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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.
文章写好了文献综述应该不难啊，其实就相当于你论文的第二章。常用的套路可以分四段写，第一段引言，介绍这个命题研究的目的意义之类的，第二段写国外对这个现象有哪些研究，评述其中重要的几个人或几个角度，第三段写国内的研究，这两段一般都按时间由远及近，第四段是一个小结，评述一下前人的研究贡献和不足之处，提出建议。其实也不用一定按照上面的来写，不过要注意一点就是要突出你自己的评述和见解，不要只是简单罗列或引用。
摘要]本文针对机械制造专业的特点，论述了建立以素质教育为目标的新课程体系的意义，分析了新课程体系的内涵，探讨了构建新课程体系的思路和目标要求。
[关键词]机械制造专业 课程体系 教学改革
机械制造专业是一个传统的工科专业，计算机的应用使机械制造业发生了根本性的变化，它渗透到从设计、工艺、制造、检测到经营管理的各个方面，构成了计算机集成制造。建立在信息技术和网络技术基础上的先进制造技术迅速发展，新的生产模式不断出现。现代制造业对人才的要求显然不同于传统机械制造业。因而，传统机械制造专业的教育体系，必须随时代的发展作相应的改革与调整。我们经过对相关企业广泛、深入的调研及几年来的教学实践和探索，根据对机械工程人才培养目标、教育模式的研究，构建出以素质教育为目标、以岗位技能要求为核心的课程体系。
一、构建新的课程体系是专业教学改革的需要
高校机械制造专业是培养机械行业研究、开发、生产、管理、服务第一线需要的工程技术人才。学校教学必须适应市场需求，积极主动地与市场经济接轨，培养职业类综合人才，随着市场经济体制的建立，科技进步和产业结构的调整，机械行业对高级应用型人才的综合能力要求越来越高，对复合型人才的要求越来越强。而反观传统的机械制造专业的培养模式、课程体系、教学方式，就会发现课程设置单一、知识面和专业面窄、课程难以形成完整的体系、教学内容陈旧、教学方法和教学手段落后等不足之处。为了改变这种状况，适应当今社会对机械工程专业人才的需求，培养出基础扎实、知识面宽、创造能力强、素质高的机械工程人才，调整教学内容，改革课程体系势在必行。
作为培养专门人才的高等学校，课程建设是最基本的教学建设。学生掌握专业知识和实践能力，是通过一系列课程的严格学习和训练来实现的。课程是决定教学质量的最基本的因素，课程的选择、课程的质量，直接影响培养目标的实现。目前我院机械类设置招生的本专科专业有：机械设计制造及其自动化、计算机辅助机械设计、机械制造与工艺设备、数控技术和机电一体化。为了使课程体系更好地适应专业整合与分流的要求，结合我们学校对大学一年级进行公共基础课通修的课程改革方案，针对机械类各专业的特点，在大学二年级开设专业基础课，然后按专业进行专业限修课和专业选修课的教学。实现课程教学的总体目标：形成良好的学风，打下坚实的基础，注重能力的培育，提供后续所需，培养高素质人才。
二、机械制造专业新课程体系的内涵
高等机械类教育是使学生获得机械工程师素质和技能的基本训练，能从事机械工程专业领域内的设计制造、科技开发、应用研究、运行管理和经营销售等方面的高等工程技术人才，即培养能将科学技术转化为生产力的机械工程技术人才。教育的核心是培养学生的整体素质和创新能力。要实现这一目标，就必须依据“重基础、宽口径、多方向、强应用”原则建立新的课程体系。
“重基础”是指重视学科基础，如高等数学、大学英语、计算机基础等要加强，只有这些基础夯实了，才能达到本科人才培养的要求，且有利于‘学生继续深造与知识更新；“宽口径”是由现代工程实践呈现知识的综合性和技术的交叉性所决定。就制造技术领域来看，学科交叉是先进制造技术发展的决定因素。先进制造技术不是指某项具体技术，而是一个综合的系统技术，是传统制造技术与基础科学、管理学、人文社会学和工程技术等领域的最新成果、理论、方法有机结合产生的适应未来制造的前沿技术的总称。它具有综合性、系统性、先进性、创新性、敏捷性、可持续性等特征与丰富内涵，并将发展成为集机械、电子、信息、材料和管理等学科于一体的新兴交叉学科。学科的发展要求现代工程师的知识宽口径；“多方向”是指每个专业有四个以上可供学生选择的专业方向，使学生学有专长，人人都有精于某道的“看家本领”；“强应用”是应用型本科对培养人才的基本要求和特色所在，要求培养的学生毕业后能在生产一线上手快，解决工程实际问题的能力强。
三、机械制造专业新课程体系的构建
新的课程体系的构建，必须根据机械制造专业培养目标定位和专业应用型人才的知识结构要求，并遵循“重基础、宽口径、多方向、强应用”的原则，设置公共基础课、专业理论课和专业技能课。
1．公共基础课。公共基础课程的设置不是针对．某一单一专业，而是针对相关职业岗位群所必需的知识和技能，注意培养学生的基本素质，着眼于学生的可持续发展，着眼于为学生继续学习打基础，着眼于专业技能的训练，着眼于转岗能力和关键能力的培养，使学生获得较宽厚的公共基础学科、专业基础学科的知识。公共基础课由文化课程类、工具课程类、能力培养课程类构成。文化课程类包括政治、高等数学(含工程数学)、大学物理和体育等课程。文化课程是所有工科专业学生必须学习的重要基础，是学习专业和提高文化素质的需要。工具课程类包括英语和计算机课程。随着科技发展的信息化、国际化，外语、计算机作为一种必不一可少的工具已日益突出。外语应全面加强读、写、听、说能力的培养，计算机应注重应用能力的培养。我院在教学管理中已明确要求学生需获得英语四级以上等级证书和全国计算机三级以上等级证书。能力培养课程类包括法律基础、职业道德、经济管理、文献检索及科技论文写作等课程，可根据学生个人兴趣选修其中的若干门课程。这类课程主要是培养学生的综合能力和综合素质。
2．专业理论课。专业理论课包括专业必修课和专业选修课，理论课的设置应以“适度、适应”为标尺，既不能片面追求学科知识的广搏，也不能片面追求单一职业技能的精深，应尽力在有限的教育教学时间中发挥课程学习的最大效益。机械类各专业的理论课程，包括机械设计模块、机械制造模块、机电测控模块和数控技术模块、基本技能模块。所设课程如文末附表所示。
3．专业技能课。专业技能课主要是培养学生的基本专业技能，教学环节包括专业理论课的课内实验、基本技能课、专业技能课、集中实践、毕业设计与实训等。各实践教学环节应达到的技能要求：钳工技能实训要求学生掌握钳工的基本技能；金工实习 (热加工)要求学生掌握热加工的基本方法、特点和作用；机加工技能(车或铣)实训要求学生掌握车床 (铣床)操作；机床精度检测要求学生掌握普通机床精度检测方法及仪表使用；数控编程与操作要求学生掌握数控编程方法及数控机床操作；生产实习要求学生了解生产现场的生产组织、技术管理及典型零件制造的全过程；机械零件课程设计要求学生掌握常用机构和通用零件的工作原理，基本设计和计算方法，会使用手册查阅参数；机械制造课程设计要求学生掌握典型设计、数控编程、机床调整及维修技术，得到较为全面的综合训练，提高学生的解决工程实际问题和创新能力。
机械制造专业的教学改革，必须紧跟机械制造行业的发展，突出工程技术教育的特点，同时要面向市场需求，立新求精，动态改革，力求培养出具有良好综合素质、体现行业特色、具有创新能力的复合型、应用型专业人才。在我院机械类专业教学改革中，我们借鉴了现代集成制造系统中的创新思想、系统理论、优化方法等先进理论，从整体到局部，从教学目标到教学实施，从宏观培养目标到教学保障体系进行了全面改革，取得了良好的效果。
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[2]刘迎春，宁立伟，邓奕等．应用型本科机械设计制造及其自动化专业人才培养课程体系的研究 [J]．湖南工程学院学报，2004，14(3)：59-62．
[3]李焕锋，刘自然．适应先进制造技术发展深化机械类专业教学改革[J]．郑州工业高等专科学校学报，2004，20(2)：50—52．
