**4.1.1 Effects of system discontinuities**

Any change of direction of actuator motion produces pressure discontinuity in its both pipelines. This discontinuity is caused by inversion of fluid flow which produce the change of connection between supply pipeline and both actuator chambers. In the moment of change of fluid flow direction each of actuator chambers change connections with system pump and return pipeline, producing corresponding discrete changes of pressure in actuator chambers. Possible pressure drop or surge is also caused by geometric asymmetry of servo valve. These effects are explained on the following figures.

On figure 30 is shown actuator motion asymmetry between direct and reverse modes. This asymmetry is result of pressure distribution along supply and return streamlines, shown on diagrams a) and c) on figure 32. Diagram a) corresponds to direct mode of actuator function

Fig. 32.

relations:

0

**4.1.3 Separate flow modeling** 

direct and reverse modes:

where ' *<sup>a</sup> r ks k k <sup>p</sup> <sup>x</sup> <sup>p</sup> <sup>A</sup>*

<sup>2</sup> . ' ( ) *Q Q Ax bx p p s kk rr s a* 

 and <sup>0</sup> ' *<sup>a</sup> a k k k <sup>p</sup> <sup>x</sup> <sup>p</sup> <sup>A</sup>*

**4.1.2 Conventional system modeling** 

and corresponding pressure difference caused by external force:

Aeronautical Engineering 435

Real state is described by pressure drops at supply and return parts of control servo valve

*ul s a p p p iz r* <sup>0</sup> *p p p* sgn( ) *a r <sup>r</sup>*

Function sgn denotes both directions of external load action, represented as direct and reverse modes of actuator function. Equations (15) defines basic formulation of system dynamic model. Closed formulation of mentioned pressure drops cannot be determined without additional approximations. If we assume that fluid flow through servo-valve is a turbulent, approximate expressions of corresponding equivalent pressure differences in accordance to the figures b) and d) are defined for incompressible fluid flow by following

0 0

Previous relations (15) can be expanded for approximately symmetric supply and return flow characteristics of servo-valve in the following form (with assumed value of p0=0) for

*k F*

<sup>2</sup> . ' ( ) *Q Q Ax bx p p s k k r* 

*<sup>p</sup> p Fx <sup>A</sup>* (15)

 *r r* 

(16)

represented by symmetrical pressure drops at supply and return branches of its servo-valve. The third step of pressure drop correspond to the actuator piston position and corresponds to the applied external force. On diagram c) is shown pressure distribution for reverse actuator mode. Main difference between these modes is in opposite directions of external force related to the streamline of fluid flow. For reverse mode external force support system pump like additional serial connected system sources. This fact appears on figure 30 as different curve gradient for direct and reverse modes. However, absolute value of gradient is greater for reverse mode. More data about gradient value will be shown corresponding to the figure 35. On figure 31 is presented actuator output on servo-valve control input assumed as transient step unit function. This approximation is very close to the real situation for digitally controlled actuators.

On diagrams b) and d) of figure 32 are shown, respectively, equivalent pressure drops for direct and reverse actuator modes corresponding to the conventional mathematical modeling of hydraulic actuator with total pressure drop on servo-valve by neglecting effects at its supply and return parts as two separated fluid flows. This usual approximation cannot be accepted if in system are included effects of hydraulic pressure drop and surge caused by fluid compressibility.

Fig. 30.

Fig. 31.

represented by symmetrical pressure drops at supply and return branches of its servo-valve. The third step of pressure drop correspond to the actuator piston position and corresponds to the applied external force. On diagram c) is shown pressure distribution for reverse actuator mode. Main difference between these modes is in opposite directions of external force related to the streamline of fluid flow. For reverse mode external force support system pump like additional serial connected system sources. This fact appears on figure 30 as different curve gradient for direct and reverse modes. However, absolute value of gradient is greater for reverse mode. More data about gradient value will be shown corresponding to the figure 35. On figure 31 is presented actuator output on servo-valve control input assumed as transient step unit function. This approximation is very close to the real

On diagrams b) and d) of figure 32 are shown, respectively, equivalent pressure drops for direct and reverse actuator modes corresponding to the conventional mathematical modeling of hydraulic actuator with total pressure drop on servo-valve by neglecting effects at its supply and return parts as two separated fluid flows. This usual approximation cannot be accepted if in system are included effects of hydraulic pressure drop and surge caused by

situation for digitally controlled actuators.

fluid compressibility.

Fig. 30.

Fig. 31.

#### **4.1.2 Conventional system modeling**

Real state is described by pressure drops at supply and return parts of control servo valve and corresponding pressure difference caused by external force:

$$
\Delta p\_{ul} = p\_s - p\_a \cdot \Delta p\_{iz} = p\_r - p\_0 \cdot p\_a - p\_r = \frac{|F|}{A\_k} \text{sgn}(F \mathbf{x}\_r) \tag{15}
$$

Function sgn denotes both directions of external load action, represented as direct and reverse modes of actuator function. Equations (15) defines basic formulation of system dynamic model. Closed formulation of mentioned pressure drops cannot be determined without additional approximations. If we assume that fluid flow through servo-valve is a turbulent, approximate expressions of corresponding equivalent pressure differences in accordance to the figures b) and d) are defined for incompressible fluid flow by following relations:

$$Q\_s = Q\_0 = A\_k \dot{\mathbf{x}}\_k = \mu^+ \dot{\mathbf{b}}\_r^+ \mathbf{x}\_r \sqrt{\frac{2}{\rho} (p\_s - \dot{p\_a})} \quad Q\_s = Q\_0 = -A\_k \dot{\mathbf{x}}\_k = \mu^- \dot{\mathbf{b}}\_r^- \mathbf{x}\_r \sqrt{\frac{2}{\rho} (p\_r^+ - p\_0)} \tag{16}$$

where ' *<sup>a</sup> r ks k k <sup>p</sup> <sup>x</sup> <sup>p</sup> <sup>A</sup>* and <sup>0</sup> ' *<sup>a</sup> a k k k <sup>p</sup> <sup>x</sup> <sup>p</sup> <sup>A</sup>*

#### **4.1.3 Separate flow modeling**

Previous relations (15) can be expanded for approximately symmetric supply and return flow characteristics of servo-valve in the following form (with assumed value of p0=0) for direct and reverse modes:

*k*

where index s denotes parameters of symmetric servo-valve. Relation (21) is final mathematical model form of control servo-valve pressure drop for the case of actuator symmetry. This formulation is well known. It must be noted that ppmax is correct term only for strong system pump. For the cases of weak pump ppmax becomes equal ps, with corresponding changes of boundary conditions formulation, which gives following model:

> 2 max max ( sgn ) *s s p kk rr p r*

*<sup>F</sup> Q Ax bx <sup>p</sup> <sup>x</sup>*

Corresponding to discussion about strong and weak regimes of pump function, it is of interest to determine actuator abilities for suppression external load. Corresponding coefficient is defined as ratio between maximal external acting load and maximal possible load which can be suppressed by the system pump. It is also shown correlation between

Effects of model nonlinearities and its corresponding linearisation for the case of incompressible flow are presented on figure 34. We can conclude from diagram that for usual reserve of actuator ability these effects are practically similar. This conclusion indicates that other effects are of higher influence than the effects of model linearisation. On figure 35 is compared nonlinear and linearised approximation on the whole domain of actuator piston stroke. Corresponding differences of actuator output between these models

nonlinear and formed linear actuator models with incompressible fluid flow.

*s s*

*k*

(22)

*A*

*r rr*

 (21)

 *bbb* 

*A*

max ( sgn ) *s s k k rr p r*

*<sup>F</sup> A x bx <sup>p</sup> <sup>x</sup>*

2 .

Fig. 33.

**4.1.5 Analysis of incompressible models** 

are presented on the figure 36.

$$p\_a = p\_s - \Delta p = \frac{1}{2}(p\_s + \frac{F}{A\_k}) \quad p\_r = p\_0 + \Delta p = \frac{1}{2}(p\_s - \frac{F}{A\_k}) \quad p\_{sr} = \frac{p\_s + p\_0}{2} \tag{17}$$

Expressions (16) needs more attention on its meaningless. Corollary of expressions (16) is that nominal system pressure for zero external load is defined as (17).It means that hydraulic system pressure for zero load must be equal to the psr. In the cases of continuous actuator function previous relation holds. In addition, this expression are satisfied for all regimes in which effects of pressure surge can be neglected. In opposite cases, presented mathematical system formulation does not hold. Then subjected mathematical model is not compatible. Corresponding to the relations (16) pressure drop can be determined in the form (18), where *pF k F A*/ represent pressure drop corresponding to external load.

$$Q\_s = Q\_0 = A\_k \dot{\mathbf{x}}\_k = \mu^+ b\_r^+ \mathbf{x}\_r \sqrt{\frac{2}{\rho} (p\_s - p\_0 - p)} \quad Q\_s = Q\_0 = -A\_k \dot{\mathbf{x}}\_k = -\mu^- b\_r^- \mathbf{x}\_r \sqrt{\frac{2}{\rho} (p\_s - p\_0 + p)} \tag{18}$$

Finally, static pressure in supply and return branches of actuator streamline can be expressed in expanded form:

$$p\_a = \frac{1}{2} \left( p\_s + p\_0 + \frac{F}{A\_k} \text{sgn} \mathbf{x}\_r \right) \\ \; p\_r = \frac{1}{2} \left( p\_s + p\_0 - \frac{F}{A\_k} \text{sgn} \mathbf{x}\_r \right) \tag{19}$$

Relations (19) are similar to the relations (16). In previous discussion hydraulic system pump is assumed as strong one. It means that the system pump is able to takes up system pressure to the maximal nominal value. This assumption is valid except for existence of system model incompatibilities. This problem can be solved by assuming system pump as a weak one at the initial moment of actuator engage. It follows that any regime of small external load must be assumed as of weak pump. This statement arise from the fact that static pressure in hydraulic system at any moment of its function is caused by external load and pressure loses. As consequence of previous statements, corresponding boundary conditions at actuator pipeline inlet must be determined at initial moment as maximal pump flow. Caused value of system static pressure exists till the moment of pressure upgrading to its nominal system value. In that moment boundary conditions changes to the determined inlet pressure (equal maximal nominal value) and caused value of fluid flow ( second part of flow cross the relive valve), which corresponds to the strong system pump. If reduced valve is built in hydraulic system at actuator supply branch mentioned effects decreases. But in initial moment of actuator engage they can't vanish completely. It means that each pump can't be strong one for the whole possible regimes, spatially at its initial moment.

#### **4.1.4 Boundary conditions**

Corresponding actuator block diagrams for the cases of weak and strong system pump are presented on figure (4) and relations (20) or (21).

$$A\_k \mathbf{x}\_k = \mu^+ b\_r^+ \mathbf{x}\_r \sqrt{\frac{2}{\rho} (p\_{p\text{max}} - p)} \quad A\_k \mathbf{x}\_k = \mu^- b\_r^- \mathbf{x}\_r \sqrt{\frac{2}{\rho} (p\_{p\text{max}} + p)} \tag{20}$$

or in expanded form

Expressions (16) needs more attention on its meaningless. Corollary of expressions (16) is that nominal system pressure for zero external load is defined as (17).It means that hydraulic system pressure for zero load must be equal to the psr. In the cases of continuous actuator function previous relation holds. In addition, this expression are satisfied for all regimes in which effects of pressure surge can be neglected. In opposite cases, presented mathematical system formulation does not hold. Then subjected mathematical model is not compatible. Corresponding to the relations (16) pressure drop can be determined in the form (18), where *pF k F A*/ represent pressure drop corresponding to external load.

0 0

Finally, static pressure in supply and return branches of actuator streamline can be

Relations (19) are similar to the relations (16). In previous discussion hydraulic system pump is assumed as strong one. It means that the system pump is able to takes up system pressure to the maximal nominal value. This assumption is valid except for existence of system model incompatibilities. This problem can be solved by assuming system pump as a weak one at the initial moment of actuator engage. It follows that any regime of small external load must be assumed as of weak pump. This statement arise from the fact that static pressure in hydraulic system at any moment of its function is caused by external load and pressure loses. As consequence of previous statements, corresponding boundary conditions at actuator pipeline inlet must be determined at initial moment as maximal pump flow. Caused value of system static pressure exists till the moment of pressure upgrading to its nominal system value. In that moment boundary conditions changes to the determined inlet pressure (equal maximal nominal value) and caused value of fluid flow ( second part of flow cross the relive valve), which corresponds to the strong system pump. If reduced valve is built in hydraulic system at actuator supply branch mentioned effects decreases. But in initial moment of actuator engage they can't vanish completely. It means that each pump

1

<sup>2</sup> *r s* sgn *<sup>r</sup>*

max ( ) *Ax bx p p kk rr p*

(20)

*p pp x*

*k F*

*A* 

1 2 ( ) *r s*

*pp p p <sup>A</sup>*

*k F*

2 . ( ) *Q Q Ax bx p p p s k k r* 

 *r s* 

(18)

2 *<sup>s</sup> sr <sup>p</sup> <sup>p</sup> <sup>p</sup>*

(17)

(19)

<sup>0</sup>

1 2 ( ) *as s*

<sup>0</sup>

*pp p p <sup>A</sup>*

0 0 2 . ( ) *Q Q Ax bx p p p s kk rr s* 

1

expressed in expanded form:

**4.1.4 Boundary conditions** 

or in expanded form

presented on figure (4) and relations (20) or (21).

2 . max ( ) *Ax bx p p kk rr p*

0

*k F*

<sup>0</sup>

can't be strong one for the whole possible regimes, spatially at its initial moment.

Corresponding actuator block diagrams for the cases of weak and strong system pump are

<sup>2</sup> .

*A* 

<sup>2</sup> *a s* sgn *<sup>r</sup>*

*p pp x*

*k F*

$$A\_k \mathbf{x}\_k^\cdot = \mu^s b\_r^s \mathbf{x}\_r \sqrt{\frac{2}{\rho} (p\_{p\max} - \frac{F}{A\_k} \text{sgn} \mathbf{x}\_r)} \quad \mu^+ b\_r^+ = \mu^- b\_r^- = \mu^s b\_r^s \tag{21}$$

where index s denotes parameters of symmetric servo-valve. Relation (21) is final mathematical model form of control servo-valve pressure drop for the case of actuator symmetry. This formulation is well known. It must be noted that ppmax is correct term only for strong system pump. For the cases of weak pump ppmax becomes equal ps, with corresponding changes of boundary conditions formulation, which gives following model:

$$Q\_{p\max} = A\_k \dot{\mathbf{x}}\_k = \mu^s b\_r^s \mathbf{x}\_r \sqrt{\frac{2}{\rho} (p\_{p\max} - \frac{F}{A\_k} \text{sgn}\,\mathbf{x}\_r)} \tag{22}$$

Fig. 33.

#### **4.1.5 Analysis of incompressible models**

Corresponding to discussion about strong and weak regimes of pump function, it is of interest to determine actuator abilities for suppression external load. Corresponding coefficient is defined as ratio between maximal external acting load and maximal possible load which can be suppressed by the system pump. It is also shown correlation between nonlinear and formed linear actuator models with incompressible fluid flow.

Effects of model nonlinearities and its corresponding linearisation for the case of incompressible flow are presented on figure 34. We can conclude from diagram that for usual reserve of actuator ability these effects are practically similar. This conclusion indicates that other effects are of higher influence than the effects of model linearisation. On figure 35 is compared nonlinear and linearised approximation on the whole domain of actuator piston stroke. Corresponding differences of actuator output between these models are presented on the figure 36.

On diagram of figure 40 is presented computer simulation of nonlinear periodic actuator output piston stroke for harmonic control input, both in non dimensional form. If corresponding relative amplitude of servo-valve throttle is equal 0.50 depending of relative time, equal 1 for total piston stroke for its maximal possible velocity. It is easy to see that approximate harmonic output is recovered approximately after 5 cycles. System nonlinearity is shown on diagram of figure 41, which represents inverse simulation of

system relative control input for harmonic relative output.

Fig. 40.

Fig. 41.

Fig. 42.

On figures 38 and 39 are shown diagrams of non dimensional coefficients of model linearisation corresponding to its nominal regimes.

#### **4.1.6 Actuator transfer characteristics**

In this paper actuator simulation is presented for step and frequent harmonic input of actuator control servo-valve. Step input is used for actuator quasi stationary characteristics and parameters identification. Harmonic impute can be used for high cyclic actuator identification.

Fig. 34. Fig. 35.

Fig. 36. Fig. 37.

Fig. 38. Fig. 39.

linearisation corresponding to its nominal regimes.

**4.1.6 Actuator transfer characteristics** 

On figures 38 and 39 are shown diagrams of non dimensional coefficients of model

In this paper actuator simulation is presented for step and frequent harmonic input of actuator control servo-valve. Step input is used for actuator quasi stationary characteristics and parameters identification. Harmonic impute can be used for high cyclic actuator identification.

On diagram of figure 40 is presented computer simulation of nonlinear periodic actuator output piston stroke for harmonic control input, both in non dimensional form. If corresponding relative amplitude of servo-valve throttle is equal 0.50 depending of relative time, equal 1 for total piston stroke for its maximal possible velocity. It is easy to see that approximate harmonic output is recovered approximately after 5 cycles. System nonlinearity is shown on diagram of figure 41, which represents inverse simulation of system relative control input for harmonic relative output.

Fig. 41.

Fig. 44.

Fig. 45.

Fig. 46.

Aeronautical Engineering 441

On figure 43 are presented simulation of actuator piston relative stroke and relative static pressure in supply and return actuator chambers for usual mathematical form of actuator dynamic model. As it is explained in abstract, initial relative pressure values (equal 0.5) can exists in ideal model only. In real cases, initial values of relative pressure in actuator chambers is the result of actuator history and fluid leakage, which produces it's ambiguity. Extreme case corresponds to the zero values of initial relative pressures. Corresponding simulation of supply and return relative pressures are presented on figures 45 and 46.

On diagram of figure 42 are presented simulation curves of relative actuator piston stroke position and its corresponding relative velocity as actuator system outputs for unit step control relative input if exists only inertial actuator load including equivalent total mass of aerodynamic control surfaces. Corresponding actuating relative time delay is less than 0,004.

#### **4.1.7 Actuator modeling with assumed quasi-static fluid compressibility**

Pressure drop in hydraulic systems can be caused by small external load or local increasing of fluid flow to be greater than maximal possible pump source flow. To prevent this it is suggested to separate corresponding branch of actuator supply by corresponding reduction valve. In these cases possible pressure surge are not of high influence and is determined by equivalent actuator stiffness together with potential external load. Pressure increases proportionally with increasing of piston displacement corresponding to its velocity. This pressure increasing is too slower than for the cases of pressure surge caused by fluid compressibility. If actuator is assumed with quasi static compressible fluid flow, system model can be presented for symmetric supply and return branch of fluid flow in the following form:

$$\begin{aligned} \mu^0 b^{r0} (\pm \mathbf{x}\_r) \sqrt{\frac{2}{\rho}} (p\_s - p\_a) &= \pm A\_k \mathbf{x}\_k + \beta A\_k (H\_{\text{cal}} \theta + \mathbf{x}\_k) \not{p}\_a + c (p\_a - p\_r) \\ \mu^0 b^{r0} (\pm \mathbf{x}\_r) \sqrt{\frac{2}{\rho}} (p\_r - p\_0) &= \pm A\_k \mathbf{x}\_k - \beta A\_k (H\_{\text{cal}} \theta - \mathbf{x}\_k) \not{p}\_a + c (p\_a - p\_r) \\ F &= A\_k (p\_a - p\_r) \end{aligned} \tag{23}$$

where are: flow coefficient, br equivalent geometric wide, xr position of control valve throttle, ps supply pressure of hydraulic system pump, pa static pressure in supply chamber of actuator cylinder, pr static pressure in return chamber of actuator cylinder, p0 static pressure in return pipeline, Ak area of actuator piston, coefficient of fluid compressibility, c coefficient of fluid leakage, Hcil piston stroke, coefficient of parasite volume of connected pipeline to actuator cylinder, xk position of piston and F applied external force (including inertial forces) to the actuator piston. Both signs in equations corresponds to the direct and reverse modes of actuator function.

Fig. 43.

Fig. 44.

440 Mechanical Engineering

On diagram of figure 42 are presented simulation curves of relative actuator piston stroke position and its corresponding relative velocity as actuator system outputs for unit step control relative input if exists only inertial actuator load including equivalent total mass of aerodynamic control surfaces. Corresponding actuating relative time delay is less than 0,004.

Pressure drop in hydraulic systems can be caused by small external load or local increasing of fluid flow to be greater than maximal possible pump source flow. To prevent this it is suggested to separate corresponding branch of actuator supply by corresponding reduction valve. In these cases possible pressure surge are not of high influence and is determined by equivalent actuator stiffness together with potential external load. Pressure increases proportionally with increasing of piston displacement corresponding to its velocity. This pressure increasing is too slower than for the cases of pressure surge caused by fluid compressibility. If actuator is assumed with quasi static compressible fluid flow, system model can be presented for symmetric supply and return branch of fluid flow in the

**4.1.7 Actuator modeling with assumed quasi-static fluid compressibility** 

0

. . () ()

()( ) ( ) ( )

 

*b x p p Ax A H x p cp p*

*b x p p Ax A H x p cp p*

where are: flow coefficient, br equivalent geometric wide, xr position of control valve throttle, ps supply pressure of hydraulic system pump, pa static pressure in supply chamber of actuator cylinder, pr static pressure in return chamber of actuator cylinder, p0 static pressure in return pipeline, Ak area of actuator piston, coefficient of fluid compressibility, c coefficient of fluid leakage, Hcil piston stroke, coefficient of parasite volume of connected pipeline to actuator cylinder, xk position of piston and F applied external force (including inertial forces) to the actuator piston. Both signs in equations corresponds to the direct and

*r s a k k k cil k a a r*

(23)

()( ) ( ) ( )

 

*r r k k k cil k a a r*

. . () ()

2

2

( )

*ka r*

*F Ap p*

*r*

reverse modes of actuator function.

*r*

following form:

Fig. 43.

On figure 43 are presented simulation of actuator piston relative stroke and relative static pressure in supply and return actuator chambers for usual mathematical form of actuator dynamic model. As it is explained in abstract, initial relative pressure values (equal 0.5) can exists in ideal model only. In real cases, initial values of relative pressure in actuator chambers is the result of actuator history and fluid leakage, which produces it's ambiguity. Extreme case corresponds to the zero values of initial relative pressures. Corresponding simulation of supply and return relative pressures are presented on figures 45 and 46.

Fig. 46.

**19** 

*Malaysia* 

**Numerical Modeling of Wet Steam Flow** 

Hasril Hasini, Mohd. Zamri Yusoff and Norhazwani Abd. Malek *Centre for Advanced Computational Engineering, College of Engineering,* 

In power station practice, work is extracted from expanding steam in three stages namely High Pressure(HP), Intermediate Pressure(IP) and Low Pressure(LP) turbines. During the expansion process in the LP turbine, the steam cools down and at some stages, it nucleates to become a two-phase mixture. It is well-acknowledged in the literature that the nucleating and wet stages in steam turbines are less efficient compared to those running with superheated steam. With the advent of water-cooled nuclear reactor, the problem becomes more prominent due to the fact that in water-cooled nuclear reactor, the steam generated is in saturated condition. This steam is then supplied to the HP steam turbine which therefore has also to operate on wet steam. One of the tangible problems associated with wetness is erosion of blading. The newly nucleated droplets are generally too small to cause erosion damage but some of the droplets are collected by the stator and rotor blades to form films and rivulets on the blade and casing walls. On reaching the trailing edges or the tips of the blades, the liquid streams are re-entrained into the flow in the form of coarse droplets. It is these larger droplets that cause the erosion damage and braking loss in steam turbine. However, the formation and behaviour of the droplets have other important thermodynamic and aerodynamic consequences that lower the performance of the wet

Interest in wet steam research was sparked by the need for efficient steam turbines used in power generation. The subject has become increasingly important in current decades with the steep increase in fuel cost. The importance of steam turbine in society is obvious considering that most of the world's power generation takes place using steam-driven turbines. Even though the importance of these machines is obvious, very little attention is given by researchers to understanding the flow behaviour inside steam turbines in comparison with other prime movers. Considerable progress has been made in the investigation of flow in gas turbines because of their applications in the aeronautical field. The findings from gas turbine research are applicable to the dry stage in steam turbine only. However, attention must also be paid to the wet stages as a significant proportion of the output is generated by them. In recent years, work in wet steam research has gained interest with the advent of high performance computing machines and measurement devices. Most of the works aim to accurately model the droplet formation using different calculation

**1. Introduction** 

stages of steam turbines.

**in Steam Turbine Channel** 

*University Tenaga Nasional,* 

#### **4.1.8 Conclusion**

All of the exposed diagrams are related to non dimensional ratio system coordinates, where are: k1 piston position, pa static pressure in actuator supply chamber, pr static pressure in actuator return chamber, r control servo valve throttle position, ratio of power reserve corresponding to applied external load. Presented system model enables its compatibility corresponding to the various initial conditions. On figure 14 are shown system simulation for incompressible fluid flow and corresponding model non compatibility of initial conditions. Possible pressure difference between supply and return actuator chambers which is not compensated by external force produces piston "shock" motion, which can not be described by incompressible flow system modeling. Pressure difference can be caused by various effects which produces fast changes of fluid static pressure and/or external load. Actuator locked position for longer time period also is the reason for described effects. Pressure drop or surge caused by fluid compressibility and initial condition discontinuity as result of closed control servo-valve throttle position are shown on the diagrams on figures 16 and 17. Piston position difference in relation with its incompressible model motion is defined on figure 44. Initial piston acceleration produces practical piston "shock" motion , expressed in the later as increasing static error of its position (less than 1% for usual types of fluids). Mentioned effects are of high interest for digitally driven actuators. Supply and return pressure surge is presented on figure 45. Supply and return pressure drop are presented on figure 46.
