Servovalve, Hydraulic - Position Control

7/30/2019 Servovalve, Hydraulic - Position Control

1/14

Servovalve, Hydraulic Position Control

Sections:

1. Introduction2. Component Considerations

3. Position Control System Dynamic Sizing

4. Position Servosystem Accuracy Calculations

5. Design Considerations to Improve Performance

1. Introduction

The objective of this section is to provide a basic understanding of an electrohydraulic position controlservosystem and to provide necessary equations to estimate performance characteristics. Having abasic understanding of the equations behind the design will help selection of appropriate system

parameters. A position servosystem has been selected since it is the most common typeimplemented.

An electrohydraulic position control servosystem can be defined as an electrically controlled hydraulicactuator that automatically and accurately follows a position command.

Figure 1.1 illustrates a simplified electrohydraulic position control servosystem. It consists of ahydraulic actuator, electohydraulic servovalve, electrical position sensor, and electronic controller.See the Servovalve, Hydraulic - Description for a description of the servovalve internal workings. Asimplified description of operation is summarized here.

Figure 1.2 is a simplified control system block diagram of the electrohydraulic position controlservosystem. This block diagram neglects position sensor dynamics, servovalve dynamics, and theload mass dynamics.

Using Figures 1.1 and 1.2 as a reference, control starts when a position command voltage signal isinput into the control electronics. The control electronics takes the position command and subtractsthe actuator measured position voltage signal. This sum, or position error signal as it is called, is thenmultiplied by an electrical gain (Ka) in order to generate a current command to the servovalve. Theservovalve spool responds to the position error signal proportionally, in that the larger the error signal the more the servovalve spool will travel, until it contacts its mechanical stroke limit. As theservovalve spool moves the metering orifices in the valve open and provide flow paths to and fromthe actuator, causing the actuator piston to move in the direction of command. As the actuator position moves the position error signal calculated in the electronic controller gets smaller andsmaller. This results in the servovalve current decreasing which tends to close the servovalve flowpaths to the actuator. Once the measured actuator piston position equals the commanded position(zero error signal), the servovalve flow paths are closed and the actuator piston is stopped (for adescription of servovalve operation, see Servovalve, Hydraulic - Description ).


2/14


3/14

Figure 1.3 Schematic Diagram of a Mechanical Feedback Position Control System

Figure 1.4 Simplified Block Diagram of a Mechanical Feedback Control System


4/14

2. Component Considerations

Actuator and Servovalve Sizing

Reference Actuator, Hydraulic - Sizing to calculate the initial actuator hydraulic areas required tomove the load. Actuator stiffness and natural frequency can be calculated once the areas are known.Then to correctly size the servovalve, calculate the actuator chamber pressures using the previouslycalculated actuator areas. Once the chamber pressures are known, the servovalve required flow ratecan be determined. This information is required when sizing the position servosystem.

Servovalve Dynamics Considerations

Servovalve dynamics are important part of the analysis. Dynamic response data, often calledfrequency response data, for a servovalve is generally provided by the servovalve manufacturer. Afrequency response graph is the relationship of the servovalve output flow to a constant amplitudesine wave input current command which is swept over a range of frequencies.

Generally the servovalve frequency response can be adequately described as a second-order response with a damping ratio between 0.8 and 1. A comparison can be made between a

manufacturers servovalve frequency response graph to a standard second order transfer functioncurves to approximate the servovalves natural frequency and damping ratio. Vendor catalogstypically provide natural frequency and damping ratio data for a selected servovalve.

When approximating a servovalve frequency response to a second order transfer function anadjustment between the servovalve supply pressure used to generate catalog data and theservosystem supply pressure used in your application must be made. Some servovalve vendorsprovide an approximate factor to correct for supply pressure differences. If the servosystem isoperating at a supply pressure above what the servovalve was frequency response tested then thefrequency response data provided by the manufacturer can be used directly, as this will beconservative. If the servosystem pressure is lower and a vendor factor is not provided, use an 80%factor on the natural frequency obtained from vendor data (no factor is required on the damping ratio).

Note, a servovalve frequency response is far better behaved than the typical frequency response on

an actuator/load response; that is its does not exhibit a large gain at its natural frequency. This isbecause servovalves second stage spool position control loop is designed to be reasonabilitydamped. Many of the same design considerations listed in this module are also used when designinga servovalve.

Servosystem Natural Frequencies

Every component in the servo loop has a natural frequency (servovalve, actuator, controller, positionsensor, attachment bracket/structure). Generally the two lowest natural frequencies in a servosystemare the load mass/actuator combination and the servovalve. Components with natural frequencies far higher than the lowest natural frequency in the system will have little performance impact on thedynamic characteristics of the servosystem and can be safely ignored when estimating initialperformance. The position sensor dynamics can also be ignored if its natural frequency is ten times

the lowest natural frequency in the servosystem.If the actuator mounts to structure have the same or lower stiffness as the actuator hydraulic stiffness,then this will introduce another natural frequency which would be lower than the actuator/load naturalfrequency. This lower frequency will have to be included in the analysis.

The controller response should be relatively fast, again 10 times the frequency response of the lowestnatural frequency in the servosystem.

Position Transducer


5/14

The position transducer senses the actuator position and sends an electrical signal to the controller.The characteristics of the transducer are very important in assuring a well designed servosystem. If possible the transducer should be located as close to the actuator itself. Many designs actuallyincorporate the transducer inside the hydraulic actuator itself. If the transducer is remotely mounted,the structural stiffness between the position sensor and the actuator could lead to the introduction of other natural frequencies into the servosystem. In this case, the structural mount stiffness wouldneed to be included in any analysis.

Position sensor items to consider are accuracy, resolution, hysteresis, and dynamic response. Ageneral rule for a transducer is it should have a natural frequency at least ten times higher than thelowest natural frequency component components in the system.

3 Position Control System Dynamic Sizing

Servosystem Open Loop Gain

The actuator/load natural frequency usually limits the maximum gain in a position control system. Insome instances, the servovalve natural frequency will be the limiting factor on open loop gain. Thissection presents closed loop performance optimization through selection of the controller gain. Itshould be noted there are other compensation techniques that can be implemented to improve aservosystem response, some of which will be covered later in this section.

To determine an initial estimate of open loop gain use the lower value calculated from the twoequations below. This will yield a conservative overall loop gain and should result in acceptableperformance. These equations are based on industry experience and control system analysis. If theactuator natural frequency limits, the open loop gain can only be a fraction of the actuator frequencysince actuators tend to be very lightly damped. If the servovalve natural frequency limits, the openloop gain can be higher since the servovalve damping is significantly higher than the actuator.

a) K open1= 0.1 load _ nat _ freq (3.1)

b) K open 2

= 0.4 servovalve _ nat _ freq

(3.2)

Open loop gain is calculated by multiplying all the terms in the servosytem loop shown in Figure 3.1from x error to x feedback (ignoring the Laplace variable s). The open loop gain is a measure of how muchvelocity will be generated for a given position error. Figure 3.1 is essentially the same as Figure 1.2in Section 1, with the exception that variables are in the blocks instead of a written description.

Figure 3.1 Simplified Control Diagram for a Servovalve Position Control System


6/14


7/14

X position X command

= G( s)1 + G( s) H ( s)

(3.5)

where s is the Laplace variable and

G( s) = K a K q

A s H ( s) = K f (3.6)

Note, G(s) is called a transfer function and is essentially a gain that varies as a function of frequency.Note K f is a gain that does not vary with frequency (so H(s) does not vary with frequency).

Substituting parameters into (3.5) and simplifying


=

1 K f

A K a K q K f

s + 1

=

1 K f

1 K open

s + 1

=

1 K f

s + 1(3.7)

where

=1

K openseconds

Here the servosystem dynamics approximate a first order system with a time constant of (1/K open ).For a step command the output would be 63% of its commanded value after one time constant.

For example, equation (3.8) below is a first order system with a time constant of 1. If a step input(Xcommand = 1) is applied at time=0, X position will equal 0.63 at time =1 seconds, equal 0.95 at time=3

seconds, and equal 0.99 at time = 5 seconds. See Figure 3.3 for a time response plot.


= 1 s +1

where: = 1 (3.8)


8/14

Figure 3.3 First Order System Response to a Step Input

For the steady state condition (s=0) we obtain,

X position= 1

K f xcommand (3.9)

Remember the first order transfer function obtained above neglects the servovalve and actuator/mass

dynamics. If the servovalve frequency is considerably more than the actuator natural frequency thenthe servosystem response will approximate a first order transfer function system with a time constantof (1/Kopen). As discussed in Servovalve, Hydraulic Sizing , the servovalve natural frequencyshould be at least 3 times greater (faster) than the hydraulic natural frequency for the actuator/loadcombination.

Servosystem Control Gain Example

For this example, define the natural frequency of the actuator/load and servovalve as follows:

Actuator natural frequency: load _ nat = 522 rad/sec

Servovalve natural frequency: f natural = 60 Hz, =0.8

Convert servovalve natural frequency into radian per second:

valve= 2 f valve

= 2 60 = 377 (rad/sec)

Determine the open loop gain:

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5

Time (seconds)

X p o s

i t i o n

/ X c o m m a n

d


9/14

Kopen1 = 0.1* load _ nat = 0.1*522 = 52

Kopen2 = 0.1* servovalve _ nat = 0.4 * 377 = 151

Select the lowest K open to use in calculating K a :

K a = A K

open K q K f

(mA/volt) (3.10)

where:

K open= 52 (sec-1 ) lowest K open calculated above

A = 1.5 (in 2) use average of bore and rod areas

Kf = 1 (volt/inch) Position sensor gain (volt/inch)

Let the servovalve have a rated flow of1.34 in 3/sec at 10 mA input current with a supply pressure =

1000 psi. Assuming the servovalve operates at a supply pressure of 3000 psi, the flow gain needs tobe ratioed by the square root of supply pressure to the rated pressure (square root comes ratioingtwo orifice flow equations at the different supply pressures).

K q=

1.34 *30001000

10= 0.232

in3sec

mAservovalve flow gain

Equation (3.10) then becomes

K a=

AK open K q K f

= 1.5*520.232 *1

= 335 (sec -1) (3.11)

This calculated controller amplifier gain would be used in the position control servosystem wheninitially setting up the system.

Computer Simulation

The previous analysis is simplified in that the various gains in the system are linear. The nonlinear servovalve flow gain is assumed linear for ease of analysis. This method is valid and does provideadequate servosystem gains.

Today numerous computer simulation programs exist that can easily incorporate non-linear gains.Using a computer simulation the position control servosystem parameters can be fine tuned. Theactuator and servovalve sizing can be better evaluated and optimized. For instance it maybe

acceptable to have the servovalve flow saturate for larger step input commands. Also, a better understanding can be obtained by varying various system parameters and observing the effect.

Control system improvements can be incorporated to observe their effect. Adjustments can be madeas required based on simulation results.


10/14

Figure 3.4 shows computer simulated results of the servosystem previously analyzed. The previouslycalculated position servosystem parameters were entered into the Figure 3.1 block diagram and astep position input applied.

Figure 3.4 Typical Simulation Response Data


11/14

4 Position Servosytem Accuracy Calculations

Servosystem Position Static Accuracy

Mechanical and electrical inaccuracies/variations will result in a slight position error in the staticcondition. Generally, mechanical inaccuracies are far larger than electrical inaccuracies. Thefollowing is a list of possible inaccuracies:

Servovalve hysteresis

Servovalve threshold

Null shifts due to temperature and supply and return pressure changes

Actuator friction

Position sensor drift

Controller amplifier draft

Blacklash (freeplay) in the system joints

Compensation for servovalve inaccuracies and actuator frictional effects should be included in theservo loop design. This is done by ensuring the servovalve command is at least 5% of its ratedcommand for the maximum allowable position error in the servosystem. The 5% is considered as aminimum, a better value would be 10% of rated current. This is one of the main reasons to ensurethe servovalve flow gain is not oversized. A large servovalve flow gain will reduce the amount of electrical gain thereby increasing the mechanical non-linear effects.

The following relationship comes from Figure 3.1 and assumes x command = 0.

I = K a K f xerror (4.1)

xerror is the difference between the command and input. To determine the maximum position error asa function of K a , re-write equation (4.1) as

I = K a

K f

X max_ allowable

(4.2)

where Xmax_allowable is the maximum acceptable position error. Equation (4.2) provides a relationshipbetween current and position error. Re-write equation (4.2) using 5% of rated current for I.

X max_ achievable=

0.05 * I rated _ valve K a * K f

(4.3)

This will give the position error when 5% of rated current is applied to the servovalve. If it is less than5% of the servovalves rated command you may exceed the maximum position error you desire. If itis above 5% then the position error required should be achievable.

External Force Disturbance

If the position servosystem is static and an external load is varied the position output will vary slightlydue to the effective stiffness of the servosystem. Generally a servovalve will output full systempressure when the servovalve signal is 2% of rated signal. That is, when the servovalve spool hasmoved 2% of its rated stroke, the pressure output at one port (say C1) will be at fully supply pressureassuming C1 is ported to a blocked chamber while the other port (C2) will be at full return pressure.

Reference the system block diagram in Figure 3.1. To generate full supply pressure we assume itwill take a command of 2% of the servovalves rated signal. Hence 0.02*I rated_valve yields full supply


12/14

pressure in one chamber of the actuator and full return pressure in the other chamber of the actuator.Equating this to the maximum actuator force we get: 0.02*I rate_valve yields A*P supply , assuming a zeroreturn pressure. By using a ratio of the applied actuator force (F external ) over the maximum forceoutput of the actuator (A*P supply ) multiplied by 0.02*I rated_valve we would obtain the required current tothe servovalve to hold the applied load.

I valve= 0.02 * I rated _ valve *

F external A * P sup ply

(4.4)

Relating the servovalve current to actuator position error using equation (4.1) yields

X due _ to _ external _ force=

I valve K a * K f

(4.5)

Combining equations 4.4 and 4.5 yields the position error as a function of external load.

X due _ to _ external _ force = 0.02 *

I rated _ valve K a * K f

*

F external A* P sup ply

(4.6)

Thus at 2% of the valve rated current, equation (4.6) provides the position error as a function of external load.

Servosystem Position Following Accuracy

When the commanded position to a servosystem is changing at a constant rate the servosytemposition will lag the output by a slight amount. For instance, using a position ramp command causesthe servosystem to move at a constant velocity. A finite position error signal is required in order togenerate the servovalve command necessary to produce the actuator velocity. The faster thevelocity, the more the following error, as shown by the following equations. Equation 4.5 and 4.6provide the actuator velocity as a function of open loop gain (determined by servo parameters andKa) and position error.

V actuator =

K a * K q * K f A

* X command X position (4.7)

V actuator =

K a * K q * K f A

* X follow (4.8)

X follow =

V actuator K open

(4.9)

Therefore, K a determines the tracking error for a ramp command. As K a increases, the tracking error will be reduced.

5 Design Considerations to Improve Overall Performance


13/14

General Considerations

Some input items to consider when designing a position control system include:

Do not oversize the servovalve flow gain. When designing a servosystem the design goalshould be to put most of the control loop gain into the electronics. A position control loop canonly have so much gain before the system becomes unstable. The servovalve flow gain only

needs to be large enough to move the load at the required velocity. Servoalve mechacialnonlinearities will tend to be minimized by incorporating most of the loop gain into theelectronics part of the loop.

Keep the servovalve as close to the actuator as possible in order to minimize the fluid volumebetween the servovalve and the actuator in order to increase the actuator stiffness.

Use hard tubing between the servovalve and the actuator in order to increase the actuator stiffness

Do not use an actuator with excessive stroke as this will decrease the actuator stiffness

Attempt to minimize the load mass the actuator has to move.

Add a DITHER signal to the command signal going to the servovalve. Dither is a sine wavecommand current applied on top of the main command that goes to the servovalve. Thefrequency of the dither signal is generally a low amplitude signal at the relatively highfrequency. Dither is intended to move the servovalve second stage spool at a very lowamplitude and high frequency so that that the valve spool movement will not result in aservosystem position response. It is intended to reduce frictional effects of the servovalveand/or actuator by keeping the servovalve spool moving all the time. Dither frequencies canrange from100 to 400 Hz.

Select an accurate position transducer. The servosystem position output can not be moreaccurate than the position transducer that measures the position.

If a very high dynamic (bandwidth) servosystem is required consider using an electricalfeedback servovalve. An electrical feedback servovalve generally will have far better dynamic response characteristics than a comparable sized mechanical feedback servovalve.

Proportional Plus Integral Control (PI)

The previous section dealt with determining the proportional gain (Ka) of the position servosystem. An integrator can be added to the controller. Integral control is a way to reduce steady stateservosystem position error. Figure 5.1 shows how the integral gain (K int) is incorporated into thebasic system.

Intergal control works to reduce steady state errors since whenever the input to an integrator is notzero the output of the integrator will keep increasing or decreasing, depending on the sign of the error signal. When the input to an integrator is zero, the integrator output will remain the same. Thisintegrator characteristic can also lead to servosystem position overshoots. If a large position stepcommand is applied, the integrator output will build while the servosystem moves the actuator to thecorrect position. By the time the actuator reaches the correct position the integral output has

increased substantially. This is called winding up the integrator. Hence the servosystem position willovershoot the commanded position and will tend to cause the position output to oscillate. If theposition command is a ramp type of command or a smooth type of command then this problem willnot occur.

One way to prevent the integrator from winding up is to switch the integrator into the circuit only whenthe servosystem position error is relatively small. Then the integrator will integrate out the remainingerror so the output exactly matches in the input.


14/14

Other compensation techniques exist but are not covered here. Many control texts present other means of controller compensation to obtain desired stability and performance and should be soughtout for more information.

Figure 5.2 Simplified Block Diagram of a Proportional + Integral (PI) Servovalve Position ControlSystem

Documents

Servovalve, Hydraulic - Position Control