assistant, Almaty University of Power Engineering and Telecommunications named after G. Daukeyev, Almaty, Kazakhstan, [email protected]
Shinar Kurmanalieva, doctoral student, senior lecturer,Almaty Technological University, Almaty, Kazakhstan, [email protected]
