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
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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
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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
– other “technical” assumptions:• Known smooth speed/flux references
• Known constant IM parameters
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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
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IM state estimation – case 1
Linear time-varying electromagnetic dynamics
Rotor flux/stator current observer
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IM state estimation – case 1
• Global asymptotic stability of the error model, thanks to passivity properties of the E.M. dynamics
Estimation error model
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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
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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)
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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
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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
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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]
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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]
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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
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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]
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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
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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
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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*
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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
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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
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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
• 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
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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
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Speed-flux controller
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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
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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
– 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
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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
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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
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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
• 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]
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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
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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
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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
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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.
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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