DE102017200839A1 - Method for controlling a rotational speed of an electrical machine - Google Patents

Abstract

The invention relates to a method for controlling the rotational speed of an electrical machine (20), in which a controller and a dynamic precontrol are used, wherein in the precontrol a dynamic, inverse model of the controlled system is stored, wherein in the controller a target speed and an actual speed are input and in the pilot control, the target speed and a derivative of the target speed can be entered, so that a pilot component and a controller component are determined, which together enter into the controlled system.

Description

The invention relates to a method for controlling a rotational speed of an electrical machine and to an arrangement for carrying out the method.

State of the art

An electric machine is an energy converter that converts kinetic energy into electrical energy as a generator and electrical energy into kinetic energy as an electric motor. All electrical machines have an electrical circuit that is essential to their function.

Electric motors are used in motor vehicles, for example. As a drive for the motor vehicle itself, but also for other tasks, such. B. used as a drive of other components. Thus, in supercharged internal combustion engines to increase the efficiency air is supplied to the engine with increased pressure. However, in the lower load range, the exhaust gas amount is not enough to bring the turbine or the compressor of the exhaust gas turbocharger to high speeds. This means that the compressor can not compress the air sufficiently high, resulting in the known turbo lag.

Remedy here additional compressor, the z. B. can be driven by electric machines. The compressors can be designed as turbomachines or displacement machines. The latter can lead to problems due to the higher friction in the control.

From the publication DE 101 24 543 A1 For example, a method and a device for controlling an electrically operated supercharger which interacts with an exhaust gas turbocharger for compressing the air supplied to an internal combustion engine are known. For controlling the charger is a drive signal, which is formed depending on a predetermined value for the compressor pressure ratio of the electric charger. In this way it is possible to avoid discontinuities in the boost pressure offer and thus discontinuities in the torque of the internal combustion engine.

Disclosure of the invention

Against this background, a method according to claim 1 and an arrangement according to claim 8 are presented. Embodiments emerge from the dependent claims and from the description.

The presented method is used to dynamically control the speed of an electric motor to a desired setpoint. The final speed is dynamic and exact, d. H. even without overshoot, hit. It should be noted that the requirements for the control are very high, so that possibly typical controller structures, such as PID controllers, are not sufficient.

In order to meet the high demands on the dynamics of the adjustment, the presented method uses a precontrol with an inverse model of the controlled system. The model is based on a theory of a differentially flat system.

A system is called flat if it has a virtual output that has the same dimension as the system input and that, together with its finite number of time derivatives, describes all the dynamic properties of the system. Flatness of a system can be verified using the following equations:

$$\text{u}\mathrm{=}{\text{f}}_2\left(\text{y}\text{,dy}{\text{,d}}^2\text{y}\text{,}\dots {\text{,d}}^{\text{p}}\text{y}\right)$$

wobei f1 und f2 beliebige Funktionen und d^Py die p-te zeitliche Ableitung von y beschreibt.Consider a linear or non-linear system with the state variables x ∈ R ⁿ and input quantities u ∈ R ^m . The system has the flatness property if there are outputs y ∈ R ^m that satisfy the following equations: $$\text{x}\mathrm{=}{\text{f}}_1\left(\text{y}\text{, dy}{\text{, d}}^2\text{y}\text{.}...{\text{, d}}^{\text{p}}\text{y}\right)$$

$$\text{u}\mathrm{=}{\text{f}}_2\left(\text{y}\text{, dy}{\text{, d}}^2\text{y}\text{.}...{\text{, d}}^{\text{p}}\text{y}\right)$$

where f1 and f2 arbitrary functions and d ^P y describes the p-th time derivative of y.

For linear systems, this property is synonymous with the controllability of the system. It should be noted that a system can have multiple flat outputs. As a rule, all mechanical systems, including nonlinear ones, have this system property.

With the aid of the shallow output, a "model-based" control can be designed by means of the above equations. For this, the flat output y and its time derivatives are replaced by a desired trajectory y _d , which is also p-times differentiable. The equations (a and b) can be used to calculate the trajectories for the system states as well as the required input quantity for the realization of the trajectory.

The subordinate torque structure is part of the controlled system. Model inaccuracies and disturbances are compensated by an additional controller. The manipulated variable for the speed control is typically the setpoint torque on the electric machine, which is set or regulated underlain. Alternatively, the size to be adjusted in the lower-level torque control circuit can also be directly adjusted be used. In PM synchronous machines (PM: permanent magnet) this is, for example, the target current.

It is thus achieved that the controller must intervene only in exceptional cases. This is advantageous because a strong controller intervention possibly leads to overshoot and other adverse effects.

The system considered here is a dynamic system, i. H. it can be described by means of differential equations. The current behavior of the system is thus dependent on the present and the past.

If the input / output behavior of the system varies greatly during operation, then the system model should also be adapted accordingly. Since the friction torques in an electric machine vary greatly over the lifetime but also over environmental conditions, the controller behavior can be improved by an adaptation. For this purpose, a recursive parameter estimator, such as, for example, an RLS algorithm, can be used which, during operation, if necessary, adjusts the model parameters appropriately online via a comparison with the measurement. Thus, the input / output behavior of the real route is modeled and possible changes in the behavior are learned. In order to avoid that the adaptation happens in poorly identifiable or invalid states, a situation-dependent activation is necessary.

The speed controller is based on an existing torque control, whereby a so-called cascade controller structure can be used. Thus, the method can be used not only for a PM synchronous machine, but for each speed control with subordinate torque structure.

Further advantages and embodiments of the invention will become apparent from the description and the accompanying drawings.

It is understood that the features mentioned above and those yet to be explained below can be used not only in the respectively specified combination but also in other combinations or in isolation, without departing from the scope of the present invention.

list of figures

• 1 shows a schematic representation of a motor vehicle with an arrangement for carrying out the method.
• 2 shows a block diagram of an embodiment of an arrangement for carrying out the method described.

Embodiments of the invention

The invention is schematically illustrated by means of embodiments in the drawings and will be described in detail below with reference to the drawings.

1 shows in a schematic representation greatly simplifies a motor vehicle 10 with an internal combustion engine 12 to which an exhaust gas turbocharger 14 is assigned, in turn, a compressor 16 is provided. To support the compressor 16 and / or the exhaust gas turbocharger 14 is an additional compressor 18 provided by an electric machine 20 , in this case powered by an electric motor. The speed of this electric motor is controlled, including an arrangement 22 is provided for control, which is set up in particular for carrying out the method presented herein.

2 shows an arrangement for carrying out the method described, in total with the reference numeral 50 is designated. The order 50 includes a feedforward control 52 in which an inverse model 53 is stored, a controller 54 and a parameter estimator 56 , Furthermore, the illustration shows a distance 60 for the torque behavior of an electric machine and a distance 62 for the speed behavior of the electric machine.

Input variables in the feedforward control 52 include a setpoint speed 70 and the derivative 72 the target speed 70 , Output is a pre-tax share 74 , Input variables in the controller 54 include the setpoint speed 70 and an actual speed 76. output is a regulator part 78 , This regulator share 78 together with the input tax share 74 , while outputs from both parts are added together, both signals together form the desired torque, forming an input variable 80 for the track 60 the moment behavior. Initial size of the route 60 is a manipulated variable 82 included in the parameter estimator 56 and enters the track 62 for the speed behavior. Initial size of this route 62 is the actual speed 76 ,

The model of the controlled system 60 and 62 is as follows:

The route for the speed control 62 can be described in general terms as follows: $$\dot{w}=\frac{1}{J}\left(M-M_v\left(w\text{.}T\right)\right)$$

In it, w describes the rotational speed, J the moment of inertia, M the moment of the PM synchronous machine and M _v the loss moment which of various sizes but essentially of the speed w and on the temperature T depends. If the losses are approximated with a viscous friction coefficient k _v and with a constant (coulombic) friction coefficient k _off , then the following equation results: $$M_v=k_{v}w+k_{Off}$$

Substituting Equation (2) into Equation (1), an exemplary approximation of the speed behavior results as follows $$J\frac{dw}{dt}+k_{v}w+k_{Off}=M$$

mit der Zeitkonstante τ und der statischen Verstärkung K beschreiben. Die statische Verstärkung K wird bei einer korrekt entworfenen Momentenregelung 1 sein. Die Ordnung der Übertragungsfunktion darf beliebig gewählt werden, dadurch ändert sich selbstverständlich die Ordnung des Gesamtsystems. Die vorgestellte Strategie für die Regelung kann aber immer noch angewendet werden.Since the moment M can not usually be put directly, but is also subject to a delay, this must also be taken into account. In the following, this delay between the actual and desired torque, for example, with a first-order delay element $$\dot{M}=\frac{1}{\tau }\left(M_{sOll}K-M\right)$$

with the time constant τ and the static gain K describe. The static gain K is at a correctly designed torque control 1 be. The order of the transfer function may be chosen arbitrarily, this of course changes the order of the entire system. However, the presented strategy for regulation can still be applied.

p₂:

= τJ

p₁:

= τk_v + J

p₀:

= k_v

p_off:

= k_off

The pilot control design is based on the theory of differential flat systems, where the speed w is the flat output. We derive equation (3) by time and the equations for w and ẅ are solved for M and Ṁ. If these equations are used in equation (4), one obtains the relationship between desired torque M _soll and angular velocity w and its first and second time derivative: $$p_2\frac{d^{2}w}{d{t}^2}+p_1\frac{dw}{dt}+p_{0}w+p_{Off}=M_{sOll}$$

p ₂ :

= τJ

p ₁ :

= τk _v + J

p ₀ :

= k _v

p _off :

= k _off

If there is a twice differentiable setpoint trajectory for the speed profile, the required setpoint torque u _v in the precontrol can be calculated by means of equation (5) in the following way: $$p_v\frac{d^2{w}_{sOll}}{d{t}^2}+p_1\frac{d{w}_{sOll}}{dt}+p_0{w}_{sOll}+p_{Off}$$

This means that a triple continuously differentiable trajectory should be specified for the desired speed curve. This property can be ensured, for example, by the use of a state variable filter for the calculation of the setpoint speed and the associated derivatives.

The estimation of the friction moments for the precontrol takes place in such a way:

wobei N_p die Polpaarzahl der Synchronmaschine, Psi der verkettete Fluss, L_d die Motorinduktivität in der D-Koordinate (direct axis), L_q die Motorinduktivität in Q-Koordinate (quadrature axis) und I_d und I_q der gemessene Strom in den D- und Q-Koordinaten beschreibt. Es ist wichtig zu wissen, dass auch Messfehler sowie Ungenauigkeiten der Motorparameter als Verlustmoment auftreten und in dieser Weise in der Vorsteuerung kompensiert werden.The relationship between the lossless moment and the speed change is given in the equation (1). In a permanent magnet synchronous machine, the ideal acceleration torque depends on the current and motor parameters and can be expressed in D / Q coordinates as follows: $$M=\frac{3}{2}{N}_p\left(Psi{I}_q+\left(L_d-L_q\right)I_d{I}_q\right)$$

where N _{p is} the pole pair number of the synchronous machine, Psi is the concatenated flux, L _{d is} the motor inductance in the D coordinate (direct axis), L _{q is} the motor inductance in the Q coordinate (quadrature axis) and I _d and I _{q is} the measured current in the Describes D and Q coordinates. It is important to know that also measurement errors and inaccuracies of the motor parameters occur as loss torque and are compensated in this way in the pilot control.

With the linear friction model given in equation (2), equation (1) can be given in the following way: $$M=j\dot{w}+M_v=\left(\dot{w}w1\right)\left(\begin{array}{c}j\\ k_v\\ k_{Off}\end{array}\right)$$

If the moment of inertia j is known and should not be estimated, then it can be eliminated by the parameter vector and the following equation results: $$M-j\dot{w}+M_v=\left(w1\right)\left(\begin{array}{c}{k}_v\\ k_{Off}\end{array}\right)$$

Also, if the moment of inertia is to be estimated, and therefore Equation (8) is used, it is important to calculate the first derivative in a suitable way, since the Angular acceleration is usually not available. If filtering is used, then all input and output signals should be filtered with the same filter to avoid phase shifting.

In both cases, the least squares method can be used to define the unknown parameters. For this, equation (8) or (9) is first made in a matrix form by writing the equations at different times among each other, as shown below for a general case: $$\begin{array}{ccc}\underset{U}{\underset{\}}{\left[\begin{array}{c}{u}_1\\ u_2\\ ⋮\\ u_2\end{array}\right]}}=& \underset{Y^T}{\underset{\}}{\left[\begin{array}{cccc}y1.1& y\mathrm{1,}\text{2}& \cdots & y\mathrm{1,}m\\ y2.1& y\mathrm{2,}\text{2}& \cdots & y\mathrm{2,}m\\ ⋮& ⋮& \ddots & ⋮\\ yn\mathrm{,1}& yn\text{2}& \cdots & yn\text{.}m\end{array}\right]}}& \underset{\mathrm{\Theta }}{\underset{\}}{\left[\begin{array}{c}{\mathrm{\theta }}_1\\ {\mathrm{\theta }}_2\\ ⋮\\ {\mathrm{\theta }}_m\end{array}\right]}}\end{array}$$

Here n describes the number of measurements because m describes the number of unknown parameters (for equation (8) 3 and for equation (9) 4).

By means of a pseudoinverse the equation can be solved in the following way: $$\begin{array}{l}U=Y^T\mathrm{\Theta }\\ \Rightarrow \mathrm{\Theta }={\left(Y{Y}^T\right)}^{-1}YU\end{array}$$

Theoretically, it is sufficient for the solution if the number of measurements is greater than or equal to the number of unknown parameters. However, in order for the estimate to be of good quality and to avoid any numerical problems, the number of measurements should be much higher than the number of unknown parameters and the linear independence of different lines should be ensured.

Especially when the friction parameters show a strong time and / or operating point dependence, it is expedient to solve the equation in a recursive manner. In the literature, possible methods are offered, one possible implementation option is given below: $$\begin{array}{l}{\mathrm{\gamma }}_k=\mathrm{+\; \lambda }{{\displaystyle y}}_k^T\begin{array}{l}{P}_{k-1}\hfill \end{array}\begin{array}{l}{y}_k\hfill \end{array}\\ P_k=\frac{1}{\mathrm{\lambda }}\left(P_{k-1}-\frac{P_{k-1}\begin{array}{l}{y}_k\hfill \end{array}\begin{array}{l}{{\displaystyle y}}_k^T\begin{array}{l}{P}_{k-1}\hfill \end{array}\hfill \end{array}}{\mathrm{\gamma }k}\right)\\ e_k=u_k-{{\displaystyle y}}_k^T\begin{array}{l}{\begin{array}{l}\mathrm{\theta }\hfill \end{array}}_{k-1}\hfill \end{array}\\ {\mathrm{\Theta }}_k={\mathrm{\Theta }}_{k-1}+\frac{P_{k-1}\begin{array}{l}{y}_k\hfill \end{array}}{\mathrm{\gamma }k}{e}_k\end{array}$$

Here λ describes the forgetting factor and P the covariance matrix. The forgetting factor allows newer measurements in the equation to be prioritized higher. The initial value of the covariance matrix describes the assumed quality of the initial values.

To compensate for modeling errors as well as for disturbance suppression, the designed feedforward control in equation (6) is supplemented by an additional controller component, eg. In the form: $$u=u_v+u_r$$

der mit k3 = 0 einem PID-Regler entspricht. Sind Stellgrößenbeschränkungen relevant, kann im Regler ein Anti-Windup-Mechanismus für den Integralanteil verwendet werden.For u _r , with e = w _soll - w z. B. a state controller can be used, $$u_r=k_3\ddot{e}+k_2\dot{e}+k_{1}e+k_0{\displaystyle \int edt}$$

with k3 = 0 corresponds to a PID controller. If manipulated variable restrictions are relevant, an anti-windup mechanism for the integral component can be used in the controller.

The model-based inversion of the distance in the feedforward control can be reconstructed from the drive signal in the speed control and thus detected. The precontrol leads to a characteristic shaping of the drive signal, which is not present by a control alone, in particular in a PID controller.

The presented method can generally be used in a speed control with a subordinate torque structure. This means that the controller can be designed in cascade structure.

Furthermore, the method can be used in a speed controller with lower-level current controller for an electric auxiliary turbocharger. Another field of application is in the speed control to zero speed when the electric motor should be brought as soon as possible in passive mode given.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 10124543 A1 [0005]

Claims (9)

Method for controlling the rotational speed of an electrical machine (20), in which a controller (54) and a dynamic precontrol (52) are used, wherein in the feedforward control (52) a dynamic, inverse model (53) of the controlled system (60, 62 ), wherein in the controller (54) a target speed (70) and an actual speed (76) are input and in the feedforward control (52) the target speed (70) and a derivative (72) of the target speed (70) are entered, so that a pilot component (74) and a controller component (78) are determined, which together enter into the controlled system (60, 62). Method according to Claim 1 in which the inverse model (53) of the controlled system (60, 62) is based on a theory of a differential flat model. Method according to Claim 1 or 2 in which the model (53) of the controlled system (60, 62), which is stored in the feedforward control (52), is a time-variant model. Method according to Claim 3 in which parameters of the time-variant model are determined with a parameter estimator (56). Method according to one of Claims 1 to 4 in which the controlled system (60, 62) comprises a torque behavior path (60) and a speed behavior path (62). Method according to one of Claims 1 to 5 in which the electric machine (20) is adapted to drive an auxiliary compressor (18). Method according to one of Claims 1 to 6 in which a cascade controller structure is used in the controller (54). Arrangement for controlling the rotational speed of an electric machine (20), which in particular for carrying out a method according to one of Claims 1 to 7 is set up. Arrangement according to Claim 8 in which a dynamic, inverse model (53) of the controlled system (60, 62) is stored in the feedforward control (52).

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