DE29610789U1 - Device for identifying a transmission path, in particular a control path - Google Patents

Description

GR 96 G 4435 DE ,. „„ ..

Description

Device for identifying a transmission path, in particular a control path
5

The invention relates to a device for identifying a transmission path, in particular a control path, according to the preamble of claim 1.

An adaptive controller for processes with delays with such a device is known from DE-OS 39 29 615. It has the ability to automatically adapt its parameters to the properties of a controlled system that change over time. To do this, the process's response to a step-like adjustment of the setpoint is recorded and an iterative process is used to search for a PTn model that can simulate this step response as well as possible. The parameters of the PTn model are considered to be optimal if they minimize the error calculated using the least squares method between the step responses of the PTn model and the real process. After process identification has been completed, a controller is designed based on the determined process model based on the optimum amount. The processes to be controlled exhibit a behavior with compensation, i.e. i.e., they represent a controlled system in which the step response enters a new steady state.

A disadvantage of this method is that when commissioning the known adaptive controller, an often time-consuming step test must be carried out before the controller can be optimized. This test is only completed when the controlled variable has approximately settled back to the new stationary final value after the setpoint jump. The criterion for a stationary state must be carefully selected, since if the criterion is too strict, the identification takes a lot of time.

GR 96 G 4435 DE

and a criterion that is formulated too broadly, on the other hand, increases the risk of incorrect identification.

Another disadvantage of the known identification method is creeping time constants, i.e. poles that are very close to the origin of the Laplace plane and lead to an integrator-like behavior of the process, so that after a step change in the manipulated variable, a steady state cannot be reached for a very long time. As a result, the known identification based on a complete step response is very time-consuming with such process behavior.

From the book by Rolf Isermann: "Identification of dynamic systems", 2nd edition, Springer Verlag Berlin Heidelberg 1996, pages 202 to 206, a least squares method for identifying a transmission path is known, which leads to an accurate model when larger amounts of data are available. A second-order ARMA model is created from the available measurement data of the input variable y and output variable &khgr; of a transmission path S.

1 + ap +S ₂ Z

identified. To do this, define a parameter vector 25

�Oacgr; ⁼ (S ₁ , S ₂ γ -O ₁ , D ₂ )

and a data vector
W _k = (-&khgr;* ,-**_! ,y _k ,y _k - _± Y

and writes the ARMA model as

GR 96 G 4435 DE

• O ·

Such an equation is set up for each measured value and all equations are combined into a system of equations

X = ΨΘ ,

X =

. ^X n.

Ψ =

&ngr;;

&psgr;*

This overdetermined linear system of equations can be approximately solved for the vector θ of the parameters sought using any numerical method. The quality criterion used is the sum

V = e e ,

e = χ -

the squared deviations e for each sampling step are minimized.

However, particularly when the data basis for identification is limited, for example when only the first part of a step response is available, there is no guarantee that a physically meaningful model will be obtained. The well-known identification method according to Isermann can, under certain circumstances, result in models with negative gains or negative time constants.

If simulation models with any fractional rational transfer function in the Laplace domain are used for identification, unfavorable combinations of model structure and actual dynamic behavior of the process can also lead to these errors or to unstable poles, for example if there are actually four relevant time constants, but the model is only 2nd order.

GR 96 G 4435 DE ■ „ . _v ..

Similar problems can arise if an actuator with too slow pulse width modulation acts like a time-variant dead time.

A poor noise/useful signal ratio, i.e. noise amplitudes that are too large, can also be the reason for the calculation of a model that does not make sense in physical terms.

Based on such physically meaningless models, a controller design is impossible. It has proven impractical to ensure model plausibility by introducing constraints in the optimization calculation, because if the problems mentioned above occur, the optimization process runs against the limitation specified by the constraint.

The invention is based on the object of creating a device for identifying a transmission path, in particular a control path, which avoids the disadvantages mentioned above.

To solve this problem, the new device of the type mentioned at the outset has the features specified in the characterizing part of claim 1. Advantageous further developments are described in the subclaims.

The invention has the advantage that it is ensured under all circumstances that a plausible, physically meaningful model is found during identification. The "qualitative" model obtained does not generally simulate a system as accurately as a model whose parameters were calculated on the basis of a large amount of data using numerical optimization methods, but it is physically meaningful even when a small amount of data is available and can serve as the basis for a controller design. The device according to the invention can advantageously be implemented in addition to a complex parameter estimator in order to

GR 96 G 4435 DE

· ·0· · ♦ I

Cases in which the complex parameter estimator has failed to identify a route. It can also be used advantageously in inexpensive, adaptive controllers, since the matrix operations required to select one of the given models place only low demands on the performance of, for example, a computing unit. Another advantage is that with the control device according to the invention, a physically reasonable model can be found as the basis for a control shortly after the process has started, which can be replaced in a further step with a larger amount of data by a more precise process model obtained using numerical optimization methods.

The invention as well as embodiments and advantages are explained in more detail below with reference to the drawing, which shows a control circuit with an identification device.

In the control loop shown, a control system S represents a transmission path whose behavior is determined using an identification device IE. The control system S has an input signal y that is identical to the manipulated variable in the control loop. The manipulated variable y is supplied by a controller R whose controller parameters, for example the gain factor Kp, the reset time Tn and the lead time Tv in the case of a PID controller, are set depending on a simulation model M. The input signal y and an output signal x of the transmission path S, which represents the controlled variable in the control loop, are fed to the identification device IE. By forming the difference, a control difference xd is formed from a reference variable w and the output signal xd, which is applied to the controller R. In automatic mode, the controller R forms the manipulated variable y depending on the control difference xd, i.e. the control loop is closed. In manual mode of the controller R, it is possible to apply a preselectable course of the manipulated variable y to the controlled system S,

GR 96 G 4435 DE „ „ ., .. „

for example with the help of a switchable function generator.

In the identification device IE, the curves of the input signal y and the output signal &khgr; are sampled and the sample values are stored.

For example, nine physical process models with VZl behavior and three typical gains K = 0.5, 1 and 2 as well as three typical time constants T = 10 s, 100 s and 1000 s are specified and the corresponding transfer functions G(s) are converted into a time-discrete representation:

G(s) =

&kgr; . ¹ ^-" ¹

Ts + 1 1 +

^ = -e"^ ^/r , Jb ₁ = K(I + aj

with T ₀ - sampling time. For a 1st order model, only the first and third columns of the matrix &psgr; are relevant according to the method described by Isermann. For each model M(j), j = 1 ... 9, the loss function 20

V(J) = e (j)e(j) , e(j) = &khgr; - [&psgr;^&ohgr;

can be calculated with a few matrix operations without having to carry out a dynamic simulation with the model. For identification, the model M{j) of the transmission path S is selected that provides the smallest loss function V(j), i.e. that best reflects the given course of the input signal y and the output signal &khgr;. Since in this way one of a finite set of plausible models is selected, the identification device always provides a physically meaningful model that can be used for a controller design.

Claims (4)

GR 96 G 4435 DE Protection claims 1. Device for identifying a transmission path, in particular a control path (S), - with means (R) for generating an input signal (y) as excitation of the path, - with means for detecting the output signal (x) of the path in response to this excitation and - with means (IE) for determining the simulation model (M) of the route with which the deviations between the recorded output signals (x) and output signals estimated using the simulation model are minimal, characterized by - that a finite number of simple and plausible, i.e. physically sensible, models are given and - that the model is selected with which the deviations are minimal. 2. Device according to claim 1, characterized in that - that the simulation models in the Laplace domain can be described by a first-order transfer function. 3. Device according to claim 2, characterized in - that the route is subject to delay and the simulation models are first order delay elements. 4. Device according to one of the preceding claims, characterized in - that the selected predefined model is replaced by a higher order model if a numerical optimization procedure for the higher order model produces physically meaningful results.