Advances in Electronic Control of Hydraulic Servo Systems

18/3/2014 Advances in electronic control of hydraulic servo systems

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Advances in electronic control of hydraulic servo systems

Peter Nachtwey

Tue, 2013-07-09 13:44

Manual tuning of electrohydraulic systems is best left to the experts. But auto tuning can adjust machine

controls to not only get a machine up and running quickly, but also optimize its operation.

Controlling electrohydraulic servo systems has always been just a little more challenging than controlling

electromechanical servomotor systems. The main reason is that electrohydraulic systems use

compressible oil to move the actuator. A hydraulic system can be thought of as a mass between two springs

where the piston and the load is the mass, and the oil on both sides of the piston represents the two springs.

Servomotor systems are simpler because, for the most part, only the inertia of the motor and the

connected load must be considered.

Enough differences exist between the two types of

systems that what is good for controlling one is not going

to be optimal for the other. Servomotor systems can be

controlled very well with PID control loop gains plus

velocity and acceleration feed-forward gains. This

control method has often been used to control

servohydraulic systems, too, but a simple PID plus feed

forwards cannot always control a hydraulic system

optimally.

Achieving design goals

For optimal design of a hydraulic system, the fastest

response to disturbances and errors should be applied. However, to achieve this goal, you must either

increase the damping factor or increase the natural frequency of the system. Adding friction will increase

the damping factor. Another way to provide damping is to add a small orifice between the A and B ports of

the valve. Unfortunately, both of these methods waste energy.

Increasing the diameter of the cylinder can increase its natural frequency, but that increases cost because a

larger cylinder, valve, accumulator, and pump will be required. It is less expensive and more effective to

use electronics to get around the limitations. To do this, the PID may be extended to include a second

derivative gain, but hurdles must be overcome before a second derivative gain can be used.

Another enhancement is to use an electronic motion controller that can add a jerk feed-forward term to the

control loop. Jerk is the derivative (rate of change) of acceleration. Feed forwards are estimates of what

the control output should be to the valve to achieve a target velocity, acceleration, and jerk.

If the model for the actuator is known exactly, and no disturbances occur, then, theoretically, you could

control a servohydraulic actuator perfectly without using closed-loop control. It should be obvious that

the valve should be opened up proportionately to the target velocity, and a velocity feed forward can do



that. Why wait for the PID to respond to an error?

The acceleration and jerk feed forwards work on the same principle, but take into account how the oil

compresses as it applies force to the load. In practice, the model for the actuator is not known exactly and

it isnt perfectly linear, so closed loop control is still required. When set correctly, the feed forwards can

estimate the control output usually to within 5% of the required control signal. Then, the PID needs only

to provide a small correction to the control signal due to non-linearities and changes in load.

Challenges of second order control

Adding a second derivative gain and jerk feed forward requires solving three major problems:

First, a high order motion profile generator must be designed that can generate smooth changes in position,

velocity, acceleration, and jerk. The velocity, acceleration and jerk should be smooth to ensure that the

control output generated using the feed forward gains is smooth.

Second, using the derivative gain requires estimating an accurate and smooth velocity. Using the second

derivative gain is more challenging because it requires estimating an accurate and smooth acceleration.

Third, how do you tune the jerk feed forward and the second derivative gain? Trial and error is time

consuming, so auto tuning must be used.

Two main advantages result from using high order motion target generators. The first is that a physical

system cannot possibly follow a linear ramp. This is because following a ramp would require instantaneous

changes in acceleration, which, likewise, would require instantaneous changes in force, pressure and flow.

The second advantage of using higher-order target generators is that velocity, acceleration, and jerk will

vary smoothly from point to point, enabling a smooth control output to be generated.

Estimating velocity and acceleration

The purpose of estimating velocity and acceleration is so that the first and second derivative gains can be

used to provide damping for the mass between two springs. The damping allows the actuator to follow the

motion profile without overshooting the target velocity and position. The first and second derivatives add

electronic damping, which is more efficient than adding friction to increase damping.

Accurately estimating the velocity and acceleration is critical to using the derivative gains. Many people

who have tuned PIDs have avoided using the derivative gains because they amplify noise and make the

control output look noisy.

The simple way of calculating velocity requires knowing the position at two different times and dividing

distance by time. This works well if the positions and times are precisely known. Calculating the

acceleration usually is done by measuring the speed at two different times, calculating the difference

between the two speeds, and dividing the difference by the time.

This seems easy enough, but in practice, it is difficult in part, due to sensors and loop times. For instance,

if the feedback device provides only 0.001 in. resolution and the sample times are at one msec intervals,

the resolution of the speed calculation is only 1 in./sec. This is a shortcoming because ramping up or down

the target velocity will smoothly ramp through speeds that are not even multiples of 1 in./sec. The

measured speed will not match the actual speed most of the time, so the measured speed will be too fast or

too slow. And when this error is multiplied by the derivative gain, the error will make the control output

look noisy. In reality, the error is not noise but quantizing error the rounding error caused by variation

in the number and values of samples taken in the sampling period.



Calculating the acceleration is even more error prone because if the velocitys resolution is only 1 in./sec,

then over a 1 msec time period the acceleration will have a resolution of 1000 in./sec2, which is not usable

at all. In practice, most hydraulic systems usually ramp up and down a rates closer to 100 in./sec2. Clearly,

a better way must be found to estimate the velocity and acceleration to make them usable for calculating

feed forwards.

A sensible solution

The answer to this problem is to use a model to estimate the velocity and acceleration as a function of the

control output. The model is simply a set of equations that use floating point numbers having practically

infinite resolution compared to a real feedback device. This eliminates the quantizing error, but the model

had better be fairly accurate. To keep the model from going astray, the measured feedback is used to

correct the model. Now, the derivative gain can be multiplied by the error between the target and

estimated velocity. Similarly, the second derivative gain can be multiplied by the error between the target

and the estimated acceleration. Doing so will make the output smoother.

Part Two

Figures 1 and 2 contain two graphs showing how one can use the measured velocity and the control output

to generate a first and second order model respectively. The measured or feedback velocity in red is

calculated using a simple method. The resolution of the feedback device is 0.001 inches but the velocity is

calculated over a time span of two milliseconds, so the resolution of the feedback velocity is 0.5 inches per

second. One can see that the estimated velocity is much

smoother because it is generated by the model, but the

feedback velocity from a first-order model doesnt

follow the changes in the actual model that well. On the

other

hand,

the

estimated velocity for the second order model follows the feedback velocity much more closely than the

first order model, and best represents how the actual system is moving. This indicates that the system is a

second order system, behaving like a mass between two springs.

So where does the model that is used to estimate the velocity and acceleration come from?

Auto Tuning

Auto tuning is a feature that is supported by some electronic motion control systems and is necessary when

using advanced features such as the second derivative gain and the jerk feed forward because few hydraulic

control system designers have any experience at tuning them manually. The two parameters can be



VCCM Equation:

Where:

Fl is the load force that must be

overcome,

PS is supply pressure,

APE is the cylinder size,

v is the speed of cylinder

propulsion,

KVPL is the degree to which the

valve is open,

v is the symmetry of the valve,

and

c is the cylinder area ratio (cap

side of piston area/rod side area).

Natural Frequency:

Where:

is the bulk modulus of oil,

A is the surface area of the piston,

V is the volume of the cylinder,

and

m is the mass of the load

determined roughly by trial and error but having a method of determining the gain, damping factor and

natural frequency quickly is important to reduce startup time and shorten the time it may take to retune a

system as the mechanics change.

Auto Tuning

Auto tuning is a way of estimating the model of the actuator and load

using the control output to the actuator and the position and velocity

response as in the two graphs above. Models can be very complex but

usually one can achieve 95% of the benefit with 5% of the effort if the

model is kept relatively simple. A hydraulic actuator and load can be

modeled simply as a mass between two springs so the model consists of

a gain, damping factor and natural frequency. It is possible to estimate

the gain and natural frequency at design time using the VCCM equation

(See sidebar) and the formula for natural frequency (See sidebar). The

damping factor is a little more difficult to estimate, but a typical

damping factor is in the range of 0.3 to 0.4. Even a rough estimate of

the damping factor can allow the person doing the motion control to

enter these parameters into the motion controllers built-in simulator

so that he or she can get started before the machinery is built. Once in

the field the controls person can do an auto tune to find the actual gain,

damping factor and natural frequency.

Auto tuning isnt totally automatic. There is a procedure where the

actuator must be moved in a specific way, usually via open loop

control. The relationship between the control output and the position

or velocity data is estimated by trying a value for each of the three

parameters (gain, damping factor and natural frequency) and then

checking to see how closely the estimated position or velocity follows

actual recorded position or velocity. An evaluation can be done by

summing the square of all the errors between the estimated and actual

position or velocity. The three parameters mentioned above are

changed in an effort to minimize the sum of the squared errors. This is

a trial and error process but a computer can do it very quickly so it

seems instantaneous. When the computer is done it has found the best

values of the gain, damping factor and natural frequency.

The Results

A true test is to move the actuator using a sine wave motion profile.

The actual or true velocity and acceleration will smoothly go through a

range of values and the goal is to estimate the velocity and acceleration

accurately so the actuator can follow the target accurately. Low

resolution feedback will make the quantizing effect obvious because

the velocity calculated directly from the feedback will change in steps. The goal of the model based control

is to estimate smooth velocities as shown below.

The graph in Figure 3 shows how an actuator with a gain of 3 inches per second, damping factor of 0.4 and

a natural frequency of 10 Hz can be controlled using a PID with a second derivative gain. The feedback is



truncated to 0.001 inches to simulate a start-stop linear

magnetostrictive displacement transducer (LMDT) rod

with a position feedback of 0.001 inches. As noted

above, the resolution of the measured velocity would be

1 inch per second and the resolution of the acceleration

would be 1000 inches per second squared. The graph

shows that the estimated position is so close to the actual

position that they look like one line. The estimated

velocity is relatively smooth compared to what could be

achieved doing simple velocity calculations where the

resolution would be one inch per second. The control

output is basically doing a 1 volt peak to peak sine wave to control the actuator. There is a little noise on

the control output due to the errors in estimating the velocity and acceleration but it isnt bad compared to

what would happen without estimating the velocity and acceleration with the model.

If the model wasnt used the control output would simply

be changing from +10 to -10 volt because of the inability

to estimate the velocity and acceleration. Without the

model based velocity and accelerations, the PID and

second derivative gains would need to be drastically

reduced in order to keep the control output from

swinging 10 volts peak to peak.

Figure 4 contains a graph of the actual and estimated

velocities. There are actually two lines in the plot, but

the estimated velocity is almost identical to the actual

velocity, so the estimated velocity line is on top of the

actual velocity line. Again, notice that there is no 1 inch per second quantizing.

As expected, the estimated acceleration(shown in Figure

5) does shows the effects of feedback quantizing, but

spikes of four or five inches per second squared are a lot

better than errors of 1000 inches per second squared.

The estimated acceleration curve still does a good job of

following the actual acceleration.

Just for comparison, compare the model based control

above to control without the model (shown in Figure 6).

The same gains are used as in Figures 3-5 above. The

control output isnt shown because it changes from -10 to +10 volts due to the affect the quantized velocity

and acceleration has on the control output. Since the control output is often saturated, the actuator is

being controlled as if the valve is a simple on-off directional control valve.

Conclusion



Implementing model based control with an

electrohydraulic motion controller that can run second-

order algorithms allows one to control systems that

would otherwise be uncontrollable because the

derivative gains couldnt be used or the gain values

would need to be keep low so the response will be slow.

The alternative is to design systems so that the damping

factor and natural frequency are high but this increases

the system cost.

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control-hydraulic-servo-systems

Advances in Electronic Control of Hydraulic Servo Systems

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