DE102007018805A1 - Controller for controlling smooth running process of reciprocating piston engine, determines cyclic control deviation, where determined deviation is processed to correcting variable by algorithm with periodically integrating characteristics - Google Patents

Abstract

The controller determines a cyclic control deviation, where an average value of an actual control deviation (e) of a period duration is added to a phase displaced basic and/or harmonic wave of the actual control deviation for the determination of the cyclic control deviation. The determined cyclic control deviation is processed to a correcting variable (u) of the controller by an algorithm with periodically integrating characteristics. A parallel branch (Kpar) processes the cyclic control deviation proportionally and/or differentiatively or nonlinearly.

Description

The The invention relates to a controller for controlling cyclic processes, z. B. to control the speed and smoothness of a Hubkolbenverbrennungsmotors.

From the prior art according to the DE 10 2005 047 829.8 is a regulation of the smoothness of reciprocating internal combustion engines known. In order to regulate the smooth running in such engines, it is proposed to implement an algorithm with the following steps in the control system:

Representation of the engine speed:

• a) For the frequency-selective representation of the engine speed, a Fourier series with Z-1 summands a _n , b _n , is used, where n = 1, 2 .... Z, where Z represents the number of cylinders of the engine. In this case, for each addend of the series representation, an individual contribution to the control deviation is calculated by means of a predetermined value k = k _n . The knowledge of k comes from a preliminary investigation and is preferably that value at which the maximum expression of the effect of the last ignition of the cylinder which will ignite next is determined. In this case, an overall deviation from the individual contributions is formed. The individual values for k are to be selected so that a specific camshaft angle is considered in order to be able to realize a chain between cause and effect in the control.

at This regulation is basically two controllers; of the first controller regulates the speed. However, this is the first controller unable to correct the associated vibrations. For this a second regulator is provided which at the speed of the vibrations which the first controller is unable to control. Vice versa is true that the second controller from the prior art is not in is able to regulate the speed for which the first Controller is responsible.

That is, the prior art controller is able to extract disturbances in the form of vibrations and to control these vibrations. The control loop is off 1 seen.

From the illustration according to 1 The result is the following: From the controlled system results in a controlled variable Y. This controlled variable Y has at certain frequencies undesirable vibrations. To regulate these vibrations is the controller 2, which is arranged parallel to the controlled system. This second controller outputs a second manipulated variable u2 on the controlled system, wherein the second manipulated variable u2 is selected such that it is compensated by vibrations, which can not be compensated by the first controller 1, which specifies the first manipulated variable u1. That is, the prior art has no leadership, and therefore is also unable to control a reference variable. Thus, it can not be used for any cyclic processes.

The that is, the object underlying the invention is in designing a controller for any cyclic Processes can be used.

The The object is achieved according to the invention that a cyclic control deviation is determined, wherein the determination the cyclical deviation of the mean of the actual Control deviation of one period to at least one phase-shifted Basic and / or harmonic of the actual control deviation is added, with the thus determined cyclic control deviation through an algorithm with periodically integrating behavior further processed to the manipulated variable of the controller becomes. Such a controller is capable of a process stationary to regulate exactly, both in terms of leadership behavior as well as the disturbance behavior in periodic management or disturbance variables.

According to a special feature of the invention, the mean value of the actual control deviation is multiplied by a weighting factor g ₀ , where g ₀ ≥ 0. This ensures that the transient response of the mean value can be set independently of the other frequencies in the control loop. The gain for the transmission behavior of the mean value in the closed loop is thus specifically and separately adjustable.

Furthermore, the fundamental and / or harmonics are to be multiplied by N-frequency-selective weighting factors g _n ≥ 0 [n = 1 to N]. This allows the gain of a specific frequency to be set separately.

With regard to the weighting factors g ₀ to g _{N, it} follows that the controller acts as a filter for certain Frequencies can act. Such a controller can thus be used as a blocking filter or as a pass filter.

advantageous Features and variants of the invention are the subclaims refer to.

So is provided in particular that the cyclic control deviation through an algorithm with periodically integrating behavior and proportional and / or differentiating or nonlinear behavior further processed to the manipulated variable of the controller becomes. This ensures that the controller is faster overall is, d. H. settles faster to the setpoint and also disturbances adjusted faster.

To Another feature of the invention is that the controller has a parallel branch, which is proportional to the deviation and / or differentially or non-linearly processed to a value, which is added to the manipulated variable of the controller. In addition to the parallel branch, the proportional and / or differentiating processing of the cyclic control deviation take place.

According to a further feature of the invention, it is provided that the cyclic control deviation is obtained by the discrete Fourier transformation and the inverse discrete Fourier transformation from the actual control deviation. In the process, individual relevant frequencies are selectively determined from the available signals and individual frequencies are selectively adjusted or regulated. That is, this extracts the relevant frequency components. This targeted control is possible because in the inverse discrete Fourier transformation a frequency-selective phase shift φ _n takes place.

Advantageous is the time period of the controller for the controller predetermined process, where in the discrete case, the period corresponds to the integer multiple of R of the sampling period. D. H. This allows the controller to be set to any period because the integer multiple is considered a parameter of the scheme represents. The temporal period is variable when the process in relation to a state variable, cyclically behaves. Ie. Hereby, processes can also be regulated the cyclicity is not on time, but on one State variable, e.g. B. related to the rotation angle of a working machine becomes.

This Algorithm is characterized by a linear or non-linear difference equation discrete in the time domain, eliminating the possibility is created, this algorithm as a digital controller in z. B. to implement a microprocessor.

in the Case of a linear execution of the regulator may be the discrete one Algorithm represented by a discrete transfer function which you get as a Z transformation of the difference equation, where by the relationship between Z-transformation and Laplace transformation also a continuous representation is possible.

According to a further feature of the invention, it is provided that for determining the phase shift of a specific frequency associated phase angle φ _n n = 1, 2 .... N <R / 2 is equated to the phase response of the controlled system, creating a simple rule for the interpretation Phase angle φ _{n is} given. It was found that the control behavior is nevertheless stable, even if the phase angle does not correspond exactly to the phase response.

Furthermore, it is provided that the parallel branch K _{par has} PD behavior and that the periodically integrating part behaves linearly.

This ensures that apart from the parameters φ _n , which are designed as described above, the other three parameters Kp, K _d and K _i are designed as if you want to interpret a conventional PID controller.

Based The following description will make the invention more apparent explained.

As the 2 shows, the control structure consists of two parallel sub-functions K _zyk and K _par , which process the control deviation e (difference between setpoint and actual value) to a cyclic manipulated variable u _zyk and a parallel manipulated variable u _par , the sum of u _zyk and u _par the entire manipulated variable u of the controller, in the following called cyclo regulator represents.

The algorithm for calculating the cyclic manipulated variable _component u _zyk extracts frequency-selective In from the current period and provides the key to the steady-state control of cyclical processes.

The algorithm for calculating the parallel manipulated variable component u _par is used to improve the dynamic behavior and possibly to stabilize the control loop.

How out 3 is recognizable, the algorithm K _zyk consists of two successive sub-functions F ^o and (I ^o + K ^o _par ).

The function F ^o processes the actual control deviation e for the cyclical control deviation e ^o . For this purpose, it successively performs two transformations of the control deviation from the past, a period Tp = RT (T: sampling period in the discrete case) wide time interval, wherein first a discrete Fourier transform and then an inverse discrete Fourier transform is performed. In the inverse discrete Fourier transformation, a frequency-selective phase shift Φn and a frequency-selective weighting by the factors g ₀ , g _n , where n = 1, 2, ..., N is. That is, a vibration sin (nω ₀ t) as a component of the actual control deviation e becomes the component sin (nω ₀ t-Φn) of the cyclic control deviation e ^o . This transformation chain represents a linear processing of the control deviation and, in the case of a discrete control in the time domain, is represented by a difference equation or by Z transformation of the difference equation by a transfer function in the frequency domain:

E ^o (z) is the Z-transform of the cyclic control deviation; E (z) is the Z-transform of the actual control deviation.

The function I ^o carries out a periodic integration of the cyclic control deviation. It can be linear or non-linear. In the linear discrete case, the following transfer function for periodic integration can be given:

T is the sampling period, the product RT is the period T _{P of} the process, K _I is the gain (inverse of the integration time constant) of the linear periodic integrator K ^o .

K _par and K ^o _par are non-linear functions or linear functions and process the actual control deviation or the cyclic control deviation. They may serve to stabilize and / or improve the dynamic behavior of the control loop.

The cyclo-controller is used in accordance with the general control theory, so that the closed loop as in 4 represents.

• W: Sollwert (Führungsgröße), Y: Istwert (Regelgröße), E: Regelabweichung, U: Stellgröße, D: Störung.

Where:

• W: setpoint (command value), Y: actual value (controlled variable), E: control deviation, U: manipulated variable, D: fault.

As a rule, microcontrollers are used in practical applications for implementing controls and regulations, so that the discrete representation of the control method is of greater importance than the continuous display. However, the cyclo controller can also be displayed as a continuous controller. If you execute the cyclo controller z. For example, if it is linear, a continuous representation can be deduced from the discrete representation of the controller's discrete transfer function by the relationship "z = e ^{(Ts )} " between Laplace transform and Z transformation.

When used on time-variant and / or non-linear controlled systems, free parameters of the cyclo-controller can be adapted to the changing behavior of the controller during operation by means of appropriate adaptation methods Controlled system can be adjusted. In engine control units, for example, the parameters of the cyclo-controller can be adapted to the respective operating state by characteristic maps or characteristics or by models or by other suitable adaptation methods depending on relevant state variables of the engine.

is the cyclicity or periodicity is not re time, but with respect to a state quantity Given x (t), the time period is variable and behaves inversely proportional to the time derivative of the state variable x (t). For example, the internal engine process variables run a reciprocating motor cyclically (or at constant load / speed Periodic) with respect to the state variable "camshaft rotation angle".

Of the ZykloRegler is then used in such a way that he with respect the state variable x (t) is periodic or cyclic Steady-state courses (at management level) and disturbances) by the actual control deviation for further processing to the cyclic control deviation over this state variable x (t) is shown, in which case the sampling of the control deviation is equidistant over x (t) and not time equidistant. The sampling period T and the period Tp of the process are then variable and behave inversely proportional to temporal Derivation of the state variable.

In the function F ^o , the frequency-selective phase shifts Φn and the frequency-selective weighting factors g ₀ , g _n (n = 1, 2,..., N) are contained as free parameters.

For the interpretation of the parameters Φn a simple rule can be given, which leads to a robust design of the controller: one takes the phase shifts Φn, where Φn is the phase shift associated with the frequency n / Tp, the phase response Φ _G = arg (G (jω) ) of the controlled system G, ie Φn = arg (G (j2πn / Tp)).

The weighting factors g ₀ , g _n can first be set to one and varied according to the design of the other parameters of the control for further optimization of the behavior of the closed circuit, that is, different from one.

The Parameters of Kpar can be interpreted as if one would want to control with a controller without a cyclic branch. For example, can you can interpret Kpar as a PD controller and then the cyclic one Switch branch on.

For the exemplary design of a linear cyclo-regulator with PD behavior in the parallel branch Kpar ("cyclic PID controller"), the following applies:
Kpar is executed as a PD controller and I ^o linear with constant gain K _I.

Thus, in addition to the phase shifts φn and the weighting factors g ₀ , g _n , which are designed as described above, one then has three gain parameters K _P , K _D , K _I : two for the parallel PD branch and one for the periodic integrator. The discrete transfer function of the cyclo controller in this case is:

aus, um diese drei Parameter K_P, K_D, K_I zu bestimmen.Now put a usual PID controller

to determine these three parameters K _P , K _D , K _I.

In the following, the cyclo-controller will be discussed by means of an example, whereby a linear variant of the cyclo-controller with proportional behavior in the parallel branch Kpar and without K ^o par is used. This corresponds to the above embodiment but with K _D = 0. That is, the cyclo controller has here in addition to the phase shifts Φn and the weighting factors g ₀ , g _n two parameters K _P , K _I.

Der Regler wird nun an einer Regelstrecke mit integrierendem Verhalten untersucht. Es wird dabei mit einem PI-Regler verglichen, wobei beide Regler dieselben Parameter K_P, K_I besitzen.The transfer function of the cyclo-regulator with Kpar = K _P and with a linear periodic integrator as well as K ^o par = 0 and g ₀ = g _n = 1 is:

The controller is now being tested on a controlled system with integrating behavior. It is compared with a PI controller, both controllers having the same parameters K _P , K _I.

In 5 shows the behavior of the cyclo controller with R = 125 and a sampling period of T = 1 ms when adjusting a periodic setpoint curve. The period of the setpoint curve is Tp = RT = 0.125s. The fundamental wave therefore has a frequency of 8 Hz. The cyclo-controller is thus designed so that, in addition to constant control / disturbance variables, it can also precisely control oscillations at 8 Hz and their multiples (up to 62 · 8 Hz, ie N = 62). Some periods are shown in the figure and it can be seen how the actual value curve after a few periods closely approximates the setpoint curve in a steady state when using the cyclo-controller (thick dotted line). For comparison, the figure shows the course of the actual size (thin dotted line) when using the PI controller. Here the setpoint is not nearly reached.

In 6 is the Bode diagram of the guide transfer function of the closed loop with the cyclo controller. R = 17. It can be seen that the amplitude response at the frequencies f _n = n / R / T, where n = 0, 1, 2, ..., 8, is one and that the phase response at these frequencies is zero , That is, signals at these frequencies are accurately controlled in-station.

In 7 the amplitude response of the Bode diagram of the loop closed with the cyclo-controller for samples R = 17 is compared with the amplitude response of the circuit closed with the PI controller (same parameter Kp, Ki). It can be seen that the steady-state behavior of both controllers between the frequencies, which the cyclo controller is able to control in a stationary manner exactly in contrast to the PI controller, is approximately identical.

used as in the example shown here, the cyclo-controller is cyclical PI-controller, so you get a controller that works like the PI controller behaves, but additionally in the Location is to fix certain frequencies stationary exactly can.

in the Following are the essential steps of the procedure briefly presented the discrete realization.

First, the controller parameters are designed so that the desired behavior results in the closed loop. For this purpose, it must be decided from the behavior of the controlled system how the parallel branches Kpar, K ^o par of the cyclo-controller are to be executed (linear or non-linear) and how the periodic integrator I ^{o is} to be executed (linear or non-linear). The parameter R is designed as a function of the sampling period T in such a way that the controller controls the fundamental frequency f ₀ = 1 / T / R desired for the process and their multiples in a stationary manner.

The Design of the free parameters now happens either manually or by means of suitable optimization methods (eg numerical optimization methods as simplex method or evolution strategy method) automated directly on the process or on a mathematical model of the controlled system.

The Steps of the method are as follows:

1. Determine current control deviation and save:

The last R samples [e _{i-R + 1} , e _{i-R + 2} ,..., E _i ] of the control deviation are always stored. From the current sampling set [e i-R + 1 , e i-R + 2 , ..., e i ] = [e i-k + R ] = [e k ] i (with k = 1, 2, 3, ..., R) the control deviation (consisting of R samples) becomes the current value e ^o _{i of} the cyclic control deviation calculated; i is the current control clock at the current time t = iT.

2. Transformation in the frequency domain:

The sample set [e _{k] i} is first shifted to a time axis t = - (i - R) · T as shown _i [e ~ _k] with e ~ k = e ~ (t ~ = k * T) = e (t = (i-R + k) * T).

Thus, for k = R: e i = e R = e ~ (t ~ = R · T = T P ).

The sample set [e ~ _k ] _i is now transformed into the frequency domain via the discrete Fourier transformation (or via the Fourier analysis):

3. Back transformation into the Time range:

The cyclical deviation e ~ ⁰ (t ~) is obtained by inverse discrete Fourier transformation (or by Fourier series representation) of the coefficients c _n , whereby a frequency-selective phase shift takes place by the angle Φn:

4. Current cyclic control deviation determine and save:

The current cyclic control deviation is

5. Calculating the cyclic manipulated variable component:

• 1. Perform Periodic Integration the cyclical control deviation;
• 2. processing of the cyclic control deviation by K ^o par;
• 3. The addition of the results of 1 and 2 provides cyclic manipulated variable u _zyk

6. Calculating the parallel manipulated variable component:

Processing the control deviation with Kpar supplies parallel manipulated variable component u _par

7. Calculate the total manipulated variable and applying to the controlled system:

Addition of u _zyk and u _par returns the entire manipulated variable of the cyclo controller, which is now applied to the controlled system via the actuator.

QUOTES INCLUDE IN THE DESCRIPTION

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Cited patent literature

• - DE 102005047829 [0002]

Claims (13)

Controller (F ^o and I ^O ) for controlling cyclic processes, eg. As the regulation of the smoothness of a reciprocating engine, characterized in that a cyclic control deviation (e ^o ) is determined, wherein for determining the cyclical control deviation (e ^o ), the mean value of the actual control deviation (e) a period (T _p ), at least a phase-shifted fundamental and / or harmonic of the actual control deviation (e) is added, wherein the thus determined cyclic control deviation (e ^o ) is further processed by an algorithm with periodically integrating behavior to the manipulated variable (u) of the controller. Controller according to claim 1, characterized in that the cyclic control deviation (e ^o ) by an algorithm with periodically integrating behavior (I ^o ) and proportional and / or differentiating behavior or non-linear behavior (K ^o _par ) further processed to the manipulated variable u of the controller becomes. A regulator according to claim 1 or claim 2, characterized in that the controller (F ^O , I ^o , K ^o _par ) has a parallel branch (K _par ), which processes the control deviation proportional and / or differentiating or non-linear to a value that is added to the manipulated variable of the controller. Regulator according to Claim 1, characterized in that the cyclic control deviation (e ^o ) is obtained from the actual control deviation (e) by the discrete Fourier transformation and the inverse discrete Fourier transformation (F ^o ). A regulator according to claim 4, characterized in that frequency-selective phase shifts φ _n take place in the inverse discrete Fourier transformation. Controller according to Claim 1, characterized in that the time period (T _p ) of the process to be controlled is specified for the controller, wherein in the discrete case the period (T _c ) corresponds to the integer multiple (R) of the sampling period (T). Regulator according to one of the preceding claims, characterized in that the time period (T _c ) is variable when the process is cyclic with respect to a state variable. Regulator according to one of the preceding claims, characterized in that the algorithm is characterized by a linear or nonlinear difference equation discretely represented in the time domain becomes. Regulator according to claim 8, characterized in that the discrete algorithm through a discrete transfer function which is represented as a Z transformation of the difference equation obtained by looking through the relationship between Z transformation and Laplacetransformation reaches a continuous representation. Controller according to claim 5, characterized in that for determining the phase shift of a certain frequency associated phase angle (φ _n ) is equated the phase response of the controlled system, whereby a simple rule for the design of the phase angle (φ _n ) is given. A regulator according to claim 3, characterized in that the parallel branch (K _par ) has PD behavior, and that the periodically integrating part behaves linearly. A regulator according to claim 1, characterized in that the mean value of the actual control deviation (e) is multiplied by a weighting factor (g ₀ ), where g ₀ ≥ o. A regulator according to claim 1 or claim 12, characterized in that the fundamental and / or harmonics are multiplied by N-frequency-selective weighting factors g _n ≥ o.