Patent Application: US-25815105-A

Abstract:
a method for sensorless estimation of rotor speed and position of a permanent magnet synchronous machine the method comprising the steps of calculating first stator flux vector estimate } d , i + j } q , i ) using the flux model and measured stator currents , calculating second stator flux vector estimate } d , u + j } q , u ) using the voltage model and measured stator voltages , comparing the directions of the first and second flux vectors to achieve a first error signal , using speed adaptation to achieve estimates for the rotor angular speed } m ) and angular position } m ) from the first error signal , injecting a known voltage signal to the stator voltage , detecting a current signal from the stator current to form a second error signal , which is dependent on the estimation error of the rotor position , augmenting the voltage model by the second error signal to keep the first and second flux vector estimates aligned and so to correct the rotor angular speed } m ) and angular position } m ) estimates .

Description:
in an adaptive observer shown in fig1 , the rotor speed and position estimation is based on flux estimation error between two different models . a speed - adaptive flux observer has been developed for induction motors in [ 5 ]. for pmsms , an adaptive observer has been disclosed in stator coordinates in [ 6 ], whereas the approach presented in this description is implemented in rotor coordinates . estimates for the stator flux are calculated using both the voltage model and the flux model . the error of the two flux vectors is used to adapt the speed estimate so that the flux vectors correspond to each other . for the use in the flux and voltage models , the stator currents and voltages are measured and some parameters for these models are measured or identified . the stator flux components obtained by the voltage model in the rotor reference frame are ⅆ ψ ^ d , u ⅆ t = u d - r ^ s ⁢ i ^ d + ω ^ m ⁢ ψ ^ q , u + λ re ⁢ i ~ d - λ im ⁢ i ~ q ⁢ ω ^ m ( 1 ⁢ a ) ⅆ ψ ^ q , u ⅆ t = u q - r ^ s ⁢ i ^ q - ω ^ m ⁢ ψ ^ d , u + λ re ⁢ i ~ q + λ im ⁢ i ~ d ⁢ ω ^ m ⁢ ⁢ where ( 1 ⁢ b ) i ^ d = ψ ^ d , u - ψ ^ pm l ^ d ( 2 ⁢ a ) i ^ q = ψ ^ q , u l ^ q ( 2 ⁢ b ) are the components of the current estimation error . estimates are marked by the symbol ˆ . { circumflex over ( r )} s is the estimated stator resistance , { circumflex over ( ω )} m is the estimated rotor angular speed , { circumflex over ( l )} d and { circumflex over ( l )} q are the estimated direct and quadrature components of stator inductance , { circumflex over ( ψ )} pm is the presumed value of the permanent magnet flux , which can be obtained from an identification run , and λ re and λ im are observer gain parameters having effect on the flux amplitude and phase , respectively . the gain parameter λ re usually has a value between 0 and { circumflex over ( r )} s . by selecting λ re ={ circumflex over ( r )} s and λ im = 0 , ( 1 ) becomes a pure voltage model , while the selections λ re = 0 and λ im = 0 yield a flux estimate that is calculated by using only the stator voltage without any feedback from the measured stator current . the gain parameter λ im stabilizes the observer in the regenerative mode , and usually has a negative value . if space vector notation for ( 1 ) is used , a complex observer gain λ re + j { circumflex over ( ω )} m λ im can be used . the flux model for estimating the stator flux components can be written as { circumflex over ( ψ )} d , i ={ circumflex over ( l )} d i d +{ circumflex over ( ψ )} pm ( 4a ) an error signal from the complex flux vectors { circumflex over ( ψ )} d , u + j { circumflex over ( ψ )} q , u and { circumflex over ( ψ )} d , i + j { circumflex over ( ψ )} q , i can be obtained by different means . here , the first error signal , which is proportional to the misalignment of the two flux vectors , is obtained by f ɛ = im ⁢ { ( ψ ^ d , u + j ⁢ ⁢ ψ ^ q , u ) * ⁢ ( ψ ^ d , i + j ⁢ ⁢ ψ q , i ) } re ⁢ { ( ψ ^ d , u + j ⁢ ⁢ ψ ^ q , u ) * ( ψ ^ d , i + j ⁢ ⁢ ψ ^ q , i ) } ( 5 ) where * denotes a complex conjugate . this first error signal is fed to a pi - type speed adaptation mechanism { circumflex over ( ω )} m = k i ∫ f ε dt + k p f ε ( 6 ) where k i and k p are the gains of the speed adaptation . the estimate for rotor position is obtained by integrating { circumflex over ( ω )} m . in fig1 block 1 includes equations ( 1a , 1b ), and receives stator voltage components u d , u q and components of the current estimation error ĩ d , ĩ q as inputs . the current estimation error is calculated according to equations ( 2a , 2b , 3a , 3b ) in block 2 . block 2 receives as its input the measured stator currents i d , i q and stator flux estimates { circumflex over ( ψ )} d , u , { circumflex over ( ψ )} q , u calculated using voltage model in block 1 . flux model block 3 includes equations ( 4a , 4b ) and calculates stator flux components { circumflex over ( ψ )} d , i , { circumflex over ( ψ )} q , i using the flux model , and outputs these components to the error calculation block 4 , which calculates an error between the inputted flux estimates according to equation ( 5 ). the first error f ε is further fed to an adaptation mechanism 5 , which calculates the estimate for the angular speed { circumflex over ( ω )} m of the rotor according to equation ( 6 ). this estimate is then fed back to voltage model 1 . an alternating voltage is used for hf signal injection [ 7 ]. a carrier excitation signal fluctuating at angular frequency ω c and having amplitude û c , i . e ., is superimposed on the d component of the stator voltage in the estimated rotor reference frame . an alternating hf current response is detected in the q direction of the estimated rotor reference frame , amplitude modulated by the rotor position estimation error . the q component of the measured current is band - pass filtered ( bpf ), giving the current signal i qc varying at the signal injection frequency . the current signal is then demodulated and low - pass filtered ( lpf ) to extract a second error signal ɛ = u ^ c ω c ⁢ l q - l d 4 ⁢ l q ⁢ l d ⁢ sin ⁡ ( 2 ⁢ ⁢ θ ~ m ) ( 9 ) where { tilde over ( θ )} m = θ m −{ circumflex over ( θ )} m is the estimation error of the rotor position . due to errors in measurements and parameter estimates , the adaptive observer can lose correct orientation at low speeds . the flux vectors obtained by the voltage model and by the flux model can drift apart , and controlled operation is no longer possible . the method of the invention uses hf signal injection to correct the stator flux estimate so that correct orientation is maintained even at low speeds . fig2 shows the adaptive observer enhanced with the error signal ε obtained by hf signal injection as explained above . the block diagram of the speed adaptation mechanism is also shown in the fig2 . fig2 is similar to the fig1 except that adaptation law 15 is shown as pi - mechanism including integrator and gains k i and k p . another integrator 16 is also added , which integrates the estimated speed { circumflex over ( ω )} m of the rotor to produce estimate for the position angle { circumflex over ( θ )} m . the stator flux estimate obtained by voltage model of equation ( 1 ) is augmented by the second error signal ε from equation ( 8 ) and a pi - type regulator shown in fig2 as 17 . the algorithm is given by ⅆ ψ ^ d , u ⅆ t = u d - r ^ s ⁢ i ^ d + ω ^ m ⁢ ψ ^ q , u + λ re ⁢ i ~ d - λ im ⁢ i ~ q ⁢ ω ^ m - ψ ^ q , u ⁡ ( γ p ⁢ ɛ + γ i ⁢ ∫ ɛ ⁢ ⅆ t ) ( 10 ⁢ a ) ⅆ ψ ^ q , u ⅆ t = u q - r ^ s ⁢ i ^ q + ω ^ m ⁢ ψ ^ d , u + λ re ⁢ i ~ q - λ im ⁢ i ~ d ⁢ ω ^ m + ψ ^ d , u ⁡ ( γ p ⁢ ɛ + γ i ⁢ ∫ ɛ ⁢ ⅆ t ) ( 10 ⁢ b ) where γ p and γ i are the gains of the pi - mechanism . the voltage model 11 of fig2 includes thus equations ( 10a , 10b ). the second error signal ε obtained by the hf signal injection keeps the estimates of the stator flux aligned . the second error signal ε is driven to zero in steady - state . according to the invention , the signal injection is used only at low speeds . with increasing speed , the signal injection amplitude û c and the gains γ p and γ i are decreased , reaching zero at a certain speed . the speed at which the amplitude and gains reach zero can be set by the end - user case - specifically depending on the machine size and other factors . the mentioned speed can be for example one fifth of the nominal speed of the machine . at low speeds , the combined observer relies both on the signal injection method and the adaptive observer . the signal injection method dominates in steady state whereas the adaptive observer commands at transients . when the proposed estimator is used for sensorless control of a pmsm , the entire control system comprising cascaded speed and current control is shown in fig3 . in fig3 a speed controller 31 receives rotor speed reference ω m , ref and outputs current references for the current controller 32 . the control is carrier out in dq - coordinates . current controller 32 outputs voltage references , which are transformed to αβ - coordinates in block 33 . the inverter 34 is further controls the pmsm motor 35 according to the voltage references . block 36 transfers measured currents into dq - coordinates , and the measured current components are fed back to current controller 32 , to combined observer 37 and to error signal calculation block 36 . block 36 calculates error signal according to equation ( 8 ), and feeds it to the combined observer 37 . the combined observer , which is shown in greater detail in fig2 , receives also voltage references from the output of the current controller 32 . these voltage references correspond to the measured voltages , since the inverter can be considered as being almost linear amplifier . as in fig2 , the combined observer outputs accurate estimates for rotor speed and position . the rotor speed estimate is fed back to speed controller and the position estimate is used in coordinate transformations in blocks 33 and 36 . signal injection is done to the output of the current controller and especially to d component of the voltage reference . it should be noted , that the described control system is only one possible system for controlling a pmsm based on the method of the invention . it will be obvious to a person skilled in the art that , as the technology advances , the inventive concept can be implemented in various ways . the invention and its embodiments are not limited to the examples described above but may vary within the scope of the claims . e . robeischl , m . schroedl , and m . krammer , “ position - 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