Lab. 3-4 in the course TMHP51 - Hydraulic servo systems
Linear position servo with stabilising
feedback - Part I and II
LiTH-IKP-FluMeS
2004-10-14
Division of Fluid Power Technology
Department of Mechanical Engineering
Linköping University, S-581 83 Linköping
LiTH / IKP
FluMeS
Lab. in the course TMHP 51 - Hydraulic servo systems
Chapter 1
Introduction
This laboratory exercise is a part of the course Hydraulic Servo Systems TMHP 51.
It is divided into two parts that is scheduled for three hours each.
The laboratory sessions will take place in the hydraulics laboratory entrance A13, C-corridor.
1.1 Part I
The first part is an introduction to hydraulic position servos. During this experiment the
student shall understand how a hydraulic servo system can be constructed and look at an
example of how you can control the system with dSpace.
In part I the position servo shall be controlled by a PID-controller. The goal with this part of
the exercise is to look at an example of a servo system and to investigate and understand the
PID-parameter’s influence and effect on the hydraulic system.
Many of the basic concepts in control theory will be used and to profit the most from the
exercise the students have to be well prepared. This is done by reading this compendium
thoroughly, doing the preparatory exercises for part I and reading up on the basic concepts of
control theory.
1.2 Part II
In part II we will study and implement a few possible methods to improve the damping of the
servo system. The methods that are brought up in this laboratory exercise are proportional and
dynamic pressure feedback. This part requires that the student understands the equations and
transfer functions that describes a hydraulic position servo.
In chapter two the theory is described briefly, the laboratory equipment is described in chapter
three. In chapters four and five there are exercise routines and tasks for the first and second
part of the laboratory exercise.
The preparatory exercises, which should be done before the laboratory sessions, are in
Chapter 6.
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Chapter 2
Theory
The following is a brief theoretical description of a hydraulic position servo. The chapter is
meant to give a short introduction of the essential concepts that will be used during the
laboratory session. In this section there are also hints and answers to the preparatory questions
in chapter six. To a more comprehensive derivation and discussion of the theory you are
referred to the course literature.
2.1 Hydraulic position servo
The figure below shows a schematic picture of a valve controlled position servo.
Figure 2.1: Position servo. Valve controlled cylinder in a constant pressure system.
In this system the output signal, in this case the cylinder position Xp, shall follow the reference
signal Xpref. The error signal Xe goes through the controller and gives a control signal, Xvref, to
the servo valve. The control signal can for example be a voltage [V] and gives a movement of
the valve position Xv. Many servo valves have a linear relationship between voltage and valve
position. With a P-controller (proportional) it means that the valve position will be
proportional to the error signal.
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The system is supplied with a constant pressure, ps [MPa].
The inertia of the system is represented by the equivalent mass M.
The cylinder can also be effected by an external disturbance force FL and a viscous friction
Bp. Bp can be regarded either as an internal friction in the cylinder and/or as an external
friction from the load. In many cases the viscous friction is relatively small and is neglected in
order to simplify the theoretical analysis.
With assumptions like e.g. a symmetric cylinder, sufficiently fast valve and symmetric and
matched valve, the system in figure 2.1 can be expressed in the frequency domain with the
following block diagram. Vt = V1 + V2
Figure 2.2: Block diagram for a linear valve controlled position servo.
where
ωh =
δh =
4β e A p
Vt M
2
hydraulic resonance frequency
Bp
K ce β e M
+
Ap
Vt
4A p
Vt
β eM
hydraulic damping
Kqu = flow gain from control voltage to load flow [m3/Vs].
Kce = effective flow-pressure coefficient [m3/sPa].
βe = bulk modulus [Pa].
Then the transfer function of the open loop system can be expressed as
Au (s) =
Kv
 s 2 2δ

s 2 + h s + 1 
ω

ωh
 h

.
If we study a system with a proportional controller, Freg = Kp, then
Kv = K p
K qu
Ap
Ks and is called the steady-state loop gain
Ks = 100 [V/m] scaling factor.
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A typical Bode plot for the open loop system has the following appearance.
Figure 2.3: Bode plot (open) for a linear valve controlled position servo.
The stability margins phase and amplitude margin are defined in the Bode plot of the open
loop system. The system in figure 2.3 has a relatively low damping (high resonance peak)
which means that the stability margin is decided by the amplitude margin Am.
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2.1.1 Stiffness
The stiffness of a system describes how an external load disturbance (FL) is propagated to the
cylinder position. The transfer function of the stiffness can be derived from the block diagram
in figure 2.2 with Xpref = 0. If you move the blocks you will get a system where the
disturbance force is the input signal and the cylinder position is the output signal, as in figure
2.4.
Figure 2.4: Block diagram for the derivation of the stiffness of a linear valve controlled position servo.
The transfer function describes how a load disturbance FL propagates to the cylinder position Xp
The stiffness S(s) is defined as
Ap 2
FL
S= −
= Kv
xp
K ce
 s3

2δ h 2
s


+
s
+
+
1
 K ω 2 K vωh

K
v
 v h

Vt
1+
s
4β e K ce
It is especially interesting to study the stationary stiffness S(s=0). It is a measure of how large
the position error (Xpref - Xp) gets when the system is loaded with a constant disturbance force.
The stationary stiffness can be written as (see preparatory exercise 1)
S(s=0) = ………………………………………
The unit of the stationary stiffness is [N/m] which can be compared with the stiffness of a
spring.
To make the system relatively insensitive to external disturbances (FL) the stiffness has to be
high (stiff spring). It can be seen in the equation above that to obtain a high stiffness the
steady state loop gain Kv has to be as large as possible and the effective flow-pressure
coefficient Kce should be kept as small as possible. Notice that there are disadvantages with a
too large value of Kv and a low Kce. Study figure 2.3. How is the Bode plot effected by Kv and
Kce. What happens with Am?
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2.2 Theory laboratory exercise part I
PID - controller
The PID-controller is the most frequently used controller structure. The major advantages
with it is that it is easy to implement and that it is rather easy to set the controller parameters
without having any deep theoretical knowledge of the system it shall control.
If u(t) is the control signal and e(t) is the error signal, the PID-controller can be written in the
time domain as
t

1
de(t ) 
u (t ) = K  e(t ) + ∫ e(τ )dτ + Td

TI t
dt 


0
In practice the PID-controller is not implemented exactly as the equations above but certain
modifications can be made. E.g. can the D-element be modified so that the high frequency
s
components of the signal are not derived and the s in the D- element is replaced with
1 + Tr s
(lead controller). In this way the D-element is “broken down” at the frequency 1/Tr.
The PID-controller then can be described in the frequency domain as

s 
1

+ Td
Freg (s) = K  1 +
1 + Tr s 
 TI s
Where K is the gain, TI and Td are called integral time and derivative time respectively. The
frequency 1/Tr can be considered as the D-element’s ”roll-off” frequency.
The controller can now be adjusted by changing the three parameters K, TI and Td.
The controller can be modified further to avoid integral wind-up, which is closer described
later in this chapter.
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2.2.1 The I-element
The I-element is introduced to increase the gain at low frequencies. This leads to a shorter
settling time for the system and that the steady-state error can be reduced or completely
eliminated. An increasing I-element increases the stationary stiffness, compare with chapter
2.1.1.
In the bode plot in figure 2.6 it is illustrated how the I-element amplifies the low frequencies
and how an increased I-element effects the system. Notice that if the I-element is too big, the
stability margin will decrease and the system can start oscillating or even become unstable.
Figure 2.6 The effect of a PI-controller on the valve controlled position servo system.
That the system starts oscillating is often a problem when you introduce an integrating
controller. This is caused by the fact that the I-element integrates the error (time discrete =
summarize) and the control signal will then grow as long as there is an error. The problem
occurs if the error signal is large, e.g. directly after a change in the input signal. If the system
is slow it takes a fairly long time before the output signal reaches the same level as the
reference signal. During this time the I-value is constantly wind up and it reaches a very high
level. The control signal becomes large and the system oscillates with a positive damping.
Intergral wind-up
The phenomenon that the I-element is added up to very large values is called intergral windup and can be solved in a few different ways. One way of limiting the size of the I-element is
to use conditional integration. The condition can be that the error must be within a certain
interval if the addition shall take place. The I-element and thus the control signal are
restrained from getting too large. The area where the I-element is effective of course has to be
large enough to bring the output signal there with only P-controlling.
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2.2.2 The D-element
Assume that we implement a controller according to the equations below. Fast changes in the
control signal u(t) is prevented by deriving the position signal y(t), i.e. the change of the
signal, and subtract it from the control signal. If the position y(t) is changed quickly, large
derivative, the control signal u(t) will decrease and the motion will be slowed down. The Delement adds damping to the system.
The implementation of a D-element can be seen as a lead compensator, i.e. the phase curve is
“broken” at a certain frequency (1/Td). Then the amplitude margin will increase and the
stability margin can be determined by the phase margin instead. The phase margin is in this
type of system relatively large and the system can be made fast with good damping. When
dimensioning the D-element there are other more unwanted qualities that you need to
consider.
A large value of the D-element gives an amplification of high frequency signals, e.g. noisy
measurement signals. To get wanted qualities of the controller, the demands on the sensors
and the signal system have to be very high. This can be solved to some extent by using a
”roll-off” frequency for the deriving.
It is sometimes good to avoid deriving the signal in order to evade deriving high frequency
components, which cause great leaps in the signal. A step in the input signal should cause a
large D-value. Thus it is only the measured signal (y(t)) that you derive. The controller is then
t

dy(t ) 
1

u (t ) = K e(t ) + ∫ e(τ )dτ − Td

dt 
TI t
0


It is this type of controller that is used in this laboratory session. The design of the controller
can be seen in chapter three.
2.2.3 Tuning rules of PID-controllers
To tune a PID-controller you can use tuning rules. The rules do of course not work on all
types of systems and should be regarded as rules of thumb. They can be used to give a basic
setting that you can start with. A tuning rule is the so-called Ziegler-Nichols method. It is as
follows: You disconnect the I- and D-elements. Then the K value is increased until you get a
sustained periodic oscillation (at constant amplitude) in the output. Write down the K-value,
K0, when this occurs and the period of the oscillation T0. The settings of K, TI and Td are then
calculated according to the table 3.1
Table 3.1. Ziegler-Nichols tuning rules
Controller
K
TI
P
0.5 K0
PI
0.45 K0
T0 / 1.2
PID
0.6 K0
T0 / 2
Td
T0 / 8
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2.3 Theory laboratory exercise part II
Improved performance (increased hydraulic damping)
A few different ways to increase the damping in a hydraulic system will be shown in this
section. By increasing the hydraulic damping the steady state loop gain Kv can be increased
without changing the amplitude margin. With an increased steady state loop gain the system
gets faster and can get a higher stationary stiffness, see the Bode plot in figure 2.7.
Figure 2.7: The Bode plot of the open loop system at two different values of the hydraulic damping. The
increased damping (decreased resonance peak) makes it possible to increase the gain (higher amplitude curve)
without reducing the amplitude margin Am.
The amplitude margin of the position servo can be written as
Am = −20 10log
Kv
− 2δ h ωh
[dB]
where a positive stability margin is obtained according to
Kv = K p
K qu
Ap
Ks < 2 ωhδh
A rule of thumb is to choose a stability margin between 6 – 10 dB, which gives a steady state
loop gain Kv < (0.6-1.0) ωhδh
In many cases you can neglect the viscous friction (Bp ~ 0) to simplify the calculations. Then
the simplified expression for the hydraulic damping δ h can be written as
δh =
K ce β e M
Ap
Vt
(Bp = 0)
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2.3.1 Load pressure feedback
In the Bode plot in figure 2.7 it was shown that increased damping can give a faster system
with a preserved stability margin. A way of increasing the damping is to measure and feed
back the load pressure. The idea is to try and inhibit fast accelerations of the load and thereby
get a system with more damping. The load pressure (PL = P1 – P2) is measured and the signal
is subtracted from the input signal to the servo valve. The effect of this is that when the load
pressure increases (”accelerating force”) the feedback will see to it that the displacement of
the valve decreases. Then the acceleration will be slowed down and the system will seem like
it has more damping.
In figure 2.8 the feedback is drawn. The load pressure is fed back with the gain Kpf.
Figure 2.8: Block diagram of a linear valve controlled position servo with an electric load pressure feedback.
Figure 2.9: Reduction of a block diagram of the load pressure feedback.
If the feedback is reduced you can define K’ce.
Figure 2.10: Proportional load pressure feedback gives a change in
the effective flow-pressure coefficient Kce → K’ce.
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When the block diagram is reduced according to figure 2.8-10, you will finally see that the
measure increases the flow-pressure coefficient Kce and thereby it also increases δh.
Kce → K’ce = Kce + KquKpf
The increased damping by increased flow-pressure coefficient also results in other unwanted
effects. The Kce -value also affects the stiffness of the system, see chapter 2.2.
The proportional pressure feedback increases the flow-pressure coefficient Kce independent of
the frequency which leads to a reduced stiffness at all frequencies. Especially bad is the
reduction of the stationary stiffness since the position error at static load increases.
2.3.2 Dynamic load pressure feedback
Actually you want to increase the damping only around the hydraulic resonance frequency ωh.
A high damping δh is not necessary at lower frequencies. To prevent Kce from increasing at
low frequencies, which lowers the stationary stiffness, you can high pass filter the load
pressure signal. Then you have created a so-called dynamic load pressure feedback.
A realizable high pass filter can be written as
G pf =
s
ωf
1+
s
ωf
Introduce the dynamic load pressure feedback KpfGpf and you will get
Kce → K’ce = Kce + KquKpfGpf
A rule of thumb is to set ω f =
G pf
ω =ωh
ωh
, then
2
≈1
G pf → 0 då ω → 0
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Chapter 3
Laboratory equipment
3.1 General description
The Laboratory equipment should work as a position servo. It is the position of a hydraulic
cylinder with a mass load that should be controlled. The load is constituted of a I-beam that
can rotate around its centre, figure 3.1. Putting weights at the ends of the beam can vary the
inertia.
The position servo is a valve-controlled cylinder in a constant pressure system. The constant
pressure is obtained by a pump with fixed displacement and a pressure relief valve set to the
wanted system pressure. The valve is a 4-way servo valve and is controlled with a voltage
signal from the controller.
A built-in potentiometer sensor in the cylinder measures the position.
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Lab. in the course TMHP 51 - Hydraulic servo systems
6. Pressure relief valve to set the system pressure ps
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5. Symmetric servo cylinder. The cylinder has a built-in position sensor (potentiometer sensor).
4. Pressure sensor for measuring the cylinder pressures, p1 and p2 and the system pressure ps
3. Servo valve MOOG D661 (140l/min), two stage flapper valve with mechanical feedback. Electrical feedback of the valve spool position.
2. dSPACE measurement and control system
1. PC With dSpace and a graphical user interface (controldesk) to monitor and change the controlling parameters.
Figure 3.1. Laboratory equipment, schematic sketch over the hydraulic system and control and measurement signals.
dSPACE
3.2 Sketch over the laboratory equipment
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25 mm
Piston rod diameter
Kqu = 3.32⋅10-4 m3/Vs
Ks = 100 V/m
Flow gain (ps = 100 bar)
Scaling factor [V/m]
ps = 10 Mpa
Kce = Kc0 = 6⋅10-12 m3/Vs
System pressure
Flow-pressure coefficient
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Vt = V1 + V2 = 0.76⋅10-3 m3
βe = 800 MPa
Bulk modulus
Total volume (hose, connections, cylinder)
M = 387 kg
Equivalent mass
System parameters
Kc0 = 6⋅10-12 m3/sPa
Internal leakage (max)
Valve, MOOG 76 two stage servo valve.
Effective area Ap = (402 – 252) π/4⋅10-6 m2 = 0.766⋅10-3 m2
Stroke Xpmax 200mm
40 mm
Cylinder diameter
Cylinder, symmetric servo cylinder, built-in position sensor.
3.3 Data for the hydraulic system
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The pressure feedback is only
used in the second laboratory
session.
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Figure 3.2. The controller structure is consisting of function blocks which gives a comprehensible picture of its function
The position signal is read and subtracted from the reference signal and the control error goes through the PID-controller to the output.
Notice!! The pressure feedback is only used in part II of the laboratory exercise..
3.4 Controller functionality of laboratory exercise part I and II
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Chapter 4
Execution of laboratory exercise part I
Surely you are finished with the preparatory exercises in chapter 6?
4.1 Basic tasks
Study the laboratory equipment, servo valve, hydraulic cylinder, programmable controller
(PSC, in this case dSPACE), PC and position sensor. Try to understand the hydraulic system
and compare with the circuit in Chapter 3.
4.2 dSPACE
In order to implement the control strategy into the hydraulic servo system, a dSPACE card is
used, see Figure below. dSPACE is measurement and control card for real-time processing. In
connection with Matlab/Simulink, the dSPACE environment provides all the tools needed for
automatic code generation, intelligent instrumentation and real-time simulation.
The configuration of dSPACE
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4.3 Programming and running dSPACE
To be able to download Matlab code on the dSPACE card (DSP) the virtual instrumental
panel ControlDesk. An example of a ControlDesk window is shown in the Figure below.
Example of a ControlDesk window
The laboratory assistant will give an introduction to dSPACE and ControlDesk.
4.4 Start the system
Ask the laboratory assistant to start the pump.
Set the system pressure ps = 10 MPa. Read the pressure level on the monitor..
Tests
To make ourselves acquainted with the system and understand the program we will start with
some easy exercises.
•
Set the PID-controller, Kp = 0.2 and KI = KD = 0. I.e. a proportional controller.
•
Try different kinds of input signals and watch how the “vagga” behaves, e.g. change the
wave pattern, amplitude, frequency and offset.
•
Plot the input signal and the cylinder position.
•
Try the emergency stop
When you understand how it works you can go on with the laboratory exercise.
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4.5 P-control
The easiest possible structure of a controller is the proportional controller (P-controller).
+
Xpref
Xvref
Kp
to servo valve
Xp
From position sensor
Now we will investigate how the controller gain Kp effects the system and compare and
explain the behaviour with theoretical reasoning. During this part is KI = KD = 0
Basic setting: Kp = 0.2, Wave pattern = sinus, Amplitude = 0, Frequency = 0, Offset = 0, KI =
KD = 0
Plot the step response for different values of the controller gain Kp. To obtain a step you can
either instantaneously change the offset of the input signal or use a square wave signal with
wanted amplitude and frequency.
Draw the step response of three different values of the controller gain Kp, e.g. Kp = 0.1, 0.3,
0.6.
Use a step of 10 [mm]
Xref
Xp
Kp =
Xref
Xp
Xref
Xp
Kp =
t
Kp =
t
t
How is the speed and stability of the system effected by the controller gain Kp?
Answer:…………….…………………………………………………………………………
………………………………………………………………………………………………….
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The Bode plot below shows the transfer function of the open loop system when Kp = 0.2.
Figure. The transfer function of the open loop system, Kp = 0.2
The following questions are answered briefly. Draw and clarify in the Bode plot above.
What is the critical stability criterion? Indicate in the Bode plot.
What happens with the amplitude and phase curve when the controller gain Kp is changed?
Answer:…………………………………………………………………………………………
…………………………………………………………………………………………………...
Try to find a P-controller with a rise time that is as small as possible and that gives no
overshoot.
Kp = ………….
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4.5.1 Stiffness
The stiffness S(s) of a hydraulic position servo is describing how an external load disturbance
FL effects the position of the cylinder. The stiffness thus is a measurement of how much the
cylinder position yields when it is loaded. S(s) is a transfer function and thereby dependent on
the frequency, chapter 2.1.1. It is often interesting to study the stationary stiffness since it is a
measurement of how large the position error will be when the servo is exposed to a constant
external load.
In the following exercises we will load the cylinder with a number of 20 kg weights.
Theoretical calculations of the stationary stiffness shall then be compared with measured
values.
According to preparatory exercise 1 the stationary stiffness can be written as
S (s=0) =………………………………..[N/m]
Notice that the stiffness is dependent on the controller gain Kp. A high value of Kp gives a
high stiffness. Since the stiffness is a measurement of how accurate a servo is and what
precision it has, it may be suitable to have a large value of Kp, but….
What is the disadvantage with having a too large value of Kp? Compare with the drawn step
responses and Bode plots from earlier exercises.
Answer:……………………………………………………………………………………….
………………………………………………………………………………………………..
In preparatory exercise 2 a theoretical value of the stationary stiffness was calculated with
Kp = 0.1
Steori (s=0) = …………………..[N/m]
Now we will check that this agrees with the real stiffness.
IMPORTANT!! When loading weights to the “vagga” the valves
to the cylinder have to be CLOSED. Make certain that the laboratory
teacher is present. Ask if you are insecure about anything!!
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Apply an external disturbance force by hanging weights on the beam.
Make three static tests with different controller gains Kp, e.g. 0.1, 0.3 and 0.6. Calculate the
stationary stiffness and compare it to theoretically calculated values Steori .
Weight on
the beam
[kg]
Res. Force on
cylinder [N]
P-controller
Kp [-]
Position error
Xe
[m]
Sverklig (s=0)
[N/m]
Steori (s=0)
[N/m]
80
80
80
Comment on the result, does it agree with the theory?
………………………………………………
………………………………………………………………………………………………….
………………………………………………………………………………………………….
As mentioned earlier the amplitude margin is directly related to Kp and too big of a value can
lead to instability. Thus the speed and stiffness versus the stability of the servo system is often
a compromise.
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4.6 PI-control
The steady-state error can be reduced if the gain at low frequencies increases. In the previous
exercise the gain was increased by increasing the controller gain Kp. The problem was that the
amplitude curve (loop gain) was raised for every frequency, which resulted in that the
amplitude margin decreased.
With an I-element in the controller a gain is introduced at low frequencies.
Draw in the Bode plot below what happens when an I-element is introduced to the Pcontrolled system.
Can you, in the Bode plot, see a risk with having a too large value of the I-element? What
happens?
Answer:……………………………………………………….. ……………………………
……….....……………………………………………………………………………………
Now we are checking that the stiffness increases, i.e. the error decreases, when a PI-controller
is introduced.
Load the beam with 80 kg.
Set Kp = 0.1, KI = 0 and KD = 0 on the controller parameters.
Centre the beam. Adjust with the Offset.
What is the error now? (KI = 0) ?
Answer: ………………………
Add an I-element and study the error signal. What happens and why?
Answer:…………………………………………………………………………………..
…………………………………………………………………………………………
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Remove the weight from the beam.
Make some step responses in the same manner as with P-control and try a few values of the Ielement. A suitable value of Kp is 0.2.
Notice !! When high values of the I-element (KI ~ 10) are used there is a risk that unstable
and uncontrollable oscillations will occur. If this should happen there is a stop button on the
”vagga” that resets the controller parameters and put the beam in a centre position
Draw the step response of three different gains KP = 0.2,and KI = 1, 5 and 10.
Use a step of 10 [mm]
Xref
Xp
KI =
Xref
Xp
Xref
Xp
KI =
t
t
KI =
t
Comment on the results.
Answer:………….……………………………………………………………………………..
.........…..………….……………………………………………………………………………..
4.7 PD-control
When you increase the D-element in a PID-controller you often say that you add damping to
the system. What is actually happening?
Explain with words and equations what happens when a D-element is introduced to the
controller.
Answer:................................................................................................................................
...........……............................................................................................................................
................................................................................................................................................
Make step response tests in the same way as earlier and try some different values of the PDcontroller. Start with a P-controller. Find a controller gain Kp that gives a rather oscillative
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settling process. Then increase the D-value and try to find a Kd-value that gives a dampened
step response.
A PD-controller with a fast and stable step response is.
Kp = .........................................................
Kd = .........................................................
4.8 PID-control
To find a good setting of the PID-controller you can try one of the tuning rules that exist for
PID-control, e.g. Ziegler-Nichols. The tuning rules are not suitable for all kinds of systems
but they can often be used to get parameter start values that can be used for further tuning.
Yet it is possible to get good or sometimes even better results with qualified guesses if you
have knowledge of the parameters of the PID-controller. In general the PID-parameters can be
said to have the following qualities.
P-element: Increased P-element results in a faster system with a smaller control error. The
system has at the same time more tendencies to overshoot.
I-element: Decreases or eliminates a steady-state error. The system reaches a reference value
faster bur a too large I-value result in a more oscillative settling process.
D-element: Counteracts fast changes in the system and thus have a damping effect. A too
large D-element causes the system to be slow. The derivation demands that the signals are
without much noise, to avoid leaps in the signal when high frequency components are
derived.
Try to find a PID-controller with good performance with respect to speed, stability and
precision.
Kp = .........................................................
KI = .........................................................
Kd = .........................................................
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Lab. in the course TMHP 51 - Hydraulic servo systems
Extra exercise
4.9 Integral wind-up
What is integral wind-up?……………………………………………………………...............
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
Make step responses and plug in the Anti-wind-up function- and try a few different conditions
for the I-element.
Describe how you are thinking when you tune the controller.
Answer:
…………….……………………………………………………………………………….....
…………………………………………………………………………………………….......
…………………………………………………………………………………………………
…………………………………………………………………………………………..........
Example of a good setting
Kp = ………………….
KI = ………………….
Xe < ……………………
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LiTH / IKP
FluMeS
Lab. in the course TMHP 51 - Hydraulic servo systems
Chapter 5
Execution of laboratory exercise part II
Surely you have done the preparatory exercises in chapter 6?
In this part of the laboratory exercise different measures to improve the performance of the
hydraulic position servo should be introduced. Increased performance means a system with
more damping and is faster and stiffer.
In part I we tried to improve the characteristics of the position servo by introducing a PIDcontroller. Probably you discovered that the system needed more damping and got the best
results with the PD-controller.
This time we are trying other ways to increase the damping and thereby the performance of
the servo. These measures are aimed at the centre of the problem with an oscillative system,
namely acceleration. By measuring and then feed back the load pressure (which gives the
acceleration) in some different ways you can increase the damping in the system. Two
methods to increase the hydraulic damping are shown below. The different methods have
their advantages and disadvantages which will be studied during the laboratory session. Read
more in chapter 2.
To reduce the complexity and to make it easier to relate theory to practice a P-controller with
the gain Kp is used in the default configuration of the system The structure of the controller
can be seen in chapter 3, but disregard the I and D-element.
5.1 Programming dSPACE
See Chapter 4.2 and 4.3. The laboratory assistant will show how to implement feedback
signals for increased damping.
5.2 Start the system
Ask the laboratory assistant to start the pump.
Set the system pressure to ps = 10 MPa. Read the pressure on the monitor.
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Lab. in the course TMHP 51 - Hydraulic servo systems
5.3 Load pressure feedback
Draw in the Bode plot and explain with words why there is a need to increase the damping in
this system.
Answer:………………………………………………………………………………….
……………………………………………………………………………………………
…………………………………………………………………………………………..
The idea with load pressure feedback is to prevent too fast accelerations of the load and
thereby get a system with more damping. The load pressure (pL = p1 – p2) is measured and the
signal is subtracted from the input signal to the servo valve. It has the effect that when the
load pressure increases (”the accelerating force”) the feedback will see to it that the
displacement of the valve decreases. The acceleration will then be slowed down and the
system will have more damping.
Draw a proportional load pressure feedback with the gain Kpf in the block diagram below.
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FluMeS
Lab. in the course TMHP 51 - Hydraulic servo systems
What happens when the feedback is reduced in the block diagram that is described in chapter
2.3.1.
What is Kce after the reduction and how is the hydraulic damping δh effected?
Answer:……………………………………………………………………………………..
…………….……………………………………………………………………………..
………………………….………………………………………………………………..
With the given data for the system, what is the hydraulic damping δh?
Answer:……………………………………………………………………………………..
Start the system and make steps of 10 mm in the input signal. Run the system without the load
pressure feedback and try to find a controller setting that gives a fast but oscillative settling
process.
Controller setting
Kp = …………………
Rise time
ts = ……………………
The calculated amplitude margin Am with Kp according to the previous task
Am = .......................................................................................
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Lab. in the course TMHP 51 - Hydraulic servo systems
Now we should engage the load pressure feedback and see if we can get a more stable
response with no change in he rise time. A rule of thumb is that the amplitude margin should
be between 6 and 10 dB.
What gain of the load pressure feedback Kpf is needed to get an amplitude margin
Am = 10 dB and speed? (First calculate δh)
Answer: ................................................................................................................................
Redo the step response tests with load pressure feedback and the gain Kpf calculated above.
Does the feedback work?
Answer:…………………………………………………………………………….................
Can you mention any disadvantages with a proportional load pressure feedback?
Answer:……………………………………………………………………………………..
To confirm the statement in the last task the “vagga” can be loaded with weights.
Place 80 kg on the beam and centre it (adjust with Offset).
Set the controller gain Kp to 0.2 and disengage the load pressure feedback.
Then the position error is: ..................................[mm]
Engage the load pressure feedback and increase the gain Kpf. What happens with the position
error and why? Explain with words and equations.
Answer:...................................................................................................................................
.............................................................................................................................................
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FluMeS
Lab. in the course TMHP 51 - Hydraulic servo systems
5.4 Dynamic load pressure feedback
The problem with a proportional feedback of the load pressure is that the damping increases
(Kce increases) at all frequencies and thereby you get the unwanted effect that the stationary
stiffness decreases. Introducing a dynamic load pressure feedback can solve this problem.
How does a dynamic pressure feedback work? Draw the feedback in the block diagram below
The dynamic and the proportional load pressure feedback work in approximately the same
way. What is the difference between the two feedbacks? Explain why the dynamic load
pressure feedback increases the performance of the position servo.
Answer: .......................................………………………………………………………………
.................................................................................................................................................
……………………………………………………………………………………………….
If the dynamic pressure feedback is that good, why is it not used all the time? Are there any
reasons to be content with a proportional pressure feedback?
Answer: …………………………………………………….................................................
...........................................................................................................................................
...........................................................................................................................................
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Lab. in the course TMHP 51 - Hydraulic servo systems
Chapter 6
Preparatory exercises
6.1 Part I
1. The stiffness of a hydraulic position servo describes how a load disturbance propagates to
the cylinder position. In the laboratory session you need an equation where the position
error can be calculated when the cylinder is loaded with a constant force.
Set up an expression for the stationary stiffness, i.e. S(s=0), by using the transfer function
in chapter 2.1.1. Assume that it is a feedback system with a P-controller with the
controller gain Kp..
Answer:................................................................................................................................
2. In chapter 3 the laboratory equipment is described. You can also find the system
parameters that are needed to solve the following exercise in that chapter.
Calculate the stiffness for the controller gain Kp is 0.1. With how many millimetres will
the position of the cylinder change when the cylinder is loaded with a constant force FL =
2 800 N ?
Answer:................................................................................................................................
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Lab. in the course TMHP 51 - Hydraulic servo systems
6.2 Part II
3. Assume that the system in chapter 3 is fed back with a proportional controller with the
gain Kp = 0.4.
What damping δh is needed to get an amplitude margin of 10 dB?
Answer:................................................................................................................................
4. What is the damping now? Mention at least one way to increase the damping to the value
calculated in exercise 3.
Answer:................................................................................................................................
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