The present teaching relates to a test bench and a method for carrying out a dynamic test run for a test setup on a test bench, the test setup comprising at least one torque generator, which is mechanically coupled on the test bench with at least one torque sink by means of a coupling element, and wherein the torque generator, the coupling element, and the torque sink are described with system parameters characterizing the dynamic response.
The development of drive units, such as internal combustion engines or electric motors, of drive trains with such drive units or of drive train components with such drive units, largely take place on test benches. Likewise, the calibration of a control function or regulation function of a vehicle, for example to meet legal requirements, such as, for example, the emission behavior, usually takes place on a test bench. To carry out a bench test on the test bench, the test object, i.e. the drive unit or the drive train or the drive train component, is connected to a load machine (usually an electric motor, also called a dynamometer) to form a test setup on the test bench in order to be able to operate the test object against a load. The test object and load machine are usually coupled using coupling elements such as test bench shafts, coupling flanges, etc. The test setup consisting of the test object, coupling element and load machine forms a dynamic system that responds according to the dynamic response of the system when excited (for example, by the combustion shocks of an internal combustion engine or by load jumps). Of course, excitations with a natural frequency of the dynamic system are critical on the test bench, since this can create critical states that can even damage or destroy certain parts, in particular the coupling elements, of the test setup on the test bench. Knowledge of the dynamic response of the test setup is therefore important for carrying out bench tests on a test bench.
However, controllers are also used on the test bench to control components of the test setup, in particular the load machine and a drive unit, for carrying out the bench test. For the design of the controller, precise knowledge of the dynamic response of the test setup is also desirable in order to be able to adapt the controller response to it and/or to ensure the stability of the control system.
Last but not least, so-called observers are often used on a test bench in order to calculate non-directly measured or non-directly measurable quantities of the test setup from other accessible or available measurement variables. An example of this is the internal torque of the drive unit, i.e. the torque actually generated and not the torque provided, that is often required or used on the test bench for the test run.
For the design of a controller and/or an observer, a model of the dynamic system, i.e. the test setup, is generally required, which requires sufficient knowledge of the dynamic system.
The dynamic response of the test setup on the test bench is primarily determined by the inertia of the components of the test setup (in particular the test object and the load machine) and by the stiffness, possibly also the damping, of the coupling between the test object and the load machine (i.e. between the mass-loaded components of the test setup), for example, the torsional rigidity of a test bench shaft. These parameters are often determined individually for each component or are known from data sheets for the respective component. In practice, however, the use of these known parameters is often unsatisfactory when carrying out the test run and has often led to poor results. The reason for this is that adaptations of the mechanical setup of the test setup are often made on the test bench, which changes the dynamic system. For example, other measuring sensors, for example a torque sensor on the test bench shaft, are used, or mechanical components are exchanged or added or removed on the test bench. For example, an adapter flange between two components of the test setup can be changed. The properties of components in the test setup can also change due to aging, which also affects the response of the dynamic system.
From DE 10 2006 025 878 A1, it is therefore already known to determine the parameters of the dynamic response directly on the test bench. For this purpose, the test setup is dynamically excited by a pseudo-stochastic speed stimulation and the parameters of a model of the dynamic system, in particular stiffness and damping of a connecting shaft, are determined using methods of the identification theory. With the identified parameters of the model of the test setup, the response of the test setup can be described with sufficient accuracy and used for the design of an observer or a controller, but also for monitoring the system. In this approach, a parametric model of the test setup is used, i.e. a model that contains the parameters of the dynamic system and that reproduces the input/output response of the dynamic system. The parameters are ascertained as the poles of the dynamic system. A difficulty with this method is that the resultant torques have to be measured as output variables of the dynamic system due to the speed stimulation, which is difficult in practice on the test bench. Apart from this, certain assumptions about the model structure must be made in advance in order to be able to determine the parameters of an adopted model. If an unsuitable model structure is selected, the real dynamic response is only partially or inaccurately reproduced by the model. In practice, however, the correct choice of the model structure is a difficult task, especially in the case of more complex test setups with a plurality of masses and couplings in between, and can only be carried out by specialists, which limits the applicability of the method. In addition, no noise of a measurement signal (e.g. a measured speed) is taken into account during identification, which can lead to a poorer identification result. In addition, identification in DE 10 2006 025 878 A1 takes place in an open loop, although the measurement signals on the test bench were measured in a closed control loop. This can also reduce the quality of identification. Last but not least, pseudo-stochastic speed stimulation cannot be set to the desired or required frequency range. This can lead to certain frequencies not being stimulated at all or more frequencies than required being stimulated, which can also have a negative effect on the quality of identification.
It is therefore an object of the present teaching to improve the identification of system parameters of a test setup of a test bench, particularly with regard to the quality of the identification.
This object is achieved according to the present teaching in that the test setup is dynamically excited on the test bench by virtue of a dynamic input signal being applied to the test setup and, in the process, measured values of the input signal of the test setup and of a resultant output signal of the test setup are recorded, a frequency response of the dynamic response of the test setup between the output signal and the input signal is determined from the recorded input signal and output signal using a nonparametric identification method, a model structure of a parametric model that maps the input signal onto the output signal is derived from the frequency response, the model structure and a parametric identification method are used to determine at least one system parameter of the test setup, and the at least one identified system parameter is used to perform the test run. This allows a systematic identification of the required system parameters, whereby a basic characterization of the dynamic response of the test setup is carried out, from which the model structure on which the test setup is based can be derived. With the nonparametric identification, a suitable choice of the model structure can be ensured regardless of the complexity of the test setup. The following parametric identification then uses the knowledge of the model structure to determine the system parameters. An additional advantage can be seen in the fact that the nonparametric identification as well as the parametric identification uses the same measurement variables, which facilitates the implementation of the identification method.
With the nonparametric identification method, measurement noise of the input signal and/or of the output signal can also be taken into account, whereby the quality of identification can be improved. In addition, the nonparametric identification method can also be used to ascertain a variance of the measurement noise of the output signal and/or a variance of the measurement noise of the input signal, and/or a covariance of the noise between input and output. These variances are then also available for use in the parametric identification process.
Model parameters of the parametric model are advantageously determined using the parametric identification method and from this, by comparing the parametric model with a physical system model having the at least one system parameter, the at least one system parameter of a system component of the test setup is determined. This can be facilitated if the parametric model is divided into sub-models, each having model parameters, and by comparing at least one sub-model with a physical sub-model with the at least one system parameter, at least one system parameter is determined from the model parameters of the sub-model.
The at least one identified system parameter can be used for carrying out the test run by using the at least one system parameter for designing a controller for at least one component of the test setup. Or by using the at least one system parameter for designing a filter that either filters a setpoint for a controller for at least one component of the test setup or a control deviation supplied to a controller for at least one component of the test setup. Or by monitoring a change in the at least one system parameter over time. Or by using the at least one system parameter to adapt the dynamic response of the test setup to a desired dynamic response.
In the following, the present teaching is described in greater detail with reference to
For carrying out a test run, the present teaching assumes a test setup PA on a test bench 1 with a test object having a torque generator DE, for example a drive unit such as an internal combustion engine 2, and a torque sink DS coupled therewith, for example a load machine 3 (dynamometer), as load, as shown in a simple embodiment in
The present teaching assumes that dynamic system parameters describing the dynamic response, in particular mass torques of inertia J, torsional rigidities c, torsional dampings d, resonance frequencies ωR or eradication frequencies ωγ, of the concrete test setup PA, are, at least in part, not known and are to be determined before a bench test is carried out on the test bench 1.
For this purpose, according to the present teaching, the basic character of the dynamic response of the test setup PA is first determined using a nonparametric identification method, from which a model structure of a model of the test setup PA with system parameters SP of the test setup PA describing the dynamic response is derived. The system parameters SP of the model are then determined using the model structure with the system parameters SP using a parametric identification method. With nonparametric identification, only the measured input signals u(t) and measured output signals y(t) are examined.
Using the nonparametric identification method, the frequency response (characterized by the amplitude, and possibly also the phase, by frequency) of the test setup PA is determined. For the frequency response, it is known to excite the physical dynamic system (here the test setup) with a dynamic signal u(t) (input signal) with a certain frequency content and to measure the response y(t) (output signal) on the test setup PA. The input signal u(t) is, for example, a speed ωD of the torque sink DS (for example load machine 3) and the output signal y(t) is, for example, a shaft torque Tsh on the test bench shaft 4 or a speed ωE of the torque generator DE. Typically, measuring sensors MS are also provided on a test bench 1 in order to detect the measured values MW of certain measurement variables (input signal u(t), output signal y(t)) (
However, it is not important what is used as the input signal u(t) and what is used as the output signal y(t). The methodology described below is independent of this.
The frequency response is determined in a known manner from the Fourier transform of the input signal u(t) and the output signal y(t). If U(k) denotes the Fourier transform of the input signal u(t) at frequency k=jωk and Y(k) denotes the Fourier transform of the output signal y(t) at frequency k=jωk, then the frequency response G(k) results as the quotient of the Fourier transforms Y(k) of the output signal y(t) and U(k) of the input signal u(t). It is also known to take into account noise of the input signal u(t) and the output signal y(t). Noise results, for example, from a measurement noise when measuring physical quantities, from deviations between a setpoint specification on the test bench and the adjustment of the setpoint at the test bench, from process noise, etc. If nu(t) denotes the noise at the input and ny(t) denotes the noise at the output, then the input signal u(t) in the time domain can also be written as u(t)=u0(t)+nu(t) or in the frequency domain as U(k)=U0(k)+Nu(k) and the output signal y(t) in the time domain as y(t)=y0(t)+ny(t) or in the frequency domain as Y(k)=Y0(k)+Ny(k), with the noise-free signals u0, y0, or U0, Y0, and the noise signals nu, ny or Nu, Ny.
In order to approximate the frequency response G in the presence of input and output noise, there are various known nonparametric identification methods, for example spectral analysis or the local polynomial method (LPM). In the spectral analysis, either the amplitude spectrum or the power spectrum of the frequency response is evaluated, such as described in L. Ljung, “System Identification: Theory for the User,” 2nd Edition Prentice Hall PTR, 1999 or in Thomas Kuttner, “Praxiswissen Schwingungsmesstechnik,” p. 325-335, Springer Vieweg 2015. The local polynomial method is described, for example, in R. Pintelon, et al., “Estimation of non-paramteric noise and FRF models for multivariable systems—Part I: Theory,” Mechanical Systems and Signal Processing, volume 24, Issue 3, p. 573-595, 2010. The determination of the frequency response G is briefly explained below using the example of LPM
In LPM, the frequency response G is locally approximated around a local frequency k via a polynomial. This is done for all frequencies jωk of the frequency response G. If a generalized frequency Ωk is used, with Ωk=jωk for the continuous-time case and Ωk=e−jωk for the time-discrete case, the input-output behavior of the dynamic system (test setup PA) can be written in the form of
Y(k)=G(Ωk)U(k)+T(Ωk)+V(k).
Therein, G(Ωk) denotes the Fourier transform of the transfer function of the dynamic system (i.e. the frequency response between the selected input and output), T(Ωk) a transient error in the output at the frequency Ωk, which is not due to the excitation, and V(k) the measurement noise of the output signal. U(k) and Y(k) are the Fourier transforms of the measured input signal u(t) and output signal y(t).
The variables dependent of the frequency Ωk are approximated via local polynomials around a local frequency Ωk. The frequencies around Ωk are indicated by the variable r=−n, −n+1, . . . , n, whereby n is specified or selected. That leads to
Therein, gs and ts denote the 2(R+1) unknown parameters of the local polynomials of the order R (which is chosen or specified). This gives a total of 2n+1 equations for 2(R+1) unknowns (gs, ts) based on the r for each frequency k. With a parameter vector Θ(k) [G(Ωk) g1(k)g2(k) . . . gR(k)T(Ωk) t1(k) t2(k) . . . tR(k)], the 2n+1 equations can be written in matrix form Y(k)≈Φ(k)Θ(k), with the matrix
Therein the resultant 2n+1 equations for the frequencies k are stacked one above the other. The advantage of this method is that the transient component T(Ωk) can be directly estimated and does not have to be determined for certain frequency ranges by window approaches, such as in spectral analysis.
The parameter vector Θ(k) can then be estimated, for example in the sense of a least squares approximation, from a parameter estimate using the equation {circumflex over (Θ)}(k)=[Φ(k)HΦ(k)]−1 Φ(k)HY(k), where “( )H” denotes the adjoint matrix (transposed and complex conjugate).
With the resultant residual e(Ωk+1=Y(k+r)−[G(Ωk+1)U(k+r) T(Ωk+1)] of the least squares approximation, the variance σY2 (k) of the measurement noise of the output signal can also be calculated with
This approximation then also provides direct estimates for the frequency response Ĝ(Ωk) and also for the transient components {circumflex over (T)}(Ωk) Subsequently, “{circumflex over ( )}” always refers to estimates. Depending on what is used as the input signal U(k) and as the output signal Y(k), there are of course different frequency responses Ĝ(Ωk).
The case of additionally noisy input signals u(t) or the case of feedback of the noisy output signal y(t) to the input (for example in the case of a closed control loop), which likewise leads to a noisy input signal u(t), can also be covered. In order to avoid systematic errors in the parameter estimation in the presence of input noise, the parameter estimation in this case is advantageously carried out on the closed control loop. This is not a significant limitation, since technical systems such as a test setup PA on a test bench 1 are usually operated in a closed control loop. A reference signal s(t) (or the Fourier transform S(k)) is assumed which corresponds to the setpoint specification for a closed control loop. The relationship between the input signal u(t) and the reference signal s(t) results from the transfer function R of the controller and the current actual values yist to u=(s−yist)·R. The frequency response Gru(Ωk) of the reference signal to the input U(k) and the frequency response Gry(Ωk) of the reference signal to the output Y(k) are then ascertained, for example as described above, which leads to estimated frequency responses Ĝru(Ωk) and Ĝry(Ωk), with Grz(Ωk)=[Gry(Ωk) Gru(Ωk) ]T. VY(k) denotes the measurement noise of the output signal Y(k) and VU(k) denotes the measurement noise of the input signal U(k). With Z(k)=[Y(k) U(k)]T and Vz(k)=[VY(k) VU(k)]T, the system equation can then be written in the form Z(k)=Grz(Ωk)R(k)+Trz(Ωk)+VZ(k), where Trz(Ωk)=[Try(Ωk) Tru(Ωk)]T denotes the transient system error on the input and the output. An estimate of the frequency response Ĝ(Ωk) in the presence of input noise and output noise then results from Ĝ(Ωk)=Ĝry(Ωk)Ĝru−1(Ωk).
Analogous to the case with only an output noise variance σY2 (k) of the measurement noise of the output signal, in the case of input noise and output noise a variance αU2(k) of the measurement noise of the input signal and a covariance σYU2 (k) of the noise between input and output can be determined.
For the excitation of the dynamic system, the torque generator DE, like the internal combustion engine 2, is preferably towed, that is to say not fired. Although also an operated torque generator DE, such as a fired internal combustion engine 2, would also be possible for excitation, this would make identification more complex because the torque generator DE itself would introduce speed oscillations. The torque sink DS coupled to the torque generator DE, the load machine 3, which can also drive by being designed as an electric motor, is therefore preferably used for the excitation. The torque sink DS introduces speed oscillations for excitation. The excitation can take place with various signals, such as a multisine signal (in which a plurality of frequencies are excited at the same time at any point in time) or a chirp signal (in which a single frequency is excited at any point in time, for example with a linear frequency increase). The excitation signal is the setpoint specification for the test bench 1 for excitation operation. For example, speed setpoint specifications for the controller of the load machine 3 are specified as the excitation signal.
Some important properties of the dynamic system can be derived from a frequency response G(Ωk), as explained by way of example in
For example, resonance frequencies ωR and/or eradication frequencies ωF can be derived from the frequency response G(Ωk). Both frequencies can be ascertained by determining minima and maxima and the gradients in the frequency response G(Ωk). An eradication frequency ωT is therefore a minimum with a gradient reversal from negative to positive. A resonance frequency ωR a maximum with gradient reversal from positive to negative. Of course, a plurality of or no eradication frequencies ωT and/or resonance frequencies ωR can occur in the frequency response G(Ωk). Furthermore, information on the zeros can also be derived from the frequency response G(Ωk). In principle, characteristic frequency responses for various systems are known, for example for a dual-mass oscillation system (
Different characteristic frequency responses G(Ωk) result for different system configurations (with oscillatable masses and mechanical couplings between them), which are however known. The characteristic frequency responses G(Ωk) can be stored, for example, in order to be able to infer a model structure of the present test setup PA by comparing the estimated frequency response Ĝ(Ωk).
The respective determined covariances σYU2 (k) are also shown in
The advantage of this procedure can also be seen in the fact that one can get by for the nonparametric identification under certain circumstances without measuring a torque on the test bench 1, for example to select a model structure. This allows a first estimate of the dynamic response of the test setup PA on the test bench 1, in particular, without including a torque measuring flange in the test setup PA.
According to the present teaching, the nonparametric identification method is followed by a parametric identification method with which the dynamic input-output behavior of the dynamic technical system (test setup PA) is approximated with a model with system parameters SP which describe the dynamic response of the test setup PA. There are also known methods for this, both in the time domain and in the frequency domain, which are briefly explained below.
The parametric identification is based on a model of the dynamic system with the model parameters θ, which calculates the output y(k) from the input u(k) and a disturbance. The mapping of the input u(k) to the output y(k) takes place with a plant model
with plant model parameters gθ and the backward shift operator q−k. A disturbance (e.g. due to measurement noise) can be modeled with a disturbance model H(q, θ) and a probability distribution e, or a probability density function fθ, with
and noise model parameters hθ. It should be noted that k does not denote a frequency as in nonparametric identification, but rather a time index of the discrete-time signals, e.g. u(k) and y(k). The model of the dynamic system can then be written in a discrete-time notation as y(k)=G(q,θ)u(k)+H(q,θ)e(k). The goal is therefore to estimate with this model the output y(k) at the time k from known past data of the input u and the output y up to the time k−1 (i.e. past data). The data ZK={u(1), y(1), . . . , u(k−1), y(k−1), u(k), y(k)} are available. There are various known approaches for this.
An example of a parametric identification method in the time domain is the so-called Prediction Error Method (PEM), as described, for example, in L. Ljung, “System Identification: Theory for the User,” 2nd Edition Prentice Hall PTR, 1999. A known method in the frequency domain is the Maximum Likelihood Estimator Method (MLE).
PEM is based on the model of the dynamic system
where θ are the model parameters. Here, v(k) denotes colored noise. If white noise is used as the probability distribution e(k), the colored noise v(k) can also be written as
Therein, m(k−1) is the mean value up to time (k−1). This can be rewritten in the form m(k−1)={circumflex over (v)}(k|k−1)=(H(q,θ)−1)e(k)=(1−Hinv(q,θ))v(k), with the inverse Hinv of H. The estimate of the output ŷ(k|k−1) from the data ZK can then be written in the following form: ŷ(k|θ,ZK)=G(q,θ)u(k)+{circumflex over (v)}(k|k−1)=Hinv (q,θ)G(q,θ)u(k)+(1−Hinv(q,θ))y(k).
The estimation error then results in ε(k,θ)=y(k)−ŷ(k,θ). In order to determine the model parameters θ, a cost function J(θ,ZK) can be used that minimizes the weighted estimation error. For example, a mathematical norm l( ), for example the Euclidean norm (2 norm) 1( )=∥( )∥2, of the weighted estimation error can be used. If εF(k,θ)=F(q)ε(k,θ) denotes the weighted estimation error with the weights F(q), then the cost function can be written as
for example. This cost function J is minimized to estimate the model parameters θ:
In order to determine the sought system parameters SP of the dynamic system from the model parameters θ, the time discrete model y(k)=G(q,θ)u(k)+H(q,θ)e(k) can also be written in an advantageous practical implementation in the form
(ARMAX model) with polynomials A(q)=1+a1q−1+ . . . +anaq−na, B(q)=1+b1q−1+ . . . +bnbq−nb, and C(q)=1+c1q−1+ . . . +cncq−nc. The model parameters θ then result in θ=[a1 . . . ana b1 . . . bnb c1 . . . cnc]. In the case of white noise e(k), this is reduced to
(ARX model) with θ=[a1 . . . ana b1 . . . bnb]. The order na, nb, nc of the polynomials A, B, C is specified in accordance with the model structure defined with the nonparametric identification.
In the case of a dual-mass oscillator, for example in a test setup according to
In order to arrive at the sought system parameters SP, an equivalence of the model parameters in the discrete-time model and the parameters of a physical model of the dynamic system is assumed.
For example, the test setup PA according to
Another example arises in the dual-mass oscillator of
In this case, the frequency response G would of course also have been ascertained with this input signal and output signal. This also shows that different models result from different input and/or output signals. These equations can be put into a discrete-time notation, which allows a comparison of the system parameters SP (JE, c, d, JD) with the estimated model parameters θ=[a1 . . . ana b1 . . . bnb]. The system parameters SP (JE, c, d, JD) can be determined from this.
As the model structure is known from the frequency response G, the model can also be divided into sub-models, which makes it easier to determine the system parameters SP (JE, c, d, JD). A dual-mass oscillator can be divided, for example, into a first sub-model for the internal combustion engine 2, a second sub-model for the test bench shaft 4, and a third submodel for the load machine 3. The discrete-time model can thus also be subdivided into corresponding sub-models, which reduces the order of the sub-models accordingly. The model parameters of the sub-models are then estimated as described above.
Physical sub-models are then used in the same way, which is described again below using the example of the dual-mass oscillator.
For the first sub-model, the torque equilibrium for the internal combustion engine 2 (
with the Laplace operator s, the speed ωE of the internal combustion engine 2, the internal torque TE of the internal combustion engine 2, and the shaft torque Tsh. As the internal combustion engine 2 is preferably operated in a towed manner, the non-stochastic part of the model structure results in TE=0 and consequently
in time-discrete notation with the known sampling time Ts (typically in the kHz range). By comparison, a1=−1 and b1=Ts/JE are directly obtained from the first sub-model, from which the system parameter JE can be ascertained. This also allows the evaluation of the quality of the parameter estimation. If the estimated model parameter a1 is close to one, then a high identification quality can be assumed.
In order to determine the system parameters SP of the coupling between the internal combustion engine 2 and the load machine 3, torsional damping d and torsional rigidity c, the second sub-model for the test bench shaft 4 is used. Starting from the torque equilibrium on the cut-out test bench shaft 4, it can be written with a Δω=ωE−ωD, with the speed ωD of the load machine 3, and again with the assumption
or in time-discrete notation Tsh(k)−Tsh(k−1)=(−cTs+d)Δω(k)−dΔω(k−1). By comparison, the system parameters a1=−1, b1=−(cTs+d) and b2=−d again result from the model parameters of the second sub-model, from which the sought system parameters c, d can be determined. The model parameters a1, b1 of the second sub-model naturally do not correspond to the model parameters of the first sub-model.
In the same way, a third sub-model can be used for the load machine 3 in order to determine the system parameter JD. The inertia JD of the load machine can of course also be ascertained for the dual-mass oscillator from the resonance frequency ωR, which is known from the nonparametric identification, for example as
The inertia JD of the load machine 3 is often known, so that the quality of the identification inertia can also be determined with the known inertia.
As already mentioned, the parametric identification can also take place in the frequency domain, for example using MLE With MLE, the model parameters θ are estimated, which maximize the so-called likelihood function. This known method is briefly explained below.
MLE uses the measurement data of the output signal y=y1, y2, . . . yN and an associated probability density function fny, assumed to be known, of the measurement noise at the output, which is described by the model parameters θ, f(y|θ0) describes the probability distribution function of the randomly dependent part of the estimation problem. With a hypothetical model y0=G(u0,θ), which describes the excitations and the parameters, the likelihood function can be written as f(y|θ,u0)=fny(y−y0) in the case of measurement noise at the output. Therein, u0 denotes the noiseless input. The unknown model parameters θ can then be determined by maximizing the likelihood function f:
In the case of additional measurement noise at the input, the likelihood function can be written as f(y,u|θ, y0,u0)=fny(y−y0)fnθ(u-u0), with the probability density function fnU of the measurement noise at the input.
A Gaussian cost function
(likelihood function f) can be written on the assumption that the noise at the input and output have a mean value of zero, are normally distributed, and are independent of the frequencies. Therein, θ is the parameter vector and Z(k)=[Y(k) U(k)] denotes the available measurement data of the input U(k) and the output Y(k). e denotes an error over all frequencies Ωk of the form e(Ωk,θ,Z(k))=Y(k)−G(Ωk,θ)U(k) and σe denotes the covariance of the error e in the form σe2 (Ωk, θ)=σY2(k)+|G(Ωk,θ)|2 σU2 (k)−2 Re({right arrow over (G)}(Ωk)σYU2(k)). Re denotes the real part. As can be seen, the variances and covariance of the measurement noise at the input σU2 (k), output σY2(k), and input-output σYU2(k) are required for the above equations. These can advantageously be obtained from the nonparametric identification as described above. Since the resultant optimization problem of maximizing the cost function VML (likelihood function) is non-linear, the optimization is solved, for example, with the well-known Levenberg-Marquardt method. The convergence of the optimality of the optimization substantially depends on the initial values of the optimization. Estimated values of the sought system parameters SP can be used as initial values or other known initialization methods, for example from a generalized total least square method can be used.
If a parametric transfer function
is used, the cost function for MLE can be rewritten to
Here, A and B are again polynomials A(q)=1+a1q−1+ . . . +anaq−na, B(q)=1+b1q−1+ . . . +bnbq−nb. The order na, nb of the polynomials again results from the frequency response Ĝ(Ωk) estimated with the nonparametric identification. From the optimization, the model parameters θ=[a1 . . . ana b1 . . . bnb] are again obtained, which in turn are again compared with a physical model of the dynamic system (test setup PA) in order to arrive at the system parameters SP (JE, c, d, JD). In the same way, sub-models can also be used again in order to simplify the determination of the system parameters SP (JE, c, d, JD).
The sub-models for the internal combustion engine 2 and the test bench shaft 4 in time-discrete notation with the z-transformation result in
from which the system parameters SP (JE, c, d, JD) result from the estimated sub-models in
The parametric identification thus supplies the system parameters SP (JE, c, d, JD in the case of the dual-mass oscillator) of the excited dynamic system (the test setup PA as shown, for example, in
A closed control loop for the test setup PA according to
The resonance frequency (frequencies) ωR ascertained with the nonparametric identification, which also represent a system parameter SP, can also be used to design a filter F that is intended to prevent possible resonances on the test bench 1. The aim of the filter F is to prevent excitation with a resonance frequency ωR In order to influence the dynamic response of the test setup PA on a test bench 1 with a filter F as little as possible, filters F may be used which filter out frequencies within a narrow frequency range, for example so-called notch filters. For this purpose, the notch filter is designed so that frequencies in a narrow frequency range around the resonance frequency ωR are filtered out. Such a filter F can be used in front of a controller R for a component of the test setup PA, for example the dyno controller RD, for filtering the control deviation w supplied to the controller R (difference between the setpoint SW and the actual value IW of the controlled variable) (as in
The identified system parameters SP (ωR, JE, c, d, JD), or at least one of them, can also be used for an observer to estimate non-measurable variables of the test setup, for example an internal effective torque TE of the internal combustion engine 2.
Likewise, the identified system parameters SP (ωR, JE, c, d, JD), or at least one of them, can be used to determine changes in the test setup PA, for example due to aging, damage, configuration changes, etc. For this purpose, the system parameters SP (JE, c, d, JD) can be newly determined at regular intervals and the change over time of the system parameters SP (JE, c, d, JD) can be monitored. The test run can be adapted or interrupted if an unusual or undesired change is detected.
Last but not least, the test setup PA for carrying out the bench test itself can also be changed in order to change the at least one identified system parameter SP in order to represent a desired dynamic response on the test bench 1. This can be used, for example, to adapt the dynamics of the test setup PA on the test bench 1 to the dynamics of a vehicle in which the torque generator DE of the test setup PA is to be used.
A test bench 1 having a test setup PA, for example with a dual-mass oscillator as in
Although the present teaching was described above using the example of a dual-mass test setup, it is obvious that the present teaching can also be expanded to any multi-mass test setup, for example in the case of a drive train test bench in which the torque generator DE is connected via a combination of shafts, couplings, shaft couplings, and/or gearboxes to a torque sink DS. In order to carry out a test run, a test object with a torque generator DE, for example an internal combustion engine 2, an electric motor, but also a combination of an internal combustion engine 2 and an electric motor, is mechanically coupled with a torque sink DS, for example a load machine 3. The coupling is made with at least one coupling element KE, for example with a test bench shaft 4, as shown in
For example, a three-mass test setup is shown in
Depending on which measurement variables are available, the following configurations are possible, for example:
Number | Date | Country | Kind |
---|---|---|---|
A 51086/2017 | Dec 2017 | AT | national |
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/EP2018/097062 | 12/28/2018 | WO |
Publishing Document | Publishing Date | Country | Kind |
---|---|---|---|
WO2019/129835 | 7/4/2019 | WO | A |
Number | Name | Date | Kind |
---|---|---|---|
11255749 | Kokal | Feb 2022 | B2 |
20130304441 | Fricke | Nov 2013 | A1 |
20180335370 | Maschmeyer | Nov 2018 | A1 |
20200333201 | Vadamalu | Oct 2020 | A1 |
20210088410 | Bier | Mar 2021 | A1 |
20210096040 | Bier | Apr 2021 | A1 |
Number | Date | Country |
---|---|---|
102006025878 | Dec 2006 | DE |
1452848 | Sep 2004 | EP |
2006300683 | Feb 2006 | JP |
2006300683 | Nov 2006 | JP |
2007163164 | Jun 2007 | JP |
2017122642 | Jul 2007 | JP |
Entry |
---|
Austrian Search Report Application No. A 51086/2017 Completed: Oct. 31, 2018 1 Page. |
Christian Matthew et al: “Chassis Dynamometer Torque Control System Design by Direct Inverse Compensation”, 6th Biennal UKACC International Control Conference (ICC '06), AT Glasgow, published Sep. 1, 2006. 8 Pages. |
Pintelon, R. et al: “Estimation of non-paramteric noise and FRF models for multivariable systems”—Part I Theory, Mechanical Systems and Signal Processing, vol. 24, Issue 3, published 2010. pp. 573-595. |
International Search Report & Written Opinion of the International Search Authority Application No. PCT/EP2018/097062 Completed: Mar. 26, 2019; dated Apr. 3, 2019 14 Pages. |
Translation of Internation Search Report Application No. PCT/EP2018/097062 Completed: Mar. 26, 2019; dated Apr. 3, 2019 3 Pages. |
Kuttner, Thomas: “Praxiswissen Schwingungsmesstechnik” Springer Vieweg, published 2015. pp. 325-335. |
L. Ljung: System Identification: Theory for the User, 2nd Edition PTR Prentice Hall Information and System Sciences Series, published 1999, ISBN 0-13-656695-2. 631 Pages. |
Chinese Office Action; Application No. 201880083971.3; dated Aug. 4, 2021; 17 Pages. |
Number | Date | Country | |
---|---|---|---|
20210063277 A1 | Mar 2021 | US |