The invention relates to an electromagnetic actuator having a moving part and a sta tionary part, where in the moving part moves with respect to the stationary part in accordance with an applied voltage.

Such electromagnetic actuators are incorporated in to various devices. For example, Fig. 1 shows a mechatronic rotary control device for an automobile comprising a number of electromagnetic actuators. The rotary control device can be rotated to var ious orientations. The rotary control device comprises said electromagnetic actuators, which serve to block the rotational movement of the knob of the rotary control device. That is, executable motions of the control device are locked and unlocked by several electromagnetic actuators. Fig. 2 shows such an electromagnetic switching actuator. Conventionally, such electromagnetic actuators have been known to produce noise when in use, especially when the moving part of such an actuator reaches and end- stop position. To reduce this noise excitation due to switching operations of these electromagnetic actuators, the mechanical end-stops of the electromagnetic actua tors have conventionally been equipped with elastomer dampers. One possibility is to modify the mechanical design of the shifter by addition of noise-absorbing materials such as foams or by increasing the stiffness of the housing. This is disadvantageous due to increased production costs, space, and weight of the product. Moreover, noise-absorbing materials may deteriorate or fail over lifetime and can be difficult to integrate into the product design at all. Since the resulting noise reduction is unsatis factory, further measures are needed to further reduce the noise production of the electromagnetic actuators

The object of the invention is therefore to reduce the noise produced by an electro magnetic actuator, in particular when the moving part of an actuator reaches an end- stop position.

The object is achieved through an improved device comprising an electromagnetic actuator and a method for operating the device with an electromagnetic actuator ac cording to the independent claims. The object is therefore achieved by a device comprising at least an electromagnetic actuator and a control unit, wherein the electromagnetic actuator comprises a moving part, a stationary part, and an electrically conducting coil for moving the moving part with respect to the conducting part, and wherein the control unit is embodied to regu late a voltage applied to the coil and to monitor the electrical current through the coil, characterized in that the control unit is further embodied to determine the collision speed of the moving part of the actuator based on the monitored current, and to regulate the voltage of applied to the coil on the basis of the determined collision speed.

Such electromagnetic actuators are used, for example, in mechatronic rotary control devices controlling various functions in vehicles. Such a rotary control device can be embodied to limit the possible executable mechanical motion of the device via the switching of electromagnetic actuators. Due to the placement of the device in a vehi cle interior, it is desired to reduce the noise emission of the switching operations.

To overcome this issue while keeping the mechanical design simple and robust, noise-reducing real-time algorithms are proposed. The algorithms run on standard automotive real time hardware with low computational effort and need no additional sensors. Robustness to series tolerances, varying operating conditions, and ageing are achieved by real-time learning strategies. The stability of the learning closed con trol loop is proven.

According to the invention, the control task is split up into the computation of a cur rent profile to achieve an acceptable collision speed and an underlying feed-forward current controller. Robustness to series tolerances, ageing, and varying operating conditions can therefore be achieved by a real-time adaptation of time-varying pa rameters of the current dynamics and an iterative improvement of the current profile based on previous impact velocities, which are estimated from the measured current. The object is further achieved by a method for controlling the movement of a moving part of an electromagnet actuator comprising the steps of regulating a voltage ap plied to a conducting coil of the actuator, monitoring the electrical current through the coil, determining the collision speed of the moving part of the actuator based on the monitored current, and regulating the voltage applied to the coil on the basis of the determined collision speed.

Therefore, the invention proposes a soft-landing control algorithm aimed at reducing the velocity of the actuator before it collides with the mechanical end stop. Such a method does not require any modifications of the mechanical design.

As opposed to some feed-forward soft-landing algorithms as proposed in conven tional lituratur, which may lack the required robustness for an automotive series product, and more robust methods, which involve a feedback of the actuator position, are often infeasible to implement on an automotive embedded real-time hardware due to the required fast sampling rate for the sensor-less estimation of the position from the voltage and the current of the actuator.

The present invention proposes a novel sensor-less soft-landing control algorithm, which runs on a typical automotive embedded real-time hardware. Computational efficiency and the required robustness for an automotive series product are achieved by a combination of simplified physical models and lean embedded learning algo rithms based on regression models. The stability of the iteratively learning closed control loop is proven.

In the following, detailed mathematical models of the relevant components of the ac tuation system will be introduce. Namely, the equation of motion of the actuator, its current dynamics in interaction with the power electronics, and the measurement chains used in the control algorithm will be explained. Following this, the embedded control algorithm for controlling the electromagnetic actuator will be explained.

To gain a better understanding of the relevant system dynamics, to systematically derive and analyze the embedded control algorithms, and to implement a sufficiently accurate behavioral simulation for their virtual validation, a detailed physically moti vated mathematical model of the actuation system is derived in this section. The mathematical model consists of the equation of motion of the actuator (Section 2.1 ), the current dynamics (Section 2.2), which couples the electronic control with the me chanical motion, and the measurement chains used in the control algorithm (Section 2.4). Additionally, a computationally efficient approximation of the current dynamics based on averaging is presented (Section 2.3) as the basis for the current controller in Section 3.1 .

2.1 Equation of motion

The equation of motion of the actuator reads

Here, m is its accelerated mass, , x< ¹⁾ , and xF are its position, velocity, and accel eration, Fmag is the magnetic force, / the current through the coil, F _{s r} the spring force, Ffricthe friction force, Fstopthe contact force at the mechanical endstops, and g the gravitational acceleration.

The characteristics Fmag( ,/) of the magnetic force are computed pointwise by stat ic FEM simulations on a grid of 100x100 combinations of positions and currents over the relevant range of operation.

The spring is a homogenous coil spring, so its retention force is modelled as Fspr( ) = cx + Fo, where c is the spring stiffness and Fothe preload at the position = o.

Since the relevant actuator motions include rapid transitions from standstill to high velocities, a sufficiently accurate friction model is required. Various friction models for an electromagnetic actuator are known in the art. In the present work, a modified Stribeck friction model

H _c . I / ,{1) sign is utilized, where i/o is a normalizing velocity, Fcthe Coulomb friction force, Fsthe stic- tion force, v _s the Stribeck velocity, and d the viscous damping coefficient. Note that the tanh term in the above equation (2) prevents unphysical discontinuities in the fric tion force at zero crossings of the velocity. The mechanical endstops comprise elastic polymers, whose visco-elastic dynam ics are difficult to capture accurately. Since only the bouncing of the actuator at the endstops is of interest for the present application, whereas an inaccuracy of the mathematical model during the contact phase is tolerable, the endstops are approxi mated as static springs and dampers:

Here, ci is the spring stiffness of the lower endstop, ah its viscous damping coeffi cient, P2 is the nonlinear spring characteristics of the upper endstop, dk its viscous damping coefficient, and xi, 2 are those positions where the armature collides with the respective endstop.

2.2 Current dynamics

Fig. 3 shows the circuit for the control of the electrical power ow into the electromag netic actuator. Except the actuator, which is represented by its coil resistance Rcu and its magnetic ux linkage y, the circuit contains a shunt resistor R _s to measure the current through the actuator, an N-channel power MOSFET, and a free-wheeling di ode. The supply voltage of the circuit is denoted by v _SUp , the voltage drop across the diode by va, the current through the diode by id, the drain-source voltage of the MOSFET by Vds, its gate-source voltage by v _gs , and the drain-source current by ids.

The gate-source voltage v _gs is pulse width modulated (PWM). The gate source voltage is thus either v _gs = v _gs ,on (during the PWM on phase) or v _gs = 0 (during the PWM o phase). During the PWM on phase, the gate-source channel of the MOSFET is conducting, so /ds = / and id = 0. During the PWM o phase, the gate-source channel of the MOSFET is open, so ids = 0 and id = i. Faraday’s law thus yields the current dy namics on, off, (3) Fig. 3. Electrical circuit for the control of a single electromagnetic actuator with the sum resistance R _å = R _s + Rc . dip dtp

The partial derivatives Oi and a* of the flux linkage are computed by static FEM simulations as mentioned in Section 2.1 for the magnetic force Fmag. Besides the stat ic FEM simulations, transient FEM simulations are evaluated to verify that eddy cur rents can be neglected in the present application.

The dependence of the coil current on the temperature is regarded by ficu = Rc u,o (1 + «Cu (T - To)) , (4) where Tis the absolute temperature, To a reference temperature, acu the linear tem perature coefficient of the resistivity of copper, and F?cu _, othe coil resistance at tem perature To.

The diode voltage can be modelled as where n is the emission coefficient, k is Boltzmann’s constant, q is the electron charge, and Is is the saturation reverse current. The saturation reverse current de pends on the temperature: with / _s, othe saturation reverse current at the reference temperature To, g the gap voltage, and the exponent x.

By the current dynamics (3), the electrical circuit in Fig. 3, and the relevant range of operation of the present application, a mathematical model of the drain source voltage Vds of the MOSFET is required for its ohmic region only. Moreover, ids ³ 0 can be assumed since the source of the MOSFET is connected to ground. Therefore the drain-source voltage is approximated by [17] where 1/th is the threshold voltage and K the transconductance coefficient. Both the threshold voltage Wiand the transconductance coefficient ^depend on the tempera ture. These dependencies are approximated by where Kb, Wi,o, and 1/th,o, respectively, are the transconductance coefficient, the threshold voltage, and its gradient with respect to the temperature at the reference temperature To.

2.3 Averaged current dynamics

For the current controller in Section 3.1 , the dynamics of the mean current over one PWM cycle is required. Averaging of (3) over the -th PWM cycle yields pwm where r _pW m is the PWM period and a^e [0,1] the duty ratio, which is defined as the fraction of a PWM cycle where the gate-source voltage of the MOSFET is v _gs = v _gs ,on. Eq. (7) can be rewritten as with the arithmetic mean values and the averaged differential inductance L _k sn6 averaged back-emf coefficient M _k , which are implicitly defined by

Due to the involved integrals over functions of / and x, which are expensive to com pute numerically, the exact averaged dynamics (8) is impractical for implementation on an automotive embedded real-time hardware. Thus an asymptotic approximation is derived in the following to replace the integrals over functions of / and x by func tions of the mean current i _k and the mean position (fc+l)T _j pwm

J / _Y * Ίi. / Jk / / pwm 'pwm

Note that the diode voltage Vds is strictly monotonic and continuously differentiable with respect to the current / as i > -l _s , which is always true in the present application. The mean value theorem for definite integrals states that a current exists such that Vds,k= Vds(f). Taylor’s theorem yields

Furthermore,

T€T€[feTp _Wm ,(fe+l)Tp _Wm ]

That is, the integral Vds./cCan be expressed by the function value v ( ) plus an error term that, for small PWM periods, vanishes asymptotically linearly in the PWM peri od:

Analogous expressions can be found for vd _,k , L _k , and M _k . Altogether, (8a) can be re written as as rpwm ® 0+.

The embedded real-time algorithms explained hereinafter use measured signals v _m of the supply voltage v _SUp and /m of the coil current /. Compared to the actual quantities vsup and /, the measurements v _m and / are deteriorated by analogue low-pass filter ing, sampling, quantization, and additive zero-mean noise. Additionally, series variations of the physical components, which are involved in the conversion of v _SUp and / into their measurements v _m and / _m , can result in systematic measurement errors which vary over the series of produced devices.

Here, the systematic measurement errors due to series tolerances are addressed by calibration procedures which are run during production. Therefore, the respective de viations between physical quantities and measurements are neglected. Furthermore, the remaining measurement errors on the supply voltage are of minor importance. That is, Vm ^s Vsup is assumed.

Concerning the current measurement, the reduction in dynamics due to analogue low-pass filtering and the measurement noise are important effects, whereas sam pling and quantization can be neglected. The importance of the low-pass filtering and the noise is due to the fact that the closed-loop soft-landing controller in Section 3.3 relies on an event detection and maximum search in time derivatives of the meas ured current.

Since the analogue low-pass filter is a single stage RC low-pass filter, the measured current is modelled as in i = im 0 + Ώ7, (10a) where $ is the measurement noise and /mothe noise-free part, which is generated from the current / by the dynamics with me the time constant of the RC low-pass filter.

As can be seen from (1), the coil current / can be considered as the control input for the motion of the actuator. In contrast to this, the actual output of the control algo- rithm is the duty ratio of the pulse width modulated gate source voltage of the MOSFET. Hence the soft-landing control task is split up into the computation of the current profile to achieve an acceptable collision speed and an underlying feed forward current controller. Robustness to series tolerances, ageing, and varying op erating conditions is achieved by a real-time adaptation of time-varying parameters of the current dynamics and an iterative improvement of the current profile based on previous impact velocities, which are estimated from the measured current.

In the following, feed forward control will be explained. Due to the limited dynamics of the low-pass filtered measured current (Section 2.4) and a relatively slow sampling rate of the real-time system in comparison to the current dynamics of the actuator, a closed-loop current control is inexpedient. Instead, a feed-forward control based on the current dynamics (3) is applied. Time-varying parameters are assumed to be known by an adaptation procedure, which is explained in the following.

The averaged current dynamics (9) motivates the feed-forward current controller over the -th PWM cycle of the current /, its time derivative / ¹⁾ , the position , and the velocity c ¹⁾ . The quantities R _å , v sup _,k , ^y v ds, and v d in (11) are predictions of their respective actual counterparts Rå, v _{SUp ,k} , y, vds, and va, which vary due to series tol erances and varying operating conditions.

Given sufficiently accurate predictions Rå, v _{SUp ,k} , ^y Vds, and va, the feedforward controller (11) allows in principle a precise control of the mean current even for fast reference trajectories. However, this requires the numerical solution of the differential equations (1) and (3) in order to compute physically consistent reference trajectories and the computation of arithmetic mean values of the state variables thereafter.

On the present application, no accurate tracking of arbitrary reference trajectories is required. By the iteratively learning soft-landing control in Section 3.3, the require ment on the current reduces to a good reproducibility over repeated switching opera tions.

.(1) (1)

Hence the instationary terms fc and ^x ^ ^k in (11 ) are neglected to obtain the simpli fied feed-forward current controller

The current controller (12) can achieve a high accuracy only in steady state, where the mean reference current /r^and the resulting position ^are quasi constant. Then, the mean current // asymptotically approaches ir _,k + ^~ ias k , where is the station ary error.

The stationary error 7 is regarded as a measure for the reproducibility of the current profile in the present application. Hence the local sensitivities of 7 with respect to the model uncertainties are used to quantify their respective relative importance on the reproducibility of the current and, thus, of the actuator motion itself.

To compute the sensitivities, the feed-forward controller (12) is substituted into (9). Doing so, the stationary current error 7 is achieved in steady state {\ ) = 0 and x^ = 0 as the solution of the implicit equation Where with the model uncertainties

By implicit differentiation of (13a), the sought sensitivities of the stationary current error read

Since the scalar factor di is common to all sensitivities, it is sufficient to ana lyze the components of the gradient to evaluate the relative importance of the constituent components of p~. Since can be assumed in the present application, the sensitivities (15) can be approximated by

Given typical parameter values and the range of operation of the present application, Eq. (16) means that the stationary current error is dominated for small currents by the model error v d{ir,k) in the diode voltage and for large currents by the error Rå in the sum of the shunt resistance and the coil resistance. Both errors are relevant in prac tice, since the diode voltage and the coil resistance greatly vary over the required temperature range and over series production.

In the following, the adaption of the coil resistance and the diode voltage will be ex plained. As shown above, an accurate knowledge of the coil resistance and the diode voltage is required to achieve a good stationary accuracy of the feedforward current controller. To this end, a real-time identification strategy based on the averaged cur rent dynamics (9) is described in this section.

To reduce the number of parameters that must be identified simultaneously, the ad-

(1) _ A aptation is run only when the actuator stands still. That is, ^x k ^{— u} can be assumed in (9). Additionally, the duty ratio O _k is varied such slowly during adaptation that Hence the averaged current dynamics (9) reduces to during the adaptation procedure.

In a next step, the drain source voltage Vds of the MOSFET is approximated by its nominal and, thus, known characteristics Vds ^? . This is motivated by the fact that Vds (¾) is relatively small in the present application, in particular during the adaptation proce dure. So, (17) is replaced by where the left-hand side consists of terms that are known or measured and the un known diode voltage and coil resistance are on the right-hand side.

The variations in the diode characteristics arise from its dependency on the tempera ture and from series deviations in the parameters n, k _, o, and x in (5). To reduce the dimensionality of the unknown parameters, the diode voltage is approximated as vd ^« z vd ^? , where vd ^? is a known nominal diode voltage at reference temperature and the unknown coefficient z subsumes all actual parameter variations of the diode charac teristics. This turns the nonlinear regression problem (18) into the linear regression problem

Before (19) is exploited for the identification of Q, it needs to be considered that not the actual mean current is available but only its measured representation / _m . Recall from Section 2.4 that / _m deviates from the actual current in particular by the RC low- pass filter. So, simply replacing by im{t _k ) in (19) would introduce a bias in the esti mate of Q due to the asynchronicity of a^and im{t _k ). Instead, a Tustin-discretized ap proximation of the RC low-pass filter (10b) is applied to <¾ in order to obtain the low- pass filtered duty ratio a k, which is synchronous to im{tk): where r _s is the sampling period. Unlike the current, the averaged supply voltage varies such slowly that no synchroni zation is required. Thus the supply voltage v _SUp,/( is replaced by its measured counter part Vm(tk) in (19). This yields the regression problem of which both the output >¾and the regressor fk can be computed in real-time.

For linear regression problems such as (20), many computationally efficient real-time algorithms, which successively determine an estimate Q of the unknown parameters Q, can be found in literature, see for example [1 ,6,7] In the present work, an expo nentially weighted recursive least-squares algorithm is used. Based on an initial guess qo of the parameter vector Q and an initial value Po of the inverse exponentially weighted autocorrelation matrix updated parameter estimates

§k — arg and the updated inverse autocorrelation matrix P _k are successively computed by with the gain vector Due to the discounting of previous output errors by A ^k~ i< 1 in the objective function (21 b), parameter variations over time can be tracked. In the present application, per sistent excitation, as required for (21 ) to converge, is guaranteed by the particular choice of the duty ratio pro le during parameter adaptation.

In the following, the iterative learning soft-landing control will be explained. To achieve a soft landing of the actuator, a three times differentiable position trajectory t 7® x(t) from standstill in the start position to standstill in the end position can be computed. Then, the equation of motion (1 ) yields the required current profile: i F mag -* T·P spr ( \ g\ ) _l_ J _f In .c I « ^L g(1·) + F stop where Fmag ^-1 is the inverse of the magnetic force characteristics Fmag with respect to the current. Finally, the current pro le can be realized by an underlying current con troller. Such a feed-forward position controller based on the differential atness prop erty of electromagnetic actuators is proposed in [4] A drawback of the aforemen tioned feed-forward position control strategy is that it may yield a poor reproducibility over series tolerances, ageing, and varying operating conditions, which cause rele vant uncertainties on the open-loop unstable dynamics of a switching electromagnet ic actuator.

This issue is addressed in literature by methods for the sensor-less closed-loop posi tion control [5, 2, 3,11]. Here, sensor-less means that no dedicated sensor for the ac tuator position is required; instead, the position is determined from the voltage and the current trajectories, which are much cheaper to measure than the position. An advantage of such closed-loop position controllers is that they allow an accurate tracking even of highly dynamic reference trajectories of the position. However, the required sampling periods for the sensor-less estimation of the position are much shorter than those realizable on the present automotive embedded real-time hard ware. Recall that no accurate tracking of a predetermined position trajectory is required. It is sufficient for the soft-landing controller to reproducibly achieve a sufficiently slow collision velocity such that the noise excitation is acceptable.

It turns out that, even with a simple step-like reference current trajectory where k ₀ n is the sampling instant when the actuator is turned on and /on is a constant value, a considerable reduction of the collision velocity and, thus, of the excited noise can be achieved. This applies despite no collision velocity 0 is possible by the step like current pro le (22), since the required current to start the motion exceeds the cur rent that is required to hold the actuator in the endstop, as it is characteristic for most switching electromagnetic actuators in practice.

Given the reference current trajectory (22), the challenge is to find a value /on, which is large enough that the actuator starts its motion but, at the same time, small enough that the collision velocity is acceptable. Unfortunately, no common value /on is found over all series tolerances, operating conditions, and ageing states of the actuator. But given a particular specimen of the actuator, the appropriate range of values for /on varies such slowly that /on can be learned iteratively on the embedded real-time hard ware.

To this end, the actual collision velocity v _c,/ at the /- th switching operation is modelled as the sum of a known function c of /on during the switching operation and an un known model error vr.

The function c is determined experimentally. Given a reference collision velocity v _r for the /-th switching operation, the current /on,/ is chosen as where the learning feedback part f/is iteratively updated by

Here, V _C, is the estimated collision velocity during the previous switching operation, achieved by the method in Section 3.4, and k is the learning rate.

To analyze the closed-loop performance of the learning soft-landing controller (24), the tracking error v~ _cj = v _c,/ -vr _,/ and the estimation error ^v i= n i-no _, i of the col lision velocity are introduced. Substituting the controller (24a) into the process model (23) then yields

V _c ,i = ¾ + Vh (25a) and the adaptation law (24b) can be rewritten as

By (25a), the tracking error v~ _c,/-i in (25b) can be replaced to obtain and, thus, from (25a) with the forward difference Avi= _+i - v/.

Eq. (26) shows that the soft-landing controller (24) yields an asymptotically stable linear shift-invariant closed-loop dynamics of the tracking error v~ _c,/ as k e (0,2), which is excited by the difference Dn/of the consecutive model errors in (23), but not by the instantaneous model error vi itself. That is, slowly varying model uncertainties ware attenuated. Additionally, the tracking error v _c,/ is excited by the error v /of the colli sion velocity estimate. In the following, the closed-loop error dynamics (26) is investigated in more detail to understand how to choose the learning rate K. From (26), the tracking error at the /- th switching operation follows as

Hence the initial model error v~ _c, o = vois attenuated the faster the closer the learning rate k is to 1.

For K = 1 , a so-called dead beat behavior is achieved, such that the tracking error v _c,i is decoupled from the model error vi already after the first switching operation. But, unfortunately, the tracking error becomes highly sensitive to the error in the estimated collision velocity:

This is a severe drawback, since the collision velocity is estimated in Section 3.4 from numerically estimated time derivatives of the noisy current measurement and, thus, is itself corrupted by noise. When, in contrast, the learning rate is chosen as k = 0, the tracking error is decoupled from the estimation error, but sensitive to the model error:

Therefore it is desirable to determine a learning rate that yields a better compro mise between the attenuation of the model error vi and the estimation error v ^{^} c .

To this end, Dn/and v i are modelled as representations of wide-sense stationary random processes, which are statistically independent of each other. Since the closed-loop error dynamics (26) is linear and shift-invariant, the expected value m _n ^~ o and the power density spectrum P _v-C { w) of the closed-loop tracking error v~ _c,/ can easily be computed from the expected values ^and cand the power density spectra PA _V (CU) and ^p v ~c{ >) of Dn/and '' /[6]. One obtains

So, after estimating m^ _n , m _n ~ ^~ o, PA _V {U>), and R _n ~ ^~ o{ώ) from experiments, the learning rate K can be tuned based on (27).

In the following, Sensor-less estimation of the collision velocity will be explained.

The closed-loop soft-landing controller (24) requires the collision velocity during the previous switching operation. To estimate the collision velocity without a dedicated position sensor or velocity sensor, the coupling from the mechanical motion of the actuator to its averaged current dynamics (9) through the back-emf term ^d — _dX (c/ _ί ,/ ^ί/ _ί ίe exploited as follows.

Consider a switching operation, where the actuator reaches the mechanical end- stop at time fc _,/ with the collision velocity v _c . After a short contact period, the actuator bounces back, where the starting velocity follows from Newton’s impact law as -ev _c,i with e the restituent coefficient [16,9]. That is, the velocity of the actuator during a short period around the collision time fc _,/ can be approximated by

Hence, the acceleration of the actuator around the collision can be approximated by a Dirac impulse, whose weight is proportional to the collision velocity: where d(ί- fc _,/ ) denotes the Dirac impulse at the collision time k _,i . Averaging (29) over the PWM periods around the collision results in

Given the feed-forward current controller (12) with the current trajectory (22) and the closed-loop soft-landing controller (24), the averaged current dynamics (9) can be approximated by around the collision time, where

The averaged second order time derivative of the current approximately thus satisfies follows. Eq. (32) basically means that, around a collision, the second order time derivative of the current comprises, amongst other components, a well known signal, namely a Dirac impulse. Vice versa, given the measured current /m, the estimation of the colli sion velocity is reduced to the estimation of its second order time derivative, the de tection of the Dirac impulse therein, and the determination of the weight of the Dirac impulse.

The primary practical challenge in doing so is the real-time computation of the sec ond order time derivative from the noisy current measurement. Additionally, the ana logue RC low-pass filter (10b) in the current measurement chain reduces the dynam ics of the measured current such strongly that for fast actuator motions no reliable separation of the motion from the collision is possible, even with a well selected de rivative estimation filter.

So, instead of using only an estimate 7 ²⁾ of the second order time derivative of the measured current /in for collision detection and velocity estimation, also an estimate 3>m of the third order time derivative of im is computed. Then, an estimate of ² > of the actual coil current is computed by approximate inversion of the analogue low-pass filter (10b):

To compute the estimated time derivatives 7 ² > _m and 7 ³ > _m , algebraic derivative estima tors are used [14,15], which are implemented on the embedded real-time hardware as discrete-time FIR filters. These filters are particularly suited for the present appli cation, since they are simple to tune [12] yet can realize a nearly optimal compromise between the resolution in time and frequency domain in the sense of the uncertainty principle [8].

Then, the estimation of the weight of the Dirac impulse and, thus, of the collision ve locity is performed by a maximum search. Therefore, based on a detailed physically motivated mathematical model of the rele vant dynamics, an embedded control algorithm for the soft landing of electromagnetic actuators is presented. The control algorithm consists of an underlying feedforward current controller, which is based on a simplified physical model of the current dy namics, and an iteratively learning closed-loop soft-landing controller, which is based on a regression model of the relationship between the coil current and the collision velocity.

The accuracy of the feed-forward current controller is improved by a recursive least- squares estimator for the dominant uncertain model parameters. These parameters are determined by a sensitivity analysis of the stationary current control error.

The learning closed-loop soft-landing controller requires the collision velocity during the previous switching operation in order to improve the upcoming switching opera tion. Since no dedicated sensor for the actuator position is available, the previous collision velocity is reconstructed from the second order time derivative of the coil current using algebraic derivative estimators. The analogue anti-aliasing filter of the current measurement is approximately inverted to achieve a sufficient resolution of the estimated collision velocity.

In combination, robustness to series tolerances, varying operating conditions, and ageing is obtained. In particular, the stability of the closed soft-landing control loop with the learning soft-landing controller is proven.

Certain embodiments of the invention will next be explained in detail with reference to the following figures. They show:

Fig. 1 a perspective view of an embodiment of the inventive device;

Fig. 2 a schematic diagram of an actuator of an inventive device;

Fig. 3 a perspective view of an embodiment of the inventive device; Fig. 4 a circuit diagram of a part of an embodiment of an inventive device comprising an electromagnet actuator;

Fig. 5 a flow diagram of an embodiment of the inventive method; and

Fig. 6 a diagram showing a simulated result of the iterative control of the de vice.

Fig. 1 shows a perspective view of an embodiment of the inventive device. The de vice is a rotary control device for shifting a vehicle to various operation modes, in cluding a drive operation mode D, a park operation mode P, a reverse operation mode R, and so forth. The device comprises at least one electromagnetic actuator 1 of implementing haptic responses of the device as the user interface 3 is rotated with respect to the housing 5. The electromagnetic actuator 1 moves the moving part of the actuator to a blocking position, when for example, the vehicle is in a drive opera tion mode, and traveling at a speed above a certain threshold such that rotating the user interface to shift the device into a park or reverse operation mode could cause failure of mechanical components in the drive chain of the vehicle.

Fig. 2 shows a schematic diagram of an actuator of an inventive device, with a mov ing part 7 and a stationary part 9. Within the stationary part is a conducting coil 11. When current is passed through the coil 11 , the moving part is subject to a force and when functioning properly begins to move with respect to the stationary part 9.

Fig 3. shows a perspective view of an embodiment of the inventive device, wherein five electromagnetic actuators 1 are positioned beneath a rotating part 13, which is fixedly connected to the user interface 3. The rotating part 13 comprises a contour 15 for receiving the moving part 7 of the electromagnetic actuators 1 , when they are fed a current. When a voltage is applied to the electromagnetic actuator 1 , the anchor, or moving part 7, moves toward the contour 15 and strikes the surface of the contour 15, thereby preventing a rotational movement of the rotating part 13 in at least one direction. Because this function is significant for the safety of vehicle occupants, is is beneficial to monitor the function of the electromagnetic actuators 1.

Fig. 4 shows a circuit diagram of a part of an embodiment of an inventive device comprising an electromagnet actuator, wherein a diode has been provided to permit the determination of the coil resistance as explained above.

Fig. 5 shows a flow diagram of an embodiment of the inventive method.

Fig. 6 shows a diagram showing a simulated result of the iterative control of the de vice.

Reference Characters electromagnetic actuator user interface of device housing of device moving part of electromagnetic actuator stationary part of electromagnetic actuator conducting coil rotating part contour control unit