DE102022203549A1 - Method and computing unit for parameterizing a current controller for an electromagnetic actuator - Google Patents

Abstract

The invention relates to a method for parameterizing a current regulator (200) for an electromagnetic actuator (101) for controlling an actual value (y) of a current through the electromagnetic actuator to a setpoint (r) having a control element (201), which has a control deviation between the Setpoint and the actual value are supplied and a first manipulated variable (ufb) is calculated from the control deviation in accordance with a control regulation with control parameters, with a total manipulated variable (u) being calculated from the first manipulated variable, the current through the electromagnetic actuator (101) being determined in accordance with the requirements the total manipulated variable (u) is generated, the actual value (y) and the total manipulated variable (u) being fed to a parameter adaptation element (206), which calculates at least one adaptation parameter (ϑ) for adapting the control parameters.

Description

The present invention relates to a method for parameterizing a current controller for an electromagnetic actuator for regulating an actual value of a current through the electromagnetic actuator to a setpoint as well as a computing unit and a computer program for carrying it out.

Background of the invention

With electromagnetically operated hydraulic valves, a pulse width modulated voltage (PWM) is usually applied to a coil, which results in a current and subsequently a magnetic force on the piston in the valve. The resulting force depends on the current. For this reason, current regulators are used in such a way that a desired current can be achieved quickly with the appropriate force and in such a way that it is robust to temperature changes. The output of the controller is the voltage or duty cycle of the PWM applied to the coil, the input is the current setpoint and the measured current.

You can use controllers with manually set control parameters or coefficients, typically PI controllers with proportional gain Kp and reset time Tn as control parameters. In order to achieve a good control result (e.g. rapid change in the current through the coil), the control parameters of typical controllers must be set manually for each valve type. This effort can be very large, and the performance of the controller may still not be very good.

Disclosure of the invention

According to the invention, a method for parameterizing a current controller for an electromagnetic actuator for regulating an actual value of a current through the electromagnetic actuator to a setpoint as well as a computing unit and a computer program for carrying it out with the features of the independent claims are proposed. Advantageous refinements are the subject of the subclaims and the following description.

As part of the invention, a self-calibrating controller is presented, i.e. the required control parameters for a specifically controlled electromagnetic actuator are determined automatically, which drastically reduces the manual effort. The control quality is significantly increased compared to the prior art by using the knowledge gained in addition to a pure feedback controller (having a control element) for a forward link (having a pilot control element). Highly nonlinear parameter behavior can be represented and controlled by the adaptation algorithm. The structure can be used to perform an initial, automatic calibration and then stop any adjustment of the controller. In addition, it can provide electrical resistance and inductance of the coil of the electromagnetic actuator during runtime, which can be used for fault detection and diagnosis. It is also possible to continuously adapt the controller to changes in resistance as a result of rising or falling temperatures in order to keep the performance of the controller high.

The adaptation process only uses the manipulated variable and the actual value of the current through the electromagnetic actuator. Neither knowledge of the magnet parameters nor the anchor position is necessary. The non-linear effects of a magnet depend heavily on the respective design and do not need to be known for the automatic adjustment of the control parameters. A very simple solution is presented, but one that still delivers very good results.

A computing unit according to the invention, for example a control device of an electromagnetic actuator, is set up, in particular in terms of programming, to carry out a method according to the invention.

The implementation of a method according to the invention in the form of a computer program or computer program product with program code for carrying out all method steps is also advantageous because this causes particularly low costs, especially if an executing control device is used for additional tasks and is therefore present anyway. Finally, a machine-readable storage medium is provided with a computer program stored thereon as described above. Suitable storage media or data carriers for providing the computer program are, in particular, magnetic, optical and electrical memories, such as hard drives, flash memories, EEPROMs, DVDs, etc. It is also possible to download a program via computer networks (Internet, intranet, etc.). Such a download can be wired or wired or wireless (e.g. via a WLAN network, a 3G, 4G, 5G or 6G connection, etc.).

Further advantages and refinements of the invention result from the description and the accompanying drawing.

The invention is shown schematically in the drawing using exemplary embodiments and is described below with reference to the drawing.

Brief description of the drawings

• 1 shows schematically a solenoid valve in which a method according to the invention can be carried out.
• 2 shows schematically a method for controlling an electromagnetic actuator according to a preferred embodiment of the invention in the form of a controller structure.

Detailed description of the drawing

In 1 A solenoid valve 100 is shown schematically, in which a method according to the invention can be carried out. The solenoid valve 100, which in the present case is designed as a proportional valve, has an electromagnetic actuator 101, which in turn has a coil 102 and an armature 103 movable therein.

A control slide 104 is connected to the armature 103 and can be moved back and forth in a valve housing 106. The control slide 104 is supported against one end of the valve housing 106 by means of a spring 105. By activating the electromagnetic actuator 101, the armature 103 is moved and the valve slide 104 is thus pressed against the spring 105. In this way, the position x of the armature 103 or the valve slide 104 can be changed. For this purpose, the coil 102 can be controlled using pulse width modulation, for example (via connections not shown here).

By moving the valve slide 104, for example, a flow through the valve housing 106 from a port A to a port B is adjusted. It goes without saying that the connections of such a valve can also be designed differently. Likewise, there can be more connections that are controlled by a valve slide.

mit γ= x, den konstanten, unbekannten Parametern ̂̅L(Induktivität der Spule 102) und R (elek. Widerstand der Spule), der mittleren Eingangsspannung u und dem mittleren Strom x = l als Grundlage für den Reglerentwurf verwendet werden.Such an arrangement can be presented as a simplified LTI model in the form $$\overline{L}\frac{dx}{dt}=u-\overline{R}x$$

with γ = x, the constant, unknown parameters ̂̅L (inductance of the coil 102) and R (electrical resistance of the coil), the average input voltage u and the average current x = l be used as a basis for the controller design.

In 2 is a preferred embodiment of a proposed general structure 200 of the adaptive control shown schematically and designated overall by 200. This is used to control an electromagnetic actuator, such as the actuator 101 according to 1 and can in particular be implemented in a computing unit such as a (valve) control device.

The control structure 200 is supplied with a setpoint r and an actual value y for the current through the coil 102. The setpoint r indicates the desired development of the output current y over time. On the one hand, the setpoint r is fed to a pilot control element 202 as a feed forward. On the other hand, the setpoint r and actual value y are calculated into a control deviation and fed to a control element 201 as a feedback controller.

The control element 201 calculates a first manipulated variable u _fb from the control deviation ry in accordance with a control regulation with control parameters. The input control element 202 calculates a second manipulated variable u _ff from the setpoint r in accordance with a input control regulation with input control parameters. A total manipulated variable u is calculated from the first and second manipulated variables in a summation element 203 and applied to the coil 102, resulting in the current y and an associated valve position.

In the present example, the route input u (manipulated variable) and the route output y (actual value) are each filtered by a linear low-pass filter 204, 205 in order to generate the signals u _a and y _a for a parameter adaptation element 206. In the parameter adaptation element 206, adaptation parameters ϑ are calculated and fed back to the control element 201 or feedforward control element 202 in order to parameterize the forward and feedback controller.

wobei z ∈ ℝ den Ausgang der Adaption darstellt, ϑ* ∈ ℝ² der echte Parametervektor ist und φ ∈ ℝ² der Regeressionsvektor ist.The adaptation process can in particular use a recursive least squares method. For this purpose, the LTI model (1) is expressed in the standard form $$\mathrm{e.g}={\phi }^T\vartheta *$$

where z ∈ ℝ represents the output of the adaptation, ϑ* ∈ ℝ ² is the real parameter vector and φ ∈ ℝ ² is the regression vector.

mit der Laplace-Variablen s und der Filterkonstanten λ_a > 0. Zusammen mit den gefilterten Eingangs- und Ausgangsgrößen $$u_a={\mathrm{\Lambda }}_{\text{a}}u\text{ und }{y}_a={\mathrm{\Lambda }}_{\text{a}}y$$

wird der gefilterte Systemeingang u_a als Ausgang der rekursiven Methode der kleinsten Quadrate gewählt, d.h. z = u_a. In diesem Fall wird der Regressionsvektor zu $${\phi }^{\text{T}}=\left[\begin{array}{cc}\frac{dt}{dt}& 1\end{array}\right]y_a,$$

und der ideale Parametervektor ergibt sich zu $${\left(\vartheta *\right)}^T=\left[\begin{array}{cc}\overline{L}& \overline{R}\end{array}\right].$$

To calculate the time derivative of the current y = x and to avoid high-frequency noise and unmodeled effects, Eq. (1) can be filtered using linear low-pass filters Λ _a : $${\mathrm{\Lambda }}_a\left(s\right)=\frac{{\lambda }_a}{s+{\lambda }_a}$$

with the Laplace variable s and the filter constant λ _a > 0. Together with the filtered input and output variables $$u_a={\mathrm{\Lambda }}_{\text{a}}u\text{and}{y}_a={\mathrm{\Lambda }}_{\text{a}}y$$

the filtered system input u _a is chosen as the output of the recursive least squares method, i.e. z = u _a . In this case the regression vector becomes $${\phi }^{\text{T}}=\left[\begin{array}{cc}\frac{dt}{dt}& 1\end{array}\right]y_a,$$

and the ideal parameter vector is given by $${\left(\vartheta *\right)}^T=\left[\begin{array}{cc}\overline{L}& \overline{R}\end{array}\right].$$

It is understood that the parameter estimation method described here is only an example and that other recursive estimation methods such as a recursively implemented gradient estimator can also be used. The estimation method can run the entire time during operation or, for example, only in a learning phase in which, for example, predetermined test current curves are run, which allow a particularly simple and precise parameter estimation. The parameters are then frozen. The output of the parameter estimator can then be used advantageously for diagnostic purposes, in particular by comparing it with reference values (e.g. those determined in the learning phase), thereby reducing the risk of unexpected disruptive effects during operation that have an unfavorable influence on the control parameters.

In contrast to the classic formulation of adaptation algorithms, where the highest derivative of the system is chosen as the adaptation output, which simplifies the mathematical treatment, in the form chosen here the resistance and inductance can be estimated independently of each other. In particular, since the resistance can be estimated under steady-state conditions, this formulation leads to a significant improvement in robustness against parameter drifts caused by low excitation. Additionally, projection methods can be used to guarantee strict limits for each parameter.

kann ein Schätzfehler ε eingeführt werden $$\epsilon =\frac{z-{\phi }^T\vartheta }{m^2},$$

mit dem Normalisierungsfaktor m² = 1 + φ^Tφ.When using the estimated parameter vector $${\vartheta }^{\text{T}}=\left[\begin{array}{cc}\widehat{L}& \widehat{R}\end{array}\right],$$

an estimation error ε can be introduced $$\epsilon =\frac{\mathrm{e.g}-{\phi }^T\vartheta }{m^2},$$

with the normalization factor m ² = 1 + φ ^T φ.

The normalization factor can be omitted if <p(t) ∈ L _∞ i.e. if the vector is essentially bounded for all times t. However, the adjustment speed is normalized with the normalization factor m, which facilitates the parameter tuning of the adjustment algorithm. In addition, the projection allows dealing with convex parameter constraints ϑ ∈ S. Given a convex set S, the orthogonal projection of ϑ onto the set S is the solution to the optimization problem $${\mathcal{P}}_{\vartheta }\left(\vartheta \right)=\text{bad}\underset{\text{v}\in \mathcal{S}}{\text{min}}{\Vert \text{v}-\vartheta \Vert }_2^2.$$

mit der konvexen Menge S = {ϑ ∈ IR²|g(ϑ) ≤ 0}, deren Rand δS und Innenraum S⁰. Dabei beschreibt die Ungleichung g(ϑ) ≤ 0 die Menge S im Parameterraum. Zur Schätzung des Parametervektors ϑ kann insbesondere der sogenannte „continuous-time constrained bounded-gain forgetting least-squares algorithm“ aus Jean-Jacques E. Slotine and Weiping Li. Applied nonlinear control. Prentice-Hall, New Jersey, USA, 1991. verwendet und um den oben beschriebenen Projektionsalgorithmus erweitert werden. Daraus ergibt sich $$\begin{array}{cc}\frac{\text{d}}{\text{dt}}\vartheta ={\mathrm{\Pi }}_{\vartheta }\left(\vartheta ,P\phi \epsilon \right),& \vartheta \left(0\right)\end{array}={\vartheta }_0,$$

$$\begin{array}{cc}\frac{\text{d}}{\text{dt}}P={\mathrm{\Pi }}_P\left(\vartheta ,\beta P-P\frac{\phi {\phi }^T}{m^2}P\right),& \text{P}\left(0\right)=P_0\text{I},\end{array}$$

mit $${\mathrm{\Pi }}_{\text{P}}\left(\vartheta ,\cdot \right)=\{\begin{array}{l}\cdot \text{ if }\vartheta \in {\mathcal{S}}^{\circ }\text{ or}\left(\text{if }\vartheta \in \delta \mathcal{S}\text{ and}{\left(\text{P}\phi \epsilon \right)}^{\text{T}}\nabla \text{g}\le 0\right)\hfill \\ 0\text{ otherwise}.\hfill \end{array}$$

The projection vector z can be defined by $${\mathrm{\Pi }}_{\vartheta }\left(\vartheta ,\mathrm{e.g}\right)=\underset{\eta \to 0}{lim}\frac{{\mathcal{P}}_{\vartheta }\left(\vartheta +\eta \mathrm{e.g}\right)-\vartheta }{\eta },$$

with the convex set S = {ϑ ∈ IR ² |g(ϑ) ≤ 0}, whose boundary δS and interior S ⁰ . The inequality g(ϑ) ≤ 0 describes the set S in the parameter space. To estimate the parameter vector ϑ, the so-called “continuous-time constrained bounded-gain forgetting least-squares algorithm” from Jean-Jacques E. Slotine and Weiping Li. Applied nonlinear control can be used in particular. Prentice-Hall, New Jersey, USA, 1991. can be used and expanded to include the projection algorithm described above. This results in $$\begin{array}{cc}\frac{\text{d}}{\text{German}}\vartheta ={\mathrm{\Pi }}_{\vartheta }\left(\vartheta ,P\phi \epsilon \right),& \vartheta \left(0\right)\end{array}={\vartheta }_0,$$

$$\begin{array}{cc}\frac{\text{d}}{\text{German}}P={\mathrm{\Pi }}_P\left(\vartheta ,\beta P-P\frac{\phi {\phi }^T}{m^2}P\right),& \text{P}\left(0\right)=P_0\text{I},\end{array}$$

with $${\mathrm{\Pi }}_{\text{P}}\left(\vartheta ,\cdot \right)=\{\begin{array}{l}\cdot \text{if}\vartheta \in {\mathcal{S}}^{\circ }\text{or}\left(\text{if}\vartheta \in \delta \mathcal{S}\text{and}{\left(\text{P}\phi \epsilon \right)}^{\text{T}}\nabla \text{G}\le 0\right)\hfill \\ 0\text{otherwise}.\hfill \end{array}$$

Here P is the positive definite gain matrix, ϑ and P ₀ I > 0 are the initial conditions, and I denotes the identity matrix.

garantiert eine obere und untere Schranke für die Verstärkungsmatrix P und einen maximalen Vergessensfaktor von β_max, siehe Jean-Jacques E. Slotine et al, ebd.The (time-dependent) forgetting factor $$\beta ={\beta }_{\text{Max}}\left(1-\frac{\Vert P\Vert }{P_{\text{Max}}}\right)$$

guarantees an upper and lower bound for the gain matrix P and a maximum forgetting factor of β _max , see Jean-Jacques E. Slotine et al, ibid.

For a more detailed one Analysis of the least squares adaptation algorithms can be found on JE Parkum, NK Poulsen, and J. Holst. Selective forgetting in adaptive procedures. In Proc. IFAC World Congress, pages 137 - 142, Tallinn, Estonia, 1990. or Vitaly Shaferman, Michael Schwegel, Tobias Glück, and Andreas Kugi. Continuous-time least-squares forgetting algorithms for indirect adaptive control. European Journal of Control, 2021 . referred.

The upper bound for the norm of the gain matrix can be given by P _max >0. The parameters β _max , P _max and the filter constant λ _α of the low pass enable independent tuning of the adaptation algorithm. Therefore, strong filtering can be used to suppress noise and filter unmodeled system dynamics.

mit der Regelabweichung e = r - y und dem Kontrollfilter $${\mathrm{\Lambda }}_c\left(s\right)=\frac{{\lambda }_c}{s+{\lambda }_c}$$

wobei λ_c > 0 die Filterkonstante bezeichnet. Der Kontrollfilter λ_c dient im Wesentlichen der theoretischen Betrachtung und kann in der Praxis entfallen, d.h. Λ_c=1.Using the principle of certainty equivalence, adaptive pole control (see e.g. Petros A. loannou and Jing Sun. Robust Adaptive Control. Dover, New York, USA, 2012.) enables the derivation of an adaptive controller with feedback $$u_{fb}={\mathrm{\Lambda }}_c^{-1}{\displaystyle {\int }_0^t\left({\widehat{k}}_p{\mathrm{\Lambda }}_c\dot{e}+{\widehat{k}}_i{\mathrm{\Lambda }}_{c}e\right)}\text{d}\tau ,$$

with the control deviation e = r - y and the control filter $${\mathrm{\Lambda }}_c\left(s\right)=\frac{{\lambda }_c}{s+{\lambda }_c}$$

where λ _c > 0 denotes the filter constant. The control filter λ _c is essentially used for theoretical considerations and can be omitted in practice, ie Λ _c =1.

mit konstanten Koeffizienten ${\alpha }_1^{*}>0$

und ${\alpha }_0^{*}>0.$

The adaptive feedback controller (12) is a PI controller with proportional and integral gains that are parameterized by adaptive pole placement according to the following formula: $${\widehat{k}}_p=\widehat{L}{\alpha }_1^{*}-\widehat{R}\text{and}{\widehat{k}}_i=\widehat{L}{\alpha }_0^{*}$$

with constant coefficients ${\alpha }_1^{*}>0$

and ${\alpha }_0^{*}>0.$

The adaptive forward controller is used to improve the tracking performance $$u_{\text{ff}}={\mathrm{\Lambda }}_c{}^{-1}\left(\widehat{L}{\mathrm{\Lambda }}_c\dot{r}+\widehat{R}{\mathrm{\Lambda }}_{c}r\right)$$

Finally, the two-degree-of-freedom adaptive control input is specified as follows: $$u=u_{ff}+u_{fb}$$

mit e_c = Λ_ce.Applying (16) with (12)-(15) to (1) and assuming that certainty equivalence holds, so that the estimated parameters L̂ and R̂ correspond to their real values L or. R correspond, the error system results in a closed control loop $${\ddot{e}}_c+{\alpha }_1^{*}{\dot{e}}_c+{\alpha }_0^{*}{e}_c=0$$

with e _c = Λ _c e.

und ${\alpha }_1^{*}$

durch Polplatzierung so gewählt werden, dass die Fehlerdynamik (17) im geschlossenen Regelkreis exponentiell stabil ist und eine gewünschte Abklingrate aufweist.It is understood that ${\alpha }_0^{*}$

and ${\alpha }_1^{*}$

can be selected by pole placement so that the error dynamics (17) in the closed control loop is exponentially stable and has a desired decay rate.

It should be noted that the filter Λ _c ^-1 can also be implemented in the form of a feedback, see Petros A. loannou et al., ibid.

This combines the feedforward and feedback control (16) with (12) - (15) with the parameter adjustment algorithm (11).

To account for the nonlinear behavior of inductance as a function of coil current (ie, L depends on I), local inductance estimates may be used according to preferred embodiments of the invention. The nonlinear curve L(1) is approximated by several adjustments of a lower order, analogous to a spline approximation. The current axis is divided into k segments, with an index being defined for all segments $$I=\left\{\mathrm{1,}\dots ,k\right\}.$$

Although the intervals below are formed for the actual current value y, this is possible in the same way for the current setpoint value r.

Die trivialen Grenzen l₀=-∞ und l_k=∞ werden für eine einheitliche Schreibweise verwendet. Außerdem wird die direkte Abhängigkeit der Signale von der Zeit t weggelassen, wenn sie sich aus dem Zusammenhang ergibt. Es wird angenommen, dass die geschätzte Induktivität L̂(y) eine stückweise konstante Funktion des Magnetspulenstroms y ist. Die konstante Induktivität über das Intervall i wird mit L_ji bezeichnet: $$\widehat{L}\left(y\right)=\{\begin{array}{c}{\widehat{L}}_1\text{ for }{l}_0\le y\le l_1\\ {\widehat{L}}_2\text{ for }{l}_1<y\le l_2\\ ⋮\\ {\widehat{L}}_k\text{ for }{l}_{k-1}<y\le l_k\end{array}$$

Note that this partitioning can be done by dividing the input space into any number of mutually disjoint polyhedral sets covering the entire space (full polyhedral partitioning). The limits l _i are introduced to divide the intervals, i.e $i\in I\backslash \left\{k\right\}.$

The trivial limits l ₀ =-∞ and l _k =∞ are used for a consistent notation. In addition, the direct dependence of the signals on time t is omitted if it results from the context. The estimated inductance L̂(y) is assumed to be a piecewise constant function of the solenoid current y. The constant inductance over the interval i is denoted by L _ji : $$\widehat{L}\left(y\right)=\{\begin{array}{c}{\widehat{L}}_1\text{for}{l}_0\le y\le l_1\\ {\widehat{L}}_2\text{for}{l}_1<y\le l_2\\ ⋮\\ {\widehat{L}}_k\text{for}{l}_{k-1}<y\le l_k\end{array}$$

Similarly, the corresponding resistance estimates for the same intervals are defined by: $$\widehat{R}\left(y\right)=\{\begin{array}{c}{\widehat{R}}_1\text{for}{l}_0\le y\le l_1\\ {\widehat{R}}_2\text{for}{l}_1<y\le l_2\\ ⋮\\ {\widehat{R}}_k\text{for}{l}_{k-1}<y\le l_k\end{array}$$

It should be made clear at this point that the (ohmic) resistance is in principle independent of the current and can therefore be equated for all intervals. However, other inaccuracies in the model can be corrected through an interval-dependent different calculation.

eingeführt, um das Intervall zu bezeichnen, das die gefilterte Magnetstrommessung yf(t) enthält. Zur Identifizierung wird das gefilterte Signal yf(t) verwendet, um das aktive Intervall a(y_f(t)) zu finden, das die Phasenverschiebung der gefilterten Regressionssignale <p(t) im Algorithmus der kleinsten Quadrate berücksichtigt.Since the identification measurements are only valid for one interval, an active index $$a\left(y_f\left(t\right)\right)=\{\begin{array}{c}1\text{for}{l}_0\le y_f\le l_1\\ 2\text{for}{l}_1<y\le l_2\\ ⋮\\ k\text{for}{l}_{k-1}<y_f\le l_k\end{array}$$

introduced to denote the interval containing the filtered magnetic current measurement yf(t). For identification, the filtered signal yf(t) is used to find the active interval a(y _f (t)), which takes into account the phase shift of the filtered regression signals <p(t) in the least squares algorithm.

For a robust parameterization, an effective value for the adaptation parameter ϑ can then be calculated from the adaptation parameter ϑ calculated piecewise depending on the current y, e.g. an average value, maximum value or similar.

• a(t) sei eine Schaltfunktion, die den gerade aktiven Index auswählt, und a(t) ∈ J für alle Zeiten t. Ferner sei $${\vartheta }_i\left(t\right)=\left[\begin{array}{c}{\widehat{L}}_i\\ {\widehat{R}}_i\end{array}\right]$$
  
• die Schätzung i, die sich aus der Induktivitätsschätzung L̂_i und der Widerstandsschätzung R̂_i zusammensetzt. Zusätzlich wird die kleinste quadratische Verstärkungsmatrix P_i(t) > 0 eingeführt, die wie der Schätzvektor durch die aktive Indexfunktion (21) geschaltet wird. Mit diesen Definitionen ist der stückweise Kleinste-Quadrate-Algorithmus gegeben durch $${\dot{\text{P}}}_i=\{\begin{array}{ll}\beta {\text{P}}_i-{\text{P}}_i\phi {\phi }^{\text{T}}{\text{P}}_i\hfill & ,\text{ if }i=a\left(t\right)\hfill \\ 0\hfill & ,\text{ if }i\ne a\left(t\right)\hfill \end{array}$$
  
  $${\dot{\vartheta }}_i=\{\begin{array}{ll}{\text{P}}_i\phi {\epsilon }_i\hfill & ,\text{ if }i=a\left(t\right)\hfill \\ 0\hfill & ,\text{ if }i\ne a\left(t\right)\hfill \end{array}$$
  
  wobei der Schätzungsfehler $${\epsilon }_i=z-{\phi }^T{\vartheta }_i$$
  
  von dem jeweiligen Schätzvektor abhängt. Es ist leicht zu erkennen, dass jeder Parametervektor ϑ_i, und jede Verstärkungsmatrix P_i, i ∈ J konstant gehalten wird, mit Ausnahme des aktiven Parametervektors ϑ_a(t) und der Verstärkungsmatrix P_a(t). Somit kann der Algorithmus als ein Least-Squares-Algorithmus mit einem geschalteten Zustand und einem Speicher für die inaktiven Zustände betrachtet werden, d.h. in anderen Worten bei der Berechnung eines Stücks ϑ_i des wenigstens einen Anpassungsparameters werden andere Stücke nicht verändert.

For an even more precise implementation of the partitioning scheme, one can advantageously proceed as follows:

• Let a(t) be a switching function that selects the currently active index, and let a(t) ∈ J for all times t. Further be $${\vartheta }_i\left(t\right)=\left[\begin{array}{c}{\widehat{L}}_i\\ {\widehat{R}}_i\end{array}\right]$$
  
• the estimate i, which is composed of the inductance estimate L̂ _i and the resistance estimate R̂ _i . In addition, the smallest square gain matrix P _i (t) > 0 is introduced, which, like the estimation vector, is switched by the active index function (21). With these definitions, the piecewise least squares algorithm is given by $${\dot{\text{P}}}_i=\{\begin{array}{ll}\beta {\text{P}}_i-{\text{P}}_i\phi {\phi }^{\text{T}}{\text{P}}_i\hfill & ,\text{if}i=a\left(t\right)\hfill \\ 0\hfill & ,\text{if}i\ne a\left(t\right)\hfill \end{array}$$
  
  $${\dot{\vartheta }}_i=\{\begin{array}{ll}{\text{P}}_i\phi {\epsilon }_i\hfill & ,\text{if}i=a\left(t\right)\hfill \\ 0\hfill & ,\text{if}i\ne a\left(t\right)\hfill \end{array}$$
  
  where is the estimation error $${\epsilon }_i=\mathrm{e.g}-{\phi }^T{\vartheta }_i$$
  
  depends on the respective estimation vector. It is easy to see that each parameter vector ϑ _i , and each gain matrix P _i , i ∈ J is kept constant, except for the active parameter vector ϑ _a(t) and the gain matrix P _a(t) . Thus, the algorithm can be viewed as a least squares algorithm with a switched state and a memory for the inactive states, that is, in other words, when calculating a piece ϑ _i of the at least one adaptation parameter, other pieces are not changed.

The choice of the number of polyhedra to partition the stream space is a compromise between fitting the data and avoiding model complexity and overfitting. Precise matching can be achieved with fine partitioning because many pieces (parameters) can be used to locally approximate the inductance. However, partitioning that is too fine leads to poor generalization to unexcited regions in the regression space. This is related to one of the most important aspects of stochastic identification methods, the so-called bias-variance dilemma (cf. Sergios Theodoridis, Aggelos Pikrakis, Konstantinos Koutroumbas, and Dionisis Cavouras. Introduction to pattern recognition: a matlab approach. Academic Press, 2010) .

$${\dot{\vartheta }}_i=\{\begin{array}{ll}{\text{P}}_i\phi {\epsilon }_i\hfill & ,\text{ if }i=a\left(t\right)\hfill \\ \hfill & \text{or}\left(i<a\left(t\right)\text{ and }{\vartheta }_i\le {\vartheta }_{a\left(t\right)}\right)\hfill \\ \hfill & \text{or}\left(i>a\left(t\right)\text{ and }{\vartheta }_i\ge {\vartheta }_{a\left(t\right)}\right)\hfill \\ 0\hfill & ,\text{ else}.\hfill \end{array}$$

To solve this problem, the inactive pieces (parameters) should be updated with new information. Multiple estimates use the information content of the regression signal even when over-parameterized. This update However, the calculation must be based on further knowledge of the inductance characteristic. Since this characteristic is monotonic, any piece that would violate this property can be updated along with the active piece. This allows multiple pieces to be updated simultaneously while ensuring a monotonic inductance characteristic. So the piecewise least squares (24) are changed to $${\dot{\text{P}}}_i=\{\begin{array}{ll}\beta {\text{P}}_i-{\text{P}}_i\phi {\phi }^{\text{T}}{\text{P}}_i\hfill & ,\text{if}i=a\left(t\right)\hfill \\ 0\hfill & ,\text{if}i\ne a\left(t\right)\hfill \end{array}$$

$${\dot{\vartheta }}_i=\{\begin{array}{ll}{\text{P}}_i\phi {\epsilon }_i\hfill & ,\text{if}i=a\left(t\right)\hfill \\ \hfill & \text{or}\left(i<a\left(t\right)\text{and}{\vartheta }_i\le {\vartheta }_{a\left(t\right)}\right)\hfill \\ \hfill & \text{or}\left(i>a\left(t\right)\text{and}{\vartheta }_i\ge {\vartheta }_{a\left(t\right)}\right)\hfill \\ 0\hfill & ,\text{else}.\hfill \end{array}$$

With this algorithm, all estimated inductance chunks are updated along with the active chunk when the respective estimate would otherwise violate the monotonicity of the inductance.

An advantageous embodiment uses triangular basis functions to calculate the inductance piecewise.

This application presents approaches to improving the identification of magnetic inductance. Typically, the nonlinear inductance characteristic of a solenoid cannot be approximated by individual polynomial functions. Although a recursive least squares algorithm converges with a linear induction model in simulation, this approach is unstable due to model uncertainties and signal noise. In particular, the slope parameter and the offset parameter exhibit significant drift and lead to negative inductance estimates when the setpoint changes. This behavior leads to destabilization of the controller.

The local identification approach through low-order models overcomes these disadvantages and leads to very fast and precise inductance identification. This can be extended to the identification of the piecewise constant inductance. The invention shows very good results, both in terms of computational complexity and the ability to approximate the nonlinear saturation of the magnetic inductance.

A further modification of the adaptation scheme uses the well-known property of the monotonicity of the adapted characteristic curve. Leveraging this knowledge can dramatically improve transient response in piecewise identification, especially when some current intervals are only sparsely excited. In this case, the information from the measurements can be used to update several parameters if their relationship to each other is known a priori.

A complete two-degree-of-freedom adaptive control scheme for a magnet is presented, where even constant parameters can be used for very fast and precise control. This approach is very suitable for the adaptive control of a wide range of electromagnets and has been experimentally validated for several electromagnets. Furthermore, through appropriate modifications, improved performance in terms of nonlinear saturation properties in the simulation was achieved. The proposed piecewise identification is a flexible approach to identify nonlinear characteristic functions and surfaces. It combines low computational and implementation complexity with precise tracking capability. Additional modifications to the adaptation scheme can further improve the transient response and robustness of the approach.

QUOTES INCLUDED IN THE DESCRIPTION

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Non-patent literature cited

• Analysis of the least squares fitting algorithms is provided by J.E. Parkum, N.K. Poulsen, and J. Holst. Selective forgetting in adaptive procedures. In Proc. IFAC World Congress, pages 137 - 142, Tallinn, Estonia, 1990. or Vitaly Shaferman, Michael Schwegel, Tobias Glück, and Andreas Kugi. Continuous-time least-squares forgetting algorithms for indirect adaptive control. European Journal of Control, 2021 [0028]

Claims (18)

Method for parameterizing a current controller (200) for an electromagnetic actuator (101) for controlling an actual value (y) of a current through the electromagnetic actuator to a setpoint (r) having a control element (201) which has a control deviation between the setpoint and the actual value is supplied and that a first manipulated variable (u _fb ) is calculated from the control deviation in accordance with a control regulation with control parameters, a total manipulated variable (u) being calculated from the first manipulated variable, the current through the electromagnetic actuator (101) being determined in accordance with the overall manipulated variable ( u) is generated, characterized in that the actual value (y) and the total manipulated variable (u) are fed to a parameter adaptation element (206), which calculates at least one adaptation parameter (ϑ) for adapting the control parameters. Procedure according to Claim 1 , wherein the at least one adaptation parameter (ϑ) is selected from an electrical resistance (R) and an inductance (L) of the electromagnetic actuator (101). Procedure according to Claim 2 , whereby the rule includes: $$u_{fb}={\mathrm{\Lambda }}_c{}^{-1}{\displaystyle {\int }_0^t\left({\widehat{k}}_p{\mathrm{\Lambda }}_c\dot{e}+{\widehat{k}}_i{\mathrm{\Lambda }}_{c}e\right)}\text{d}\tau \text{,}$$

with the first manipulated variable u _fb , the time t, a proportional gain k̂ _p , an integral gain k̂ _i, a control deviation e as the difference between the setpoint (r) and the actual value (y) and a control filter ${\mathrm{\Lambda }}_c\left(s\right)=\frac{{\lambda }_c}{s+{\lambda }_c},$

where s is the Laplace variable and λ _c > 0 is the filter constant, or Λ _c =1. Procedure according to Claim 3 , where the proportional gain k̂ _p and the integral gains k̂ _p are calculated according to: $${\widehat{k}}_p=\widehat{L}{\alpha }_1^{*}-\widehat{R}\text{and}{\widehat{k}}_i=\widehat{L}{\alpha }_0^{*}$$

with constant coefficients ${\alpha }_1^{*}>0$

and ${\alpha }_0^{*}>0.$

Method according to one of the preceding claims, wherein the current regulator (200) has a pilot control element (202) to which the setpoint value (r) is supplied and which calculates a second manipulated variable (u _ff ) from the setpoint value (r) in accordance with a pilot control rule with pilot control parameters , whereby the total manipulated variable (u) is calculated from the first and second manipulated variables, the parameter adaptation element (206) also calculating the adaptation parameters (ϑ) to adapt the pilot control parameters. Procedure according to Claim 5 and 2 whereby the input tax provision includes $$u_{\text{ff}}={\mathrm{\Lambda }}_c{}^{-1}\left(\widehat{L}{\mathrm{\Lambda }}_c\dot{r}+\widehat{R}{\mathrm{\Lambda }}_{c}r\right)$$

with the second manipulated variable u _ff , and a control filter ${\mathrm{\Lambda }}_c\left(s\right)=\frac{{\lambda }_c}{s+{\lambda }_c},$

where s denotes the Laplace variable and λ _c > 0 the filter constant, or λ _c = 1. Method according to one of the preceding claims, wherein the parameter adaptation element (206) calculates the at least one adaptation parameter (ϑ) according to a recursive estimation method, in particular according to a recursive least squares method or according to a recursively implemented gradient estimator. Method according to one of the preceding claims, wherein the actual value (y) and the total manipulated variable (u) are filtered in accordance with a filter, in particular a low pass, and the filtered variables are fed to the parameter adaptation element (206). Procedure according to Claim 7 and 8th , where the filtered total manipulated variable (u) is chosen as the output of the recursive estimation method. Method according to one of the preceding claims, wherein the parameter adaptation element (206) calculates the at least one adaptation parameter (ϑ) repeatedly during operation to adapt the control parameters, or wherein the parameter adaptation element (206) calculates the at least one adaptation parameter (ϑ) at a teach-in time to adapt the Control parameters calculated and repeatedly calculated during operation for diagnosis. Method according to one of the preceding claims, wherein the parameter adaptation element (206) calculates the at least one adaptation parameter (ϑ) piece by piece depending on the actual value (y) or the setpoint value (r) of the current through the electromagnetic actuator. Procedure according to Claim 11 , where an effective value for the at least one adaptation parameter (ϑ) from the piecewise depending on the actual value (y) or the setpoint (r) of the current through the electromagnetic actuator calculated at least one adjustment parameter (ϑ) is calculated. Procedure according to Claim 11 or 12 , wherein the parameter adaptation element (206) calculates the at least one adaptation parameter (ϑ) in a piecewise constant or linear manner. Procedure according to one of the Claims 11 until 13 , wherein the parameter adaptation element (206) does not change other pieces when calculating a piece of the at least one adaptation parameter (ϑ). Procedure according to one of the Claims 11 until 13 , wherein the parameter adaptation element (206) changes other pieces when calculating a piece of the at least one adaptation parameter (ϑ), if a monotonic course of the at least one adaptation parameter (ϑ) is otherwise not achieved. Computing unit which is set up to carry out all method steps of a method according to one of the preceding claims. Computer program that causes a computing unit to carry out all process steps of a process according to one of the Claims 1 until 15 to be carried out when it is executed on the computing unit. Machine-readable storage medium with a computer program stored on it Claim 17 .

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