Embed Size (px)
Citation preview
Speed-sensorless control of induction motors:trends and perspectives
Marcello Montanari
Center for Research on Complex Automated Systems (CASY)Department of Electronics, Computer Science and Systems (DEIS)
University of Bologna
Bologna
2
Outline• Introduction• Induction motor (IM) model and general definitions • Control requirements
– Speed/flux amplitude control– Concept of field orientation
• Speed/flux estimation– Observability properties of IM– Lack of observability at zero frequency
• Speed sensorless control approaches– Full-order observer– Reduced-order observer– Observerless controller
• Speed sensorless control of IM based on high-gain speed observer– Main features– Experimental and simulation results
• Concluding remarks
3
Control of induction motors
• Low-performance IM drives: V/f control strategy– Open-loop control
• Control design based on simplified steady-state IM model
• Frequency/amplitude of the applied stator voltages are adjusted depending only on the desired speed
• Low-performances:
– Highly nonlinear dynamical model
– Poor speed regulation and torque rejection capability
– Slow dynamic performance
– Reduced range of operating conditions (e.g. at low speed, high torques)
4
Control of induction motors
• High performance IM drives• Feedback controllers based on measurements of
– Stator currents
– Speed/position
• Speed/flux trajectory tracking with high dynamics
• Large bandwidth torque disturbance rejection
• “Safe” behavior in a wide range of operating conditions
– speed range from standstill up to 200% rated speed
– load and regenerative torque up to 500% rated value
5
High performance IM controllers
• Field oriented (FO) control– Standard IFOC
[Ortega & Taoutaou, TAC 1996], [Peresada et al., Power Elec. 2003]
– Improved IFOC [Peresada & Tonielli, IJAC&SP 2000]
• Feedback linearization– [Kim et al., IJC 1990],
[Marino, Peresada, Valigi, TAC 1993]
• Passivity based– [Ortega et al., Automatica 1996]
• Direct Torque Control– [Vas, Oxford Univ. Press 1998]
• …
6
Speed sensorless control of induction motors
• Induction motor drive:– without mechanical sensor (for speed/position measurement)– with medium/high dynamic performance
• Main objective: minimize performance degradation with respect to classical IM controllers with speed sensor
– Advantages• Reduced hardware complexity, reduced size, no sensor cable• Increased reliability, less maintenance requirements• Lower cost• Better noise immunity
7
Applications of speed-sensorless controlled IM motors
• Speed regulation/load torque rejection– Pumps, fans, compressors
– Electric vehicles, trolleys
– Belt conveyors
• Low (or medium) performance speed tracking – Cranes, lifts
– Simple manufacturing machines
• Trends:– Better accuracy
– Increased bandwidth
– Wider operating conditions
8
Two-phase IM model in the stationary reference frame (a,b)
• State variables:
– Stator currents ia, ib– Rotor fluxes ψa, ψb
– Rotor speed ω
• Control inputs:
– Stator voltages ua, ub
• Disturbance input:
– Load torque TL
IM electromagnetic/mechanical parameters:
9
Speed/flux control requirements
• Speed control– Asymptotic tracking of smooth speed reference trajectory ω*
• Rejection of load torque disturbance
• Arbitrarily selectable bandwidth of the speed control loop
10
Speed/flux control requirements
• Flux (amplitude) control– Asymptotic tracking of smooth flux amplitude reference trajectory
ψ*>0 (normally constant ψ*)
• Variable flux:
– For efficiency/energy purposes
– In the field weakening regime
– To ensure persistency of excitation of estimation methods– avoidance of “unsafe” operating conditions (e.g. dc
excitation)
– e.g. for simultaneous speed/rotor resistance
11
Concept of field orientation (F.O.)
• Time-varying state space transformation– Equivalent to define a rotating reference frame (d,q) with angular
position ε0 w.r.t. the stationary reference frame
– How to design ε0 (or equivalently ω0)?
�
�
��
ε0 ,ω0
12
IM model in the generic rotating (d,q) reference frame
• State variables : id, iq, ψd, ψq, ω• Control inputs: ud, uq, ω0
• Disturbance: TL
13
Field orientation principle• Decoupling between speed/flux subsystems
– The IM behaves “similarly” to a dc motor with separated excitation
– Motor torque is proportional to iq (if ψd=const)– Flux dynamics is not perturbed by the mechanical one
• Field orientation requirement– Rotating reference frame with the d-axis aligned with the rotor flux
vector
IM torque
14
Perfect field orientation
• flux control
Torque/flux coupling terms
• Torque/speed control
IM torque
• Decoupled speed/flux control• Inner loops for d-axis (flux) and q-axis (torque) current control
15
Direct/indirect field orientation• Perfect field orientation is achievable only with known rotor flux vector
• Direct field orientation
– Based on measurement (or estimation) of the rotor flux vector, independently of the controller
– Not trivial stability proof for the full-order controller and observer dynamics
• Indirect field orientation
– Asymptotic field orientation is achieved without flux vector measurement or estimation
– Stability is guaranteed through the design of a proper output feedback controller
16
Sensorless control of IM
• Control requirements are identical to those of standard IM control– Controlled outputs: ω, ψd, ψq
– Control inputs: ud, uq, ω0 (with indirect FO approach)
• Assumptions:– Measured stator currents: ia, ib (i.e. id, iq)
– other “technical” assumptions:• Known smooth speed/flux references
• Known constant IM parameters
17
IM state estimation – case 1
• Rotor flux/stator current observer assuming– Measured (and bounded) speed
– (Unknown load torque)
– No measurements of stator current/rotor flux
– Unknown initial conditions for id, iq, ψd, ψq
18
IM state estimation – case 1
Linear time-varying electromagnetic dynamics
Rotor flux/stator current observer
19
IM state estimation – case 1
• Global asymptotic stability of the error model, thanks to passivity properties of the E.M. dynamics
Estimation error model
20
IM state estimation – case 2
• Speed estimation under hypothesis of– Known stator currents and voltages
– Unknown rotor flux and speed
• Practically achievable hypothesis for speed sensorless controlled IM
• Observability/detectability properties of IM– See [Canudas De Wit et al., CDC 2000], [Ibarra-Rojas et al.,
Automatica 2004], [Holtz, Proc. IEEE 2002]
– Existence of indistinguishable trajectories with particular control inputs (i.e. internal trajectories that are different under the same input/output behavior)
– Speed sensorless controlled IM is not globally (or locally) observable/detectable through stator currents
21
IM state estimation – case 2
• IM is not observable with zero excitation frequency (i.e. with ω0=0)
– Zero excitation frequency corresponds to• Zero speed operation with null load torque• Regenerative mode (i.e. speed and torque are opposite in sign)
22
IM state estimation – case 2 physical interpretation
• State-space transformation with variables proportional to stator fluxes
• IM model
• During dc excitation, constant stator voltages (ua, ub) are applied, i.e.– ω0=0, ud=const, uq=const
• Steady-state behavior– constant stator currents, independently of stator flux and speed dynamics– No information from stator currents and voltages for speed estimation
23
IM state estimation – case 2 physical interpretation
• Steady-state behavior with dc exctitation:
– Lack of speed information in the back-emf signal
– Speed observers based on the back-emf signal (IM electromagneticenergy conversion) fail to work at zero frequency
24
IM state estimation – case 3A• Speed observer based on
1. known stator current and rotor flux
2. known load torque
� known time derivative of the speed dynamics
• Adaptive speed observer based on current/flux tracking errors
– Speed estimation and control with global stability properties
– [Marino et al., IFAC 2002, Automatica 2004]
25
IM state estimation – case 3B• Speed observer based on
1. known stator current and rotor flux2. unknown load torque
• Adaptive speed observer based on current tracking errors
• Standard indirect field oriented control
– Speed estimation and control with local stability properties
• [Montanari et al., ECC 2003]
26
IM state estimation – case 3• Assumption of known flux is not practically achievable.
However, it is equivalent to assume not measurable rotor flux, but with known initial conditions
– Rotor flux estimation can be performed through the “stator flux model”
• Robustness issues related to open-loop pure integration– Drift problems due to measurement offset, distortion of voltage actuation,
etc.
– Sensitivity to IM electrical parameter knowledge
27
Speed sensorless controllers: literature overview
• Known load torque and rotor flux
– Semiglobal exponential speed/flux tracking [Dawson et al., CST 2001]
– Adaptive controller with global exponential speed/flux tracking properties [Marino et al., Automatica 2004]
• Known rotor flux initial conditions, unknown load torque
– Adaptive observer/controller with local stability property [Montanari et al., ACC 2003, ECC 2003]
• Known load torque, unknown rotor flux
– Adaptive observer/controller with local stability property [Montanari et al., CDC 2004]
• Unknown load torque and rotor flux
– Sliding mode torque/flux control with sliding mode speed observer with local stability properties [Utkin et al., Ind.Elec. 2000]
– Sensorless IFOC with two-time scale separation with local stability properties [Montanari et al., IECON 2002]
28
Speed sensorless control approaches
• Full-order observer– E.g. MRAS, adaptive, Luenberger-like, sliding-mode observers,
Kalman Filter
IM
Observer
Controller
ω∗, ψ∗ uω, ψ
i
u
29
Speed sensorless control approaches
• Full-order observer– Estimation of speed/rotor flux/(stator current)
• Observer design independent of the control
• Full state estimation is not strictly necessary– E.g. flux tracking can be guaranteed thanks to stability properties of
the IFO-controlled IM without flux measure/estimation
• High computational burden and overall controller complexity
– Direct or indirect FO control architecture• Issues related to stability of the full-order error dynamics
– separation principle for nonlinear time-varying system
30
Speed sensorless control approaches
• Reduced-order observer– Adaptive control techniques exploited for the controller/observer
design
– E.g. [Marino et al., Automatica 2004], [Montanari et al. IECON 2002, ACC 2003, ECC 2003, CDC 2004]
IM
Observer
Controller
ω∗, ψ∗ u ω, ψ
ii*
31
Speed sensorless control approaches• Reduced-order observer
– The observer is embedded in the controller• Reduced number of state estimations is necessary (e.g. only
speed)• Speed estimation can be achieved since, when speed is not
correctly estimated, imperfect speed tracking causes imperfect vector flux regulation and hence non-null current tracking errors
• Adaptation law based on current tracking errors (essentially, itrelies on the estimation of back-emf signal βωψd perturbing the q-axis current dynamics)
• Observer and controller must be designed in a joined way• Simple controller/observer structure• Stability properties more related to the physical behavior of the
IM
• Lack of control at zero frequency if the stator flux model is not exploited, due to observability properties of the IM
32
Speed sensorless control of IM based on high-gain speed estimation
• No exploitation of the stator flux model for state estimation– Rotor/stator flux are not estimated
• “true” speed-sensorless control– Reduced-order high-gain speed observer based on back-emf signal
• Adaptation law based on the q-axis current tracking error• Two-time scale separation is exploited (by means of singular
perturbation technique)– Fast estimation dynamics– Slow mechanical and electromagnetic dynamics
• Controller structure– Vector-flux control based on improved indirect field oriented control
strategy• Auxiliary terms designed according to Lyapunov-like technique
for the stability of the reduced-order flux subsystem– Speed controller based on P-I + feed-forward action for speed
tracking with unknown constant load torque adaptation– Inner current control loop
33
Speed sensorless control of IM based on high gain speed estimation
• Full-order error dynamics
– Feedback interconnected mechanical, electromagnetic and estimation subsystems
– Exponentially stable estimation dynamics
• “Slow” system
– Speed estimation error dependent on flux tracking error– Series interconnection of
• Linear asymptotically stable mechanical subsystem
• Nonlinear asymptotically stable electromagnetic subsystem
• Local stability properties of the full-order error dynamics
– In the adaptive control framework, Persistency of Excitation, related to observability of the IM, is required for the stability of the reduced-order flux subsystem
34
Speed sensorless control of IM based on high gain speed estimation
• Reduced-order high-gain speed observer based on back-emf signal– Adaptation law based on the q-axis current tracking error– Two-time scale separation is exploited (by means of singular
perturbation technique)• Fast estimation dynamics
• Slow mechanical and electromagnetic dynamics
• Notation
35
Speed-flux controller
36
Reduced-order speed observer
• Speed and q-axis current estimation– q-axis current estimation is introduced for technical motivations
• Decomposition of error dynamics in standard form for singular perturbation theory
• “simpler” speed estimation:
• No exploitation of the stator flux model for state estimation– Rotor/stator flux are not estimated
• “true” speed-sensorless control
37
Mechanical/estimation error dynamics
• Two feedback-interconnected 2nd order linear systems– Time-scale separation obtained imposing the estimation dynamics to
be faster than the mechanical one
– Perturbation from flux dynamics ξi, due to lack of flux estimation• Quasi-steady state for the estimation error dynamics
38
Slow subsystem• Reduced-order tracking error dynamics
• 4th LTV flux dynamics xe
– Stability dependent on Persistency of Excitation conditions• avoid zero-frequency excitation, i.e. ω0r�0• Relation with observability properties of speed-sensorless
controlled IM without flux reconstruction from stator flux model
• 2nd order LTI exponentially stable mechanical dynamics xm
• Interconnection terms with linear/bilinear properties
– Series-interconnection, considering the linearized dynamics• Bilinear terms lead to local stability
39
LTV slow flux subsystem
• Exponentially stable d & q-axis current tracking error dynamics
• Classical structure of adaptive control systems with skew-symmetric dynamical matrix (see [Morgan & Narendra, SIAM JC&O 1977])– Stability is related to Persistency of Excitation conditions
40
Persistency of excitation condition• The LTV flux subsystem is GES if the Persistency of Excitation condition
is satisfied, i.e. if there exist T, k such that:
• PE condition corresponds to avoid zero-frequency excitation, i.e. ω0r�0– Relation with observability properties of speed-sensorless controlled
IM without flux reconstruction from stator flux model
41
Simulation and experimental results• Rated Power 1.1 kW • Rated speed 1410 rpm @ 50Hz• Rated Torque 7.0 Nm
• Two pole pairs• Rated current 2.8A rms• Rated voltage 220V rms
• kω=120, kω i=7200 (τω=11.8 ms)• ko=240, koi=93400 (τo=3.3 ms)• kid=150, kiq=300
• Ts=200 µs
42
Speed/flux reference, load torque profile
0 0.5 1 1.5
0
50
100
Speed reference and load torque profile (*10)
rad/
s, N
m
time (s)
0 0.5 1 1.50
0.5
1Flux reference
Wb
time (s)
43
0 0.5 1 1.5
-10
0
10
Speed tracking error
rad/
s
0 0.5 1 1.5
-10
0
10
Estimated speed tracking error
rad/
s
0 0.5 1 1.5
-10
0
10
Speed estimation error
rad/
s
time (s)0 0.5 1 1.5
-1
-0.5
0
0.5
1q-axis current estimation error
A
time (s)
0 0.5 1 1.5-5
0
5Reference for q-axis current
A
0 0.5 1 1.5-1
-0.5
0
0.5
1q-axis current error
A
time (s)
0 0.5 1 1.5-5
0
5Reference for d-axis current
A
0 0.5 1 1.5-1
-0.5
0
0.5
1d-axis current error
A
time (s)
0 0.5 1 1.5
-200
0
200
d-axis voltage (ud)
V
time (s)0 0.5 1 1.5
-200
0
200
q-axis voltage (uq)
V
time (s)
0 0.5 1 1.5
-0.02
0
0.02
d-axis flux error
Wb
time (s)0 0.5 1 1.5
-0.02
0
0.02
q-axis flux error
Wb
time (s)
ωωωω*=100rad/s, TL=7.0Nm
44
0 0.5 1 1.5
-10
0
10
Speed tracking error
rad/
s
0 0.5 1 1.5
-10
0
10
Estimated speed tracking error
rad/
s
0 0.5 1 1.5
-10
0
10
Speed estimation error
rad/
s
time (s)0 0.5 1 1.5
-1
-0.5
0
0.5
1q-axis current estimation error
A
time (s)
0 0.5 1 1.5-5
0
5Reference for q-axis current
A
0 0.5 1 1.5-1
-0.5
0
0.5
1q-axis current error
A
0 0.5 1 1.5-5
0
5Reference for d-axis current
A
0 0.5 1 1.5-1
-0.5
0
0.5
1d-axis current error
A
0 0.5 1 1.5-5
0
5a current (ia)
A
time (s)0 0.5 1 1.5
-5
0
5b current (ib)
A
time (s)
0 0.5 1 1.5
-200
0
200
a-axis voltage (ua)
V
time (s)0 0.5 1 1.5
-200
0
200
b-axis voltage (ub)
V
time (s)
0 0.5 1 1.5
-200
0
200
d-axis voltage (ud)
V
0 0.5 1 1.5
-200
0
200
q-axis voltage (uq)
V
ωωωω*=100rad/s, TL=7.0Nm
45
0 0.5 1 1.5
-10
0
10
Speed tracking error
rad/
s
0 0.5 1 1.5
-10
0
10
Speed estimation error
rad/
s
0 0.5 1 1.5-5
0
5q-axis current
A
0 0.5 1 1.5-5
0
5d-axis current
A
0 0.5 1 1.5-5
0
5a current (ia)
A
time (s)0 0.5 1 1.5-5
0
5b current (ib)
A
time (s)
ωωωω*=0rad/s, TL=7.0Nmstandstill
46
0 0.5 1 1.5
-10
0
10
Speed tracking error
rad/
s
0 0.5 1 1.5
-10
0
10
Speed estimation error
rad/
s
0 0.5 1 1.5-5
0
5q-axis current
A
0 0.5 1 1.5-5
0
5d-axis current
A
0 0.5 1 1.5-5
0
5a current (ia)
A
time (s)0 0.5 1 1.5-5
0
5b current (ib)
A
time (s)
ωωωω*=10rad/s, TL=-7.0Nm
47
PE condition and reference flux selection
• In order to avoid lack of PE (ω0s=0), the reference flux ψ* can be selected such that– |ω0s| is maximum– ψ* ∈ [ψ*m,ψ*M]
48
0 0.5 1 1.5-5
0
5q-axis current
A
time (s)0 0.5 1 1.5
-5
0
5d-axis current
A
time (s)
0 0.5 1 1.5
-10
0
10
Speed tracking error
rad/
s
0 0.5 1 1.5
-10
0
10
Estimated speed tracking error
rad/
s
0 0.5 1 1.5
-10
0
10
Speed estimation error
rad/
s
0 0.5 1 1.5-20
0
20
40Synchronous speed ω0
rad/
s
time (s)
0 0.5 1 1.5-10
-5
0
5
10Load torque (real and estimated)
Nm
0 0.5 1 1.50
0.5
1Flux reference
Wb
time (s)
0 0.5 1 1.5-5
0
5q-axis current
A
time (s)0 0.5 1 1.5
-5
0
5d-axis current
A
time (s)
0 0.5 1 1.5
-10
0
10
Speed tracking error
rad/
s
0 0.5 1 1.5
-10
0
10
Estimated speed tracking error
rad/
s
0 0.5 1 1.5
-10
0
10
Speed estimation error
rad/
s
0 0.5 1 1.5-20
0
20
40Synchronous speed ω0
rad/
s
time (s)
0 0.5 1 1.5-10
-5
0
5
10Load torque (real and estimated)
Nm
0 0.5 1 1.50
0.5
1Flux reference
Wb
time (s)
ωωωω*=7.5rad/s, TL=-7.0Nm
Constant flux reference Variable flux reference
49
Concluding remarks
• Achievable performances– At high speed with load or regenerative torque
• Performance similar to standard IFO control with medium-cost encoder
– mechanical time constant � 10ms
• Safe behavior up to 2-3 Hz with rated load/regenerative torque– Lack of speed regulation/torque generation (or even instability)
– Performance degradation near zero frequency due to robustness issues
– sensitivity to stator resistance, inductances– Measurement noise and actuation distortion
50
Concluding remarks• Sensorless control of IM under “realistic” assumptions (unknown speed,
rotor flux and load torque) is still a research topic both from the theoretical and application viewpoint
– A solution based on high-gain reduced-order observer and IFO control seems to be promising
– Based on fundamental laws of electromechanical energy conversionof IM (back-emf estimation)
• Local stability results, but with sufficiently large domain of attraction, at least at high speed
– Local results seem to be unavoidable with unknown rotor flux
• PE condition related to observability of IM with dc-excitation– Structural property of speed-sensorless controlled IM– Solutions:
– Avoidance of dc-excitation by proper selection of reference flux– Injection of high frequency signals
51
Concluding remarks• Other solutions based on stator flux model are deeply investigated
– Reconstruction of rotor/stator fluxes from stator flux model
• Estimation is independent of speed
• It is necessary to cope with pure integrator dynamics
– Low-pass filtering, stator resistance and inverter model estimation, other technological remedies [Holtz, Proc. IEEE 2002], [Profumo et al., Trans. IAS 1998], adaptive observers [Montanari et al., CDC 2004], etc.
52
Other research activities
• Control of electrical drives– Speed-sensorless control of induction motors
• Learning-based adaptive control• Hybrid systems modeling and control• Modeling and control of a car driveline
– Clutch, gear-box actuators, transmission shaft modeling
– Application of hybrid control techniques
