礦井提升機盤式制動器的整體設(shè)計及仿真含11張CAD圖
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翻譯部分
英文原文
Disturbance Control of the Hydraulic Brake in a Wind Turbine
Frank Jepsen,Anders Sborg,and Zhenyu Yang Department of Electronic Systems Aalborg University,Esbjerg Campus
Niels Bohrs Vej 8,6700 Esbjerg,Denmark.
Abstract—This paper discusses control of the brake torque from the mechanical disc brake in a wind turbine. Brake torque is determined by friction coefficient and clamp force; the latter is the main focus of this paper. Most mechanical disc brakes are actuated by hydraulics, which means that controlling caliper pressure is the key to controlling clamp force. A pressure controller is implemented on a laboratory-sized test system and uses a disturbance estimator to reject disturbances in order to track a reference curve. The estimator is capable of estimating both input equivalent disturbances and disturbances caused by brake disc irregularities. The controller can reject input equivalent disturbances and a strategy for cancelling the disturbance from the brake disc is proposed.
I. INTRODUCTION
The mechanical brake is one of the two independent brake systems in a wind turbine. As a consequence of the gearing in the turbine, the mechanical brake is often placed on the high-speed shaft as this allows the brake system to be small as opposed to placing it on the low-speed shaft. This is shown in figure 1. The downside of this design is however, that the gearbox has to be able to handle a large amount of torque when the brake is applied.
Fig. 1: Overview of drive train in a wind turbine[1]
Most brake systems in today’s wind turbines supply the hydraulic brake caliper with maximum pressure when applied. Results in show that such brake systems produce back- lashes in the gearbox, that in the end may cause the fatigue load to be underestimated by current gearbox design methods.
Furthermore, results from show that when maximum brake torque is applied it excites oscillations in the rotor shaft, that have an amplitude nearly twice as high as the norminal shaft torque. Therefore, it is possible that the mechanical brake is the cause of a large amount of the gearbox failures. One such failure has been seen recently at Hornslet in Denmark, where a gearbox suffered a catastrophic failure caused by load from the mechanical brake system[4].
In recent years the term ”soft brake” has been subject to great interest from companies such as Svendborg Brakes, General Electric and Nordex. All three companies have filed patents for ”soft brake” systems as described in [5], [6], [7]. All three patents are concerned with reducing the excessive dynamic load peaks and vibrations during emergency stops. Comparing ”soft brake” with the classic approach, where full pressure is applied, it is clear the soft brake is superior. However, ”soft brake” still leave room for improvement as relatively large oscillations still occur – especially after the shaft has stopped [5].
This paper focuses on a smart brake system which has the objective of controlling the brake torque through precise control of the calipers clamp force. Since none of the ”soft brake” systems directly control the force but depends on other factors such as rotational speed or time; controlling the brake torque is believed to further damp the vibrations during emergency stops. At this first development stage, the control design focused on controlling the hydraulic pressure in the brake caliper using a laboratory-sized hydraulic brake system. However, it was observed that disturbances made it hard to keep a constant pressure in the caliper. As a result, a disturbance estimator was used to assist the design of a con- troller that can track a reference curve. The estimator is able to estimate disturbances caused by brake disc irregularities and a strategy for cancelling out these disturbances is proposed.
The rest of the paper is organized in the following way: Section II describes the physical setup; Section III discusses the mathematical modeling and parameter identification of the hydraulic system; Section IV briefs the development and implementation of the disturbance estimator while section V describes the disturbance rejection scheme applied; and finally discussion and conclusion as found sections VI and VII.
II. SETUP
In order to investigate how the brake torque can be con- trolled by the mechanical brake, a laboratory-sized setup consisting of a test rig and a hydraulic power pack has been constructed. As shown in 2, the torque from the rotor is represented by a motor which is connected to the brake disc and caliper through a single shaft.
Fig. 2: The test rig
As the angle of twist in the shaft increases when the brake is applied, a set of wireless strain gauges are used to meassure the brake torque. In addition, two other sensors are also placed on the test rig; a tachometer to measure the angular velocity of the shaft and a IR temperature sensor to measure the temperature of the brake disc.
The hydraulic power pack, which provides oil to the caliper, is divided into two subsystems; hydraulic control system and hydraulic power system. The purpose of the power system is to provide a contant pressure to the control system. The hydraulic control system is the part that actually controls the pressure in the caliper using a proportional pressure valve; as shown in figure 3. On the system there are two pressure sensors; one to measure the outlet pressure of the proportional pressure valve and one to meassure the pressure in the caliper.
Fig. 3: The hydraulic control loop
III. MODELLING AND IDENTIFICATION
To model the hydraulic control system, a series of prelim- inary experiments was conducted. These tests served as on- hands experience with the system to insure that no important phenomenons was left out in the model and to see how the proportional valve would react to different input voltages; regarding rise time, steady state gain, overshoot and dead time. Also it was of great interest to know if the shaft rotation affects the hydraulic system.
A. Dynamic Response of the Proportional Valve
The first thing that was observed when experimenting with the valve was the fact that it is necessary to use 7V as a virtual zero, because voltages below this limit did not have any effect on the outlet pressure. Figure 4 shows the measured step responses of the hydraulic system, when applying input steps of 8V , 9V , and 10V respectively.
Fig. 4: Measured step responses with input steps of 8V , 9V , and 10V
From these steps it can be observed that the outlet pressure po has a rise time of approximately 0.05s, a settling time between 0.2s and 0.3s and an overshoot of around 0.04M P a. A dead time of about 0.01s to 0.02s was also observed. It seems that the hydraulic line and the caliper acts as a lowpass filter, where the settling time of caliper pressure pc is approximately equal to the one of po .
The dynamic response when lowering the voltage from 8V ,9V , and 10V to 7V showed that both pc and po settles in approximately 0.2s without any overshoot.
B. Effect of Brake Disc Irregularities
Brake disc irregularities is caused by variations in the contact surface between the pads and the disc on the micro level[8]. Three experiments was conducted to see the effect of brake disc irregularity; one at 0 rpm, one at 200 rpm, and one at 400 rpm. The rotational speed was kept constant using the servo motor. In each experiment the valve voltage was set to 8V , 9V , and 10V while measuring the hydraulic pressure. The measurements at 200 rpm is shown in figure 5.
The disturbance from the brake disc is periodic with a frequency close to the frequency of the shaft rotation and as shown in the figure, it has a significant impact on the hydraulic pressure. At 200 rpm the disturbance affects the caliper pressure with an approximately constant value of about ±0.15M pa, whereas the disturbance effect at 400 rpm would depend slighty on the input voltage. To verify that the oscillations has a significant impact on the brake performance, the measured dynamic shaft torque from the experiments was also measured. It showed that in comparision with the motors maximum torque, of 147N m, the oscillations in the shaft torque of
±20N m where quit e significant.
Fig. 5: Pressure at 8V , 9V , and 10V , and rotational speed at 200 rpm
C. Overview of the Model
A mathematical model of the hydraulic system is developed to assist the design of a pressure controller. For this, a simple linear model with a constant input-equivalent disturbance and sinusoidal input to the caliper is proposed. The idea is to make a rough model and use real-time estimation of the disturbances to account for modelling errors and disturbance from the brake disc irregularities. A sketch of the model’s structure is illustrated in figure 6 and is based on experience from the experiments described above.
Fig. 6: Sketch of the model’s structure
By looking at figure 4 and neglecting the overshoot in rising direction, the model from both valve voltage to outlet pressure and outlet pressure to caliper pressure can be seen as first order systems. From the sketch it can be seen that the model has the following inputs, outputs, and states:
? 2 states: outlet pressure and caliper pressure; po and pc
? 1 output: caliper pressure; pc
? 1 controllable input: valve voltage; uv
? 2 uncontrollable inputs: constant disturbance and sinu- soidal disturbance; w1 and w2
The differential equations describing the model can then be expressed as eq. (1) and (2), where kpc is a constant related to the resistance of the hydraulic line and the volume of the caliper, kpo is related to the speed of the internal regulation in the valve while kdc is the steady state gain.
p&c = kpc g( po + w2 - Pc )
p&o = kpo × (kdc × (u + w1) - po ) + kpc × ( pc - po )
(1)
(2)
The model for the disturbance is based on eq. (3) and (4), which describe the two disturbance signals, where the constant ω0 is the frequency of the disturbance, that in turn is related to the brake disc irregularities. To use this model, the rotational speed has to be constant;
however, by extending the model to a nonlinear case where w0 is a function of rotational speed, this requirement could be dropped.
2 0 2
w&1 = 0
(3)
D. Plant Model
The state vector X is defined as
w&&
= -w 2 × w
(4)
X = é x1ù = é pc ù
êx2ú ê p ú
? ? ? o ?
to form a standard state space system for the plant of the form:
where:
X& = A× X + Bu ×u + Bw × w
y = C × X
(5)
(6)
u = u
- 7V ,
w = é w1 ù ,
y = é y1 ù = é pc ù
v êw ú ê y ú ê p ú
? 2 ? ? 2 ? ? o ?
Using eq. (1) and (2) yields the following system matrice
ê
A = é-kpc
k
kpc ù
-k - k ú
é 0 ù
Bu = êk × k ú
? pc pc po ? ? po dc ?
é
Bw = ê
?
0
k
po × kdc
kpc ù
0
ú
?
C = é1 0ù
ê0 1ú
? ?
By adding a delay of 0.02s and tuning the coefficients to match the real response, the following values are found:
kpc = 40 , kpo = 70 , kdc = 0.35
A simulation of the model with no disturbance, but include ing the 0.02s delay is seen in figure 7. Here it is compared to the real response of the hydraulic system and it is seen that the model resembles the system somewhat, but especially the overshoot is missing.
The missing overshoot in the model is however a deliberate choice, since there is no overshoot when applying a step in negative direction. The model is considered satisfactory seen in relation to its simplicity. However, there are features not captured by the model, these are: nonlinear steady-state gain; ripples on po during a step in position direction; second order behaviour of po during a step in positive direction; different dead-time at step responses in both positive and negative direction.
In order to produce the simulation shown in figure 7, the valve voltage was set to match the experiment and the disturbance input was set to zero. This means that a more realistic disturbance signal should be constructed, if the model should fit perfectly to the experimental data. w1 can be used to compensate for the input equivalent model error, while w2 can be used to compensate for errors that enters the model through pc .
Fig. 7: Comparison of real hydraulic system and model with 0.02s delay
Figure 8 shows step responses of the model at different valve voltages. A sinusiodal disturbance signal is applied through w2 , where the amplitude is constant but the frequency in the first plot corresponds to a rotational speed of 200 rpm and in the two last plots it corresponds to 400 rpm. It is seen that the response of the model shows the same features as figure 5.
Fig. 8: Comparison of simulated step responses using different w2 and input u
E. Disturbance Model
A model of the disturbance is made with the purpose of augmenting the plant model and estimate both the disturbance and the states, and thereby use a control algorithm for disturbance rejection.
The disturbance model has no input and it’s structure is seen in the following equations:
X˙ d = Ad ·Xd w = Cd ·Xd
where:
é x3 ù é w1 ù
é w ù
X = ê x ú = êw ú , w = 1
d ê 4 ú ê 2 ú
êw ú
ê x ú êw ú
? 2 ?
? 5 ? ? 3 ?
Eq. (3) and (4) describes w1 as a constant disturbance and w2 as a sinusdiodal disturbance with constant frequency and amplitude. These are used to form the system matrices of the disturbance model:
é0 0 0ù
ê ú
0
d
A = ê0 0 1ú ,
Cd =
é1 0 0ù
ê0 1 0ú
ê?0
-w 2
0ú? ? ?
where ω0 determines the frequency of w2 and the initial conditions determine the amplitude of w1 and w2 respectively
F. Augmented Model
The plant model is augmented with the disturbance with the purpose of using a disturbance rejection scheme, which will be described in section V.
The structure of the augmented model is seen in the following equations.
X˙ a = Aa · Xa + Ba · u y = Ca ·Xa
where:
é x1ù é pc ù
ê x ú ê p ú
ê 2 ú ê o ú
X a = ê x3 ú = ê w1 ú
ê x ú êw ú
ê 4 ú ê 2 ú
ê x ú êw& ú
And
é-k pc
? 5 ? ? 2 ?
k pc 0
k pc 0ù
ê k -k - k k gk 0 0ú
ê pc pc pc po dc ú
Aa = ê
ê
0 0 0 0 0ú
0 0 0 0 1ú
ê ú
o
?ê 0 0 0 -w 2 0ú?
é 0 ù
êk gk ú
ú
ê po dc ú
é1 0 0 0 0ù
Ba = ê 0
ê 0
ú , Ca = ê0 1 0 0 0ú
? ?
ê ú
?ê 0 ú?
IV. DISTURBANCE ESTIMATOR
A disturbance estimator is designed to estimate w1 and w2 in the augmented model. For that purpose, a current estimator with equations (7) and (8) is used. xˉ is the predicted states and x? is the current estimate, while Φ, Γ, and H are the discretized versions of Aa , Ba , and Ca respectively
x [k] = F × x?[k -1]+ G ×u [k -1]
x?[k ] = x [k ]+ Lc ×(y[k ]- H × x [k ])
(7)
(8)
The estimator gain Lc is designed by pole placement and the two dominant poles are:
z = 0.8673 ± 0.05554i
Figure 9 shows the estimated disturbances together with the measured pressure for a data set where the valve voltage is 10V and the rotational speed is 400 rpm.
Fig. 9: Estimation of disturbance signals during constant speed and constant valve voltage
A comparison of the measured pressure and the model described in eq. (5) and (6), is made by using the estimated disturbances (shown in figure 9) as input signals to the model. In the comparison, which is shown in figure 10, it is seen that a good estimation of the disturbance is obtained, since the output of the model fits the experimental data.
Fig. 10: Comparison of experimental data and simulation, where the estimated disturbance is used as
input for the simulation model.
V. DISTURBANCE REJ ECTION
A controller with disturbance rejection of w1 is designed, using the scheme shown in figure
11. The estimator described in the previous section is used together with an LQR controller. K is calculated by disregarding Bw , using eq. (5) and (6),and by using the following weightings:
ê0 1ú
R=0.1, Q = é5 0ù
? ?
It was found necessary to apply a low-pass filter to the estimation of w1 , before using it for control purposes, since it would induce oscillations in the control loop otherwise. A forth order Buttorworth filter with a cutoff frequency of 3H z was found suitable.
On figure 12 it is seen that the caliper pressure tracks the reference in an acceptable maner; this is also what was expected, since there should be no disturbance from w2 when the speed is 0 rpm and the estimation of w1 compensates for modelling errors. However, in figure 13, it is clear that the disturbance from w2 affects the performance of the controller and that this disturbance is not cancelled by the applied control scheme.
Fig. 11: Block diagram for input disturbance rejection [9]
Fig. 12: Performance of controller when speed is 0 rpm
VI. DISCUSSION
Fig. 13: Performance of controller when speed is 400 rpm
It is not possible to rewrite the disturbance from w2 to be input equivalent. Therefore, the control scheme applied in section V cannot be used to cancel that disturbance. However, by improving the disturbance model, it is believed that the disturbance from w2 can be integrated into the plant model and used when designing the controller. The work presented in this paper points toward making the frequency of w2 dependent on the shaft speed and creating an
amplitude modulation which is dependent on the brake pad’ position on the disc
VII. CONCLUSION
Through experiments it has been found that the disturbance from the brake disc/caliper to the hydraulic pressure is dependent on the shaft’s speed and the position of the brake pads on the disc. An estimator has been designed, which is proven succesfull in estimating the amplitude of this disturbance. The estimator uses a linear model, which is known to have some uncertainties that can be described as input equivalent disturbances. A disturbance rejection scheme has been applied to show that it is possible to reject the input equivalent disturbance. Future research should focus on obtaining a frequency and amplitude model of the disturbance from the brake disc/caliper, which can be used when designing a controller that controls the caliper pressure and cancels out disturbance from the brake disc/caliper.
REFERENCES
[1] AVN Energy A/S. Overview of nacelle internals
[2] A. Heege, J. Betran, and Y. Radovcic. Fatigue Load Computation of Wind Turbine Gearboxes by Coupled
[3] B. Schlecht and S. Gutt. Multibody-System-Simulation of Drive Trains of Wind Turbines. Fifth World Congress on Computational Mechanics.
[4] Ris? DTU. Endelig rapport for Ris? DTU’s unders?gelse af m?llehavarier pa? Vestas m?ller den 22. og 23. februar 2008. Technical report. 2008.
[5] Svendborg Brakes A/S. Hydraulic Braking System. US6254197B1. 2001.
[6] General Electric Company. Hydraulic Brake System for a Wind Energy Plant. US7357462B2. 2008.
[7] Nordex Energy GmbH. Wind Energy Plant with a Hydraulically Actuated Rotor Brake. US7494193B2. 2009.
[8] Mikael Eriksson. Friction and Contact Phenomena of Disc Brakes Related to Squeal.
Uppsala University, PhD thesis. 2000
[9] G. F. Franklin, J.D. Powell, and M.Workman Digital Control of Dynamic Systems. Pearson Education. 2006.
中文譯文
風(fēng)力渦輪機液壓制動的擾動控制
弗蘭克.杰普什 安德.伯格 楊振宇
（奧爾堡大學(xué)電子系統(tǒng)系 丹麥艾斯堡）
摘要：這篇論文討論了控制風(fēng)力渦輪機中盤式制動器的制動力矩問題。制動力矩是有摩擦系數(shù)和夾持力決定的，本文主要研究后者的影響。由于大多數(shù)盤式制動器是有液壓系統(tǒng)驅(qū)動的，因此，控制控制夾持力的關(guān)鍵是控制卡鉗壓力。將壓力控制器應(yīng)用在一個實驗室規(guī)模的測試系統(tǒng)上，通過使用干擾估計器消除擾動來跟蹤參考曲線。干擾估計器能夠同時估計輸入干擾和由于制動盤不平整所造成的干擾?？刂破髂軌蛞种戚斎胄盘柛蓴_，并提供了一種消除制動盤的干擾的方法。
一、簡介
機械制動器是風(fēng)力渦輪機的兩套獨立制動系統(tǒng)中的一套，由于風(fēng)力渦輪機中空間有限， 制動閘常安置在變速箱的高速軸上，以便節(jié)省空間，如圖 1 所示。然而這種設(shè)計的缺點就是，當制動器抱閘時，變速箱必須能夠很大的制動力矩。
圖 1 風(fēng)力渦輪機驅(qū)動鏈圖[1]
如今大多數(shù)風(fēng)力渦輪機使用液壓制動卡鉗以提供最大制動壓力。在文獻[2]中指出，此類制動系統(tǒng)制動時會對變速箱產(chǎn)生沖擊力，最終變速器產(chǎn)生的疲勞載荷會影響變速箱的使用壽命。
此外，文獻[3]中表明，當施加最大制動力矩時，在轉(zhuǎn)子軸上激起的振蕩其振幅幾乎是額定轉(zhuǎn)矩的產(chǎn)生的兩倍。因此，機械制動可能是導(dǎo)致大量變速箱故障的原因。最近發(fā)生在丹麥的 hornlet 市的變速箱損壞事故，就是由于機械制動系統(tǒng)[4]施加的載荷造成的。
近年來，一些如斯溫伯格制動器、通用電氣和恩德等的大公司開始對“軟制動”感興趣。這三家公司都已經(jīng)申請了如文獻[5]、[6]、[7]所描述的關(guān)于“軟制動系統(tǒng)”的專利。這三項專利都講到減少在緊急制動時施加的動態(tài)載荷峰值和振
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