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Sensorless torque control scheme of
induction motor for hybrid electric vehicle
Yan LIU 1,2, Cheng SHAO1
(1.Research Institute of Advanced Control Technology, Dalian University of Technology, Dalian Liaoning 116024, China;
2.School of Information Engineering of Dalian University, Dalian Liaoning 116622, China)
Abstract: In this paper, the sensorless torque robust tracking problem of the induction motor for hybrid electric vehicle
(HEV) applications is addressed. Because motor parameter variations in HEV applications are larger than in industrial
drive system, the conventional field-oriented control (FOC) provides poor performance. Therefore, a new robust PI-based
extension of the FOC controller and a speed-flux observer based on sliding mode and Lyapunov theory are developed in
order to improve the overall performance. Simulation results show that the proposed sensorless torque control scheme is
robust with respect to motor parameter variations and loading disturbances. In addition, the operating flux of the motor is
chosen optimally to minimize the consumption of electric energy, which results in a significant reduction in energy losses
shown by simulations.
Keywords: Hybrid electric vehicle; Induction motor; Torque tracking; Sliding mode
1 Introduction
Being confronted by the lack of energy and the increasingly
serious pollution, the automobile industry is seeking
cleaner and more energy-efficient vehicles.A Hybrid Electric
Vehicle (HEV) is one of the solutions. A HEV comprises
both a Combustion Engine (CE) and an Electric Motor
(EM). The coupling of these two components can be in
parallel or in series. The most common type of HEV is the
parallel type, in which both CE and EM contribute to the
traction force that moves the vehicle. Fig1 presents a diagram
of the propulsion system of a parallel HEV [1].
Fig. 1 Parallel HEV automobile propulsion system.
In order to have lower energy consumption and lower pollutant
emissions, in a parallel HEV the CE is commonly
employed at the state (n > 40 km/h or an emergency speed
up), while the electric motor is operated at various operating
conditions and transient to supply the difference in torque
between the torque command and the torque supplied by
the CE. Therefore fast and precise torque tracking of an EM
over a wide range of speed is crucial for the overall performance
of a HEV.
The induction motor is well suited for the HEV application
because of its robustness, low maintenance and low
price. However, the development of a drive system based
on the induction motor is not straightforward because of the
complexity of the control problem involved in the IM. Furthermore,
motor parameter variations in HEV applications
are larger than in industrial drive system during operation
[2]. The conventional control technique ranging from the
inexpensive constant voltage/frequency ratio strategy to the
sophisticated sensorless control schemes are mostly ineffective
where accurate torque tracking is required due to their
drawbacks, which are sensitive to change of the parameters
of the motors.
In general, a HEV operation can be continuing smoothly
for the case of sensor failure, it is of significant to develop
sensorless control algorithms. In this paper, the development
of a sensorless robust torque control system for HEV
applications is proposed. The field oriented control of the induction
motor is commonly employed in HEV applications
due to its relative good dynamic response. However the classical
(PI-based) field oriented control (CFOC) is sensitive to
parameter variations and needs tuning of at least six control
parameters (a minimum of 3 PI controller gains). An improved
robust PI-based controller is designed in this paper,
Received 5 January 2005; revised 20 September 2006.
This work was supported in part by State Science and Technology Pursuing Project of China (No. 2001BA204B01).
Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46 43
which has less controller parameters to be tuned, and is robust
to parameter variation.The variable parameters model
of the motor is considered and its parameters are continuously
updated while the motor is operating. Speed and
flux observers are needed for the schemes. In this paper,
the speed-flux observer is based on the sliding mode technique
due to its superior robustness properties. The sliding
mode observer structure allows for the simultaneous observation
of rotor fluxes and rotor speed. Minimization of the
consumed energy is also considered by optimizing operating
flux of the IM.
2 The control problem in a HEV case
The performance of electric drive system is one of the
key problems in a HEV application. Although the requirements
of various HEV drive system are different, all these
drive systems are kinds of torque control systems. For an
ideal HEV, the torque requested by the supervisor controller
must be accurate and efficient. Another requirement is to
make the rotor flux track a certain reference λref . The reference
is commonly set to a value that generates maximum
torque and avoids magnetic saturation, and is weakened to
limit stator currents and voltages as rotor speed increases.
In HEV applications, however, the flux reference is selected
to minimize the consumption of electrical energy as it is one
of the primary objectives in HEV applications. The control
problem can therefore be stated as the following torque and
flux tracking problems:
min
ids,iqs,we Te(t) − Teref (t), (1)
min
ids,iqs,we λdr(t) − λref (t), (2)
min
ids,iqs,we λqr(t), (3)
where λref is selected to minimize the consumption of electrical
energy. Teref is the torque command issued by the
supervisory controller while Te is the actual motor torque.
Equation (3) reflects the constraint of field orientation commonly
encountered in the literature. In addition, for a HEV
application the operating conditions will vary continuously.
The changes of parameters of the IM model need to be accounted
for in control due to they will considerably change
as the motor changes operating conditions.
3 A variable parameters model of induction
motor for HEV applications
To reduce the elements of storage (inductances), the induction
motor model used in this research in stationary reference
frame is the Γ-model. Fig. 2 shows its q-axis (d-axis
are similar). As noted in [3], the model is identical (without
any loss of information) to the more common T-model in
which the leakage inductance is separated in stator and rotor
leakage [3]. With respect to the classical model, the new
parameters are:
Lm = L2
m
Lr
= γLm, Ll = Lls + γLlr,
Rr = γ2Rr.
Fig. 2 Induction motor model in stationary reference frame (q-axis).
The following basic w−λr−is equations in synchronously
rotating reference frame (d - q) can be derived from the
above model.
⎧⎪
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
dλdr
dt
= −ηλdr + (we − wr)λqr + ηLmids,
dλqr
dt
= −(we − wr)λdr − ηλqr + ηLmiqs,
dids
dt
= ηβλdr+βwrλqr−γids+weiqs+
1
σLs
Vds,
diqs
dt
=−βwrλdr+ηβλqr−weids−γiqs+
1
σLs
Vqs,
dwr
dt
= μ(λdriqs − λqrids) −
TL
J
,
dθ
dt
= wr + ηLm
iqs
λdr
= we,
Te = μ(λdriqs − λqrids)
(4)
with constants defined as follows:
μ = np
J
, η = Rr
Lm
, σ = 1−
Lm
Ls
, β =
1
Ll
,
γ = Rs + Rr
Ll
, Ls = Ll + Lm,
where np is the number of poles pairs, J is the inertia of the
rotor. The motor parameters Lm, Ll, Rs, Rr were estimated
offline [4]. Equation (5) shows the mappings between the
parameters of the motor and the operating conditions (ids,
iqs).
Lm = a1i2
ds + a2ids + a3, Ll = b1Is + b2,
Rr = c1iqs + c2.
(5)
4 Sensorless torque control system design
A simplified block diagram of the control diagram is
shown in Fig. 3.
44 Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46
Fig. 3 Control structure.
4.1 PI controller based FOC design
The PI controller is based on the Field Oriented Controller
(FOC) scheme. When Te = Teref, λdr = λref , and
λqr = 0 in synchronously rotating reference frame (d − q),
the following FOC equations can be derived from the equations
(4).
⎧⎪
⎪⎪⎪⎪⎪⎨⎪
⎪⎪⎪⎪⎪⎩
ids = λref
Lm
+ λref
Rr
,
iqs = Teref
npλref
,
we = wr + ηLm
iqs
λref
.
(6)
From the Equation (6), the FOC controller has lower performance
in the presence of parameter uncertainties, especially
in a HEV application due to its inherent open loop
design. Since the rotor flux dynamics in synchronous reference
frame (λq = 0) are linear and only dependent on the
d-current input, the controller can be improved by adding
two PI regulators on error signals λref − λdr and λqr − 0 as
follow
ids = λref
Lm
+ λref
Rr
+ KPd(λref − λdr)
+KId (λref − λdr)dt, (7)
iqs = Teref
npλref
, (8)
we = wr + ηLm
iqs
λref
+ KPqλqr + KIq λqrdt. (9)
The Equation (7) and (9) show that current (ids) can control
the rotor flux magnitude and the speed of the d − q rotating
reference frame (we) can control its orientation correctly
with less sensitivity to motor parameter variations because
of the two PI regulators.
4.2 Stator voltage decoupling design
Based on scalar decoupling theory [5], the stator voltages
commands are given in the form:
⎧⎪
⎪⎪⎨⎪⎪⎪⎩
Uds = Rsids − weσLsiqs = Rsids − weLliqs,
Uqs = Rsiqs + weσLsids + Lm
Lr
weλref
= Rsiqs + weσLsids + weλref .
(10)
Because of fast and good flux tracking, poor dynamics decoupling
performance exerts less effect on the control system.
4.3 Speed-flux observer design
Based on the theory of negative feedback, the design of
speed-flux observer must be robust to motor parameter variations.
The speed-flux observer here is based on the sliding
mode technique described in [6∼8]. The observer equations
are based on the induction motor current and flux equations
in stationary reference frame.
⎧⎪
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
d˜ids
dt
= ηβ˜λdr + β ˜ wr˜λqr − γ˜ids +
1
Ll
Vds,
d˜iqs
dt
= −β ˜ wr˜λdr + ηβ˜λqr − γ˜iqs +
1
Ll
Vqs,
d˜λdr
dt
= −η˜λdr − ˜ wr˜λqr + ηLm
˜i
ds,
d˜λqr
dt
= ˜wr˜λ dr − η˜λqr + ηLm
˜i
qs.
(11)
Define a sliding surface as:
s = (˜iqs − iqs)˜λdr − (˜ids − ids)˜λqr. (12)
Let a Lyapunov function be
V = 0.5s2. (13)
After some algebraic derivation, it can be found that when
˜ wr = w0sgn(s) with w0 chosen large enough at all time,
then ˙V = ˙s · s 0. This shows that s will converge to
zero in a finite time, implying the stator current estimates
and rotor flux estimates will converge to their real values
in a finite time [8]. To find the equivalent value of estimate
wr (the smoothed estimate of speed, since estimate wr is a
switching function), the equation must be solved [8]. This
yields:
˜ weq = wr
˜λ
qrλqr + λdr˜λdr
˜λ
2q
r +˜λ2
dr −
η
np
˜λ
qrλdr − λqr˜λdr
˜λ
2q
r +˜λ2
dr
. (14)
The equation implies that if the flux estimates converge to
their real values, the equivalent speed will be equal to the
real speed. But the Equation (14) for equivalent speed cannot
be used as given in the observer since it contains unknown
terms. A low pass filter is used instead,
˜ weq =
1
1 + s · τ
˜ wr. (15)
Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46 45
The same low pass filter is also introduced to the system
input,which guarantees that the input matches the feedback
in time.
The selection of the speed gain w0 has two major constraints:
1) The gain has to be large enough to insure that sliding
mode can be enforced.
2) A very large gain can yield to instability of the observer.
Through simulations, an adaptive gain of the sliding
mode observer to the equivalent speed is proposed.
w0 = k1 ˜ weq + k2. (16)
From Equation (11), the sliding mode observer structure
allows for the simultaneous observation of rotor fluxes.
4.4 Flux reference optimal design
The flux reference can either be left constant or modified
to accomplish certain requirements (minimum current,
maximum efficiency, field weakening) [9,10]. In this paper,
the flux reference is chosen to maximum efficiency at steady
state and is weaken for speeds above rated. The optimal efficiency
flux can be calculated as a function of the torque
reference [9].
λdr−opt = |Teref| · 4Rs · L2r
/L2
m + Rr. (17)
Equation (17) states that if the torque request Teref is
zero, Equation (8) presents a singularity. Moreover, the
analysis of Equation (17) does not consider the flux saturation.
In fact, for speeds above rated, it is necessary to
weaken the flux so that the supply voltage limits are not exceeded.
The improved optimum flux reference is then calculated
as:
⎧⎪
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
λref = λdr-opt,
if λmin λdr-opt λdr-rated ·
wrated
wr-actual
,
λref = λmin, if λdr-opt λmin,
λref = λdr-rated ·
wrated
wr-actual
,
if λdr-opt λdr-rated ·
wrated
wr-actual
.
(18)
where λmin is a minimum value to avoid the division by
zero.
4.5 Simulations
The rated parameters of the motor used in the simulations
are given by
Rs = 0.014 Ω, Rr = 0.009 Ω, Lls = 75 H,
Llr = 105 H, Lm = 2.2 mH, Ls = Lls + Lm,
Lr = Llr + Lm, P = 4, Jmot = 0.045 kgm2,
J = Jmot +MR2
tire/Rf, ρair = 1.29, Cd = 0.446,
Af = 3.169 m2, Rf = 8.32, Cr = 0.015,
Rtire = 0.3683 m, M = 3000 kg, wbase = 5400 rpm,
λdr−rated = 0.47 Wb.
Fig.4 shows the torque reference curve that represents
typical operating behaviors in a hybrid electric vehicle.
Fig. 4 The torque reference curve.
Load torque is modeled by considering the aerodynamic,
rolling resistance and road grade forces. Its expression is
given by
TL = Rtire
Rf
(
1
2ρairCdAfv2 +MCr cos αg +M sin αg).
Figures in [5∼8] show the simulation results of the
system of Fig.3 (considering variable motor parameters).
Though a small estimation error can be noticed on the observed
fluxes and speed, the torque tracking is still achieved
at an acceptable level as shown in Figs. [5, 6, 8]. The torque
control over a wide range of speed presents less sensitivity
to motor parameters uncertainty.
Fig.5 presents the d and q components of the rotor flux.
Rotor flux λr is precisely orientated to d-axis because of the
improved PI controllers.
Fig.8 shows clearly the real and observed speed in the
different phases of acceleration, constant and deceleration
speed with the motor control torque of Fig.4. The variable
model parameters exert less influence on speed estimation.
Fig.7 shows the power loss when the rotor flux keeps constant
or optimal state. A significant improvement in power
losses is noticed due to reducing the flux reference during
the periods of low torque requests.
Fig. 5 Motor rotor flux λr.
46 Y. LIU et al. / Journal of Control Theory and Applications 2007 5 (1) 42–46
Fig. 6 Motor torque.
Fig. 7 Power Losses.
Fig. 8 Motor speed.
5 Conclusions
This paper has described a sensorless torque control system
for a high-performance induction motor drive for a
HEV case. The system allows for fast and good torque
tracking over a wide range of speed even in the presence of
motor parameters uncertainty. In this paper, the improved
PI-based FOC controllers show a good performance in the
rotor flux λdr magnitude and its orientation tracking. The
speed-flux observer described here is based on the sliding
mode technique, making it independent of the motor parameters.
Gain adaptation of the speed -flux observer is used to
stabilize the observer when integration errors are present.
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浅谈山区桥梁高墩施工的质量控制
为达到质量要求所采取的作业技术和活动称为质量控制。这就是说，质量控制是为了通过监视质量形成过程，消除质量环上所有阶段引起不合格或不满意效果的因素。以达到质量要求，获取经济效益，而采用的各种质量作业技术和活动。下面我为大家带来一篇关于浅谈山区桥梁高墩施工的质量控制
论文摘要: 随着我国社会主义经济的发展和科技水平的普遍提高，我国不断加大对山区桥梁的投入建设，并且在近几十年里取得了重大成就，但同时不能忽视的是由于山区地势地形复杂，山区桥梁的建设还存在众多的隐患，如何不断提高山区桥梁质量，是目前急需思考和解决的问题。本文就针对这一问题，从目前山区桥梁高墩施工中存在的不足入手，继而指出影响山区桥梁高墩施工质量的因素，最后就如何加强山区桥梁高墩施工的质量控制提出几点建议。
关键词: 山区桥梁;高墩施工;质量控制
众所周知，桥梁的建设对促进一个国家的政治经济文化有着不容忽视的作用，在充分开发国土资源，合理布局生产力，不断改善国际国内的投资环境等各个方面发挥着重要的作用。我国山区的桥梁建设更是在加强区域合作发展，提高山区人们的生活水平方面产生重要影响。近些年来，随着经济的发展，国家对山区桥梁的质量安全提出了更高的要求，这将有助于进一步发展我国基础工程设施，将工业化和信息化更有力的`向前推进。
一、山区桥梁高墩施工现状桥梁在进行高墩施工的过程中，本身就很容易出现竖向的中轴线呈现S 形的情况，对人们的生命财产安全产生极大的威胁。
一般来说，出现这种情况的原因在于桥梁高墩的节数过多，因为节数越多，墩柱越高，越容易产生这种状况。在平原地形下的桥梁高墩施工还不时出现这种情况，山区的桥梁高墩施工更是面临着严峻的挑战。此外，在施工的具体过程中，在模板安装、振捣等其它多种因素的影响下，有可能发生竖向中轴线偏离施工控制轴线的危险局面。我们一方面应该充分肯定近几十年来，山区桥梁取得的伟大成就，但绝不能忽视其存在的潜在威胁。当然，出现这一问题是由多方面因素共同作用而成，如何加强山区桥梁高墩施工的质量控制是当前桥梁施工需要解决的问题。
二、影响山区桥梁高墩施工质量的因素
(一)施工人员自身素质的因素人是所有实践活动的主体，因此在影响山区桥梁高墩施工质量的因素中，最首要最活跃的就是施工人员的意识和综合素质的原因。首先是施工人员的综合素质不高，责任意识不强，不能充分认识到山区桥梁的高墩施工安全的重要性。加上相关管理人员在桥梁高墩施工的过程中，只追求速度，不讲究质量，造成在设计和选料方面都没有经过仔细的实践调查。其次是施工人员的专业素质较差，对山区桥梁高墩施工的关键技术不能够熟练掌握和灵活运用，专业知识不扎实，十分不利于桥梁高墩施工的质量控制。
(二)地理环境因素据相关数据统计，有至少一半的交通安全事故是地理环境造成的，山区的桥梁高墩施工在地形地貌方面面临着巨大的挑战。
众所周知，我国山区地形落差大，垂直海拔较高，地质结构复杂，此外还不时发生狂风、暴雨、泥石流等自然灾害，给山区的桥梁施工带来了巨大的困难。具体来说，山区的桥梁工程有其自身的特征，其中最明显的一点就是桥梁的墩柱高度落差十分明显，在某些地方甚至达到几十米，施工难度巨大。由于山区的桥梁施工环境十分恶劣，且施工作业的机械化程度较低，这就需要施工人员耗费大量的体力。
三、山区桥梁高墩施工的质量控制措施
(一)制定严格的山区桥梁高墩施工规范要想真正保证施工工程的质量就必须严格遵守和贯彻国家规定的强制性的相关法律法规和行业标准，规范施工的流程。在山区桥梁高墩施工之前，各个部门应该做好全方位的准备工作，只有这样才能有效保证施工工程的顺利开展。高墩施工部门首先要对施工的全体工作进行全面了解，从而逐渐适应具体的自然环境和施工环境，其次要针对桥梁施工过程中可能遇到的突发情况，做出相应的预防措施。
(二)加强对山区桥梁高墩施工的技术控制桥梁高墩施工的质量控制首先应该严格控制原材料的质量，对于水泥、碎石和钢材这类的主要原材料应该严格按照业主准入厂家进行购买。其次，在钢筋的制作和安装控制中，应该满足材料技术的要求，在钢筋绑扎成形时，必须把扎丝扎紧，不允许出现折断或位移的现象。为了方便桥梁高墩施工，在制作钢筋的时候，应该依据规定的要求，控制好断面钢筋接头的钢筋长度和数量，以达到满足外观需要和设计规范的要求。施工中应加强测量监控及试验检测工作，控制好墩身的垂直度。
(三)爬模、滑模和翻模技术在山区桥梁高墩施工中的运用我国在桥梁高墩施工的过程中，一般采用爬模、滑模和翻模这三种施工技术。这三个施工工艺各有优缺点，在施工中，应从安全、质量、经济这三个方面去详细的比较论证，选择切实符合现场实际情况的施工工艺，并对高墩的施工安全技术方案进行专家评审论证，保证施工方案的安全性和可操作性。
结语：
综上所述，山区的桥梁高墩施工的质量控制是一项具体而繁琐的工程，需要施工单位人员具备较高的专业技术素质和良好的安全责任意识，还能够不断学习新的与山区桥梁高墩施工相关技术，并巧妙地运用到具体的实践中去。总之，山区桥梁高墩施工的质量控制是一项艰巨的任务，需要从制度、人才和环境等多面进行逐步的创新和改革，只有这样才能够不断加强山区桥梁高墩施工的质量控制。
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