DE102007018805B4 - Method for controlling cyclic processes - Google Patents

Abstract

The invention relates to a controller for controlling cyclic processes, e.g. the control of the smoothness of a reciprocating motor, with which a cyclic control deviation (e °) is determined, wherein for determining the cyclical control deviation (e °) the mean value of the actual control deviation (e) a period (T <SUB> p </ SUB>) , is added to at least one phase-shifted fundamental and / or harmonic of the actual control deviation (e), wherein the thus determined cyclic control deviation (e °) is further processed by an algorithm with periodically integrating behavior to the manipulated variable (u) of the controller.

Description

The invention relates to a method for controlling cyclic processes, for. As for controlling the speed and smoothness of a reciprocating internal combustion engine, comprising at least two successive transfer functions F ^O and I ^O.

From the prior art according to the post-published DE 10 2005 047 829 B3 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 do the related Correct vibrations. For this purpose, a second controller is provided, which corrects the vibrations at the speed to which the first controller is not able. Conversely, the second regulator is off the prior art is unable to control the speed, for the the first controller responsible is.

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 shows the following:
The controlled system results in a controlled variable Y. This controlled variable Y has unwanted oscillations at certain frequencies. 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 regulator 2 has no guiding performance and therefore is unable to control a cyclic or periodic command. Thus, it can not be used for any cyclic or periodic processes.

The scheme according to the DE 195 27 218 B4 , of the DE 102 35 665 A1 and also the DE 43 19 677 C2 insofar resemble the teaching previously described according to the DE 10 2005 047 829 B3 because even with these controllers from the prior art only periodic disturbances can be corrected; they are unable to demonstrate leadership behavior relative to the process size they are intended to influence. That is, the prior art regulators are not designed to process variables, but only to eliminate certain interfering components from the process variable.

The is called, the object underlying the invention is to provide a To design the regulator for Any cyclic processes can be used.

The Task is inventively characterized solved, that a cyclic control deviation is determined, wherein the determination the cyclical deviation of the mean of the actual Control deviation from the immediately preceding, a period duration wide time interval, at least one phase-shifted basis and / or harmonic of the actual Control deviation is added, with the thus determined cyclic Control deviation by an algorithm with periodically integrating Behavior continues to the manipulated variable of the control method is processed. Such a controller is capable of a process stationary to regulate exactly, both in terms of leadership behavior as well as the fault behavior in periodic management or disturbance variables.

According to a special feature of the invention, the mean value of the actual Regelabwei 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].

hereby can the reinforcement be set separately for a specific frequency.

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

advantageous Features and variants of the invention are to the dependent claims remove.

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 continue to the manipulated variable of the controller is processed. This ensures that the controller is faster overall is, d. H. settles faster to the setpoint and also disturbances faster corrects.

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, to the manipulated variable of the controller is added. additionally to the parallel branch can be the proportional and / or differentiating Processing of the cyclical control deviation.

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 for the controller the temporal period of the process to be controlled given, wherein in the discrete case, the period of the integer Multiples of R of the sampling period. Ie. this can the controller can be set to any period, because the integer multiple represents itself as a parameter of the regulation. The time period is variable if the process in relation to a state variable itself behaves cyclically. Ie. Hereby, processes can also be regulated in which the cyclicity is not to the time, but to a state variable, z. B. the angle of rotation of a Working machine.

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

in the Case of a linear execution the controller can use the discrete algorithm through a discrete transfer function which can be represented as a Z transformation of the difference equation gets 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 equated to the phase response of the controlled system, creating a simple rule for the interpretation of the 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 K _p , K _d and K _{i will} be interpreted as if you wanted to interpret a conventional PID controller.

Based The following description explains the invention in more detail.

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 u _zyk frequency-selectively extracts information from the previous period measured from the current time, and represents the key to the steady-state control of cyclic 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 cyclic 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 transform is a frequency-selective phase shift is φn and a frequency selective weighting factors by g _0, g _n instead, where n = 1, 2, ..., N. 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 error; 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 cyclical 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.

Where:
W: setpoint (reference variable), 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.

at Use on time-variant and / or non-linear controlled systems can be free Parameters of the cyclo controller during the operation by appropriate adaptation to the changing Behavior of the controlled system can be adjusted. In engine control units, for example, can the parameters of the cyclo controller by maps or characteristics or by models or by other suitable adaptation methods depending on relevant state variables of the Motors are adapted to the respective operating condition.

is the cyclicity or periodicity not regarding the time, but concerning given a state variable x (t), so 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 of a Reciprocating motor cyclic (or periodically at constant load / speed) in terms of the state variable "camshaft rotation angle".

Of the ZykloRegler is then used so that it respects the State variable x (t) stationary or cyclical courses (exactly on and disturbances related) governs by the actual Control deviation for further processing for cyclic control deviation above this State variable x (t) in which case the sampling of the control deviation is equidistant over x (t). and not time equidistant carried out becomes. The sampling period T and the period Tp of the process are then variable and behave inversely proportional to time derivative of the state variable.

In the function F ⁰ , 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 design of the parameters φn, a simple rule can be given which leads to a robust design of the regulator: ## EQU1 ## The phase shifts φn, where φn is the phase shift associated with the frequency n / Tp, are taken from 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 you were using a controller without want to regulate the cyclic branch. For example, you can interpret Kpar as a PD controller and subsequently to switch on the cyclic branch.

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 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 two parameters K _P , K _{I in} addition to the phase shifts φn and the weighting factors g ₀ , g _n .

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 = 0.125 s. The fundamental wave therefore has a frequency of 8 Hz. The cyclo-controller is thus designed so that it can control not only constant control / disturbance variables but also 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 the cyclo controller is used (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 (Gg (jω) of the cyclo-closed loop, where 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 regulated at a steady state.

In 7 the amplitude response of the Bode diagram of the closed loop for the cyclo regulator for 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 So a controller that behaves like the PI controller, but also in is able to control certain frequencies stationary stationary.

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 is now done either manually or by means of suitable optimization methods (eg numerical optimization methods such as simplex method or evolution strategy ver drive) automated directly on the process or on a mathematical model of the controlled system.

• 1. Aktuelle Regelabweichung ermitteln und abspeichern: Es werden stets die letzten R Abtastwerte [e_i-R+1, e_i-R+2, ..., e_i] der Regelabweichung gespeichert. Aus dem aktuellen Abtastsatz [ei-R+1, ei-R+2, ..., ei] = [ei-R+k] = [ek]i (mit k = 1, 2, 3, ..., R)der Regelabweichung (bestehend aus R Abtastwerten) wird der aktuelle Wert e^O _i der zyklischen Regelabweichung berechnet; i ist dabei der aktuelle Regeltakt zum aktuellen Zeitpunkt t = iT.
• 2. Transformation in den Frequenzbereich: Der Abtastsatz [e_k]_i wird zunächst auf einer verschobenen Zeitachse t ~ = t – (i – R)·T als [e ~_k]_i dargestellt mit e ~k = e ~(t ~ = k·T) = e(t = (i – R + k)·T). Damit gilt für k = R: ei = eR = e(t = R·T = T).Der Abtastsatz [e ~_k]_i wird nun über die Diskrete Fouriertransformation (oder über die Fourieranalyse) in den Frequenzbereich transformiert:
  
• 3. Rücktransformation in den Zeitbereich: Die zyklische Regelabweichung ee ~^O(t ~) erhält man nun durch Inverse Diskrete Fouriertransformation (oder durch Fourierreihendarstellung) der Koeffizienten c, wobei eine frequenzselektive Phasenverschiebung um den Winkel ϕn stattfindet:
  
• 4. Aktuelle zyklische Regelabweichung ermitteln und abspeichern: Die aktuelle zyklische Regelabweichung lautet
  
• 5. Berechnen des zyklischen Stellgrößenanteils: 1. Durchführen der Periodischen Integration der zyklischen Regelabweichung; 2. Verarbeiten der zyklischen Regelabweichung durch K^Opar; 3. Die Addition der Ergebnisse von 1. und 2 liefert zyklischen Stellgrößenanteil u_zyk
• 6. Berechnen des parallelen Stellgrößenanteils: Verarbeiten der Regelabweichung mit Kpar liefert parallelen Stellgrößenanteil u_par
• 7. Berechnen der gesamten Stellgröße und Anlegen an die Regelstrecke: Addition von u_zyk und u_par liefert gesamte Stellgröße des ZykloRegler, die nun über das Stellglied an die Regelstrecke angelegt wird.

The steps of the method are as follows:

• 1. Determine and save the current control deviation: 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), the current value e ^O _{i of} the cyclic control deviation is calculated; i is the current control clock at the current time t = iT.
• 2. Transformation in the frequency domain: The sampling set [e _k ] _i is first on a shifted time axis t ~ = t - (i - R) * T represented as [e ~ _k ] _i 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). 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 domain: The cyclic deviation ee ~ ^O (t ~) is now obtained by inverse discrete Fourier transformation (or by Fourier series representation) of the coefficients c, whereby a frequency-selective phase shift takes place by the angle φn:
  
• 4. Determine and save the current cyclic control deviation: The current cyclic control deviation is
  
• 5. Calculation of the cyclic manipulated variable component: 1. Performing the periodic integration of 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 system deviation with Kpar supplies a parallel manipulated variable component u _par
• 7. Calculation of the total manipulated variable and application 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.

W

Reference variable,

Y

Controlled variable,

e

Deviation,

u1

Control value of controller 1,

u2

Control value of controller2

u _par

Manipulated variable contribution of K _par ,

u _cyc

_{Control value contribution} from K _zyk ,

K _par

processed the current control deviation e,

K _cyc

processed Information from the course of e in the past, a period wide, time interval

u

Manipulated variable of the method according to the controller

F ^O

Performs twofold transformation of e and yields e ^O

e ^o

cyclic Control deviation (synthetic)

I ^O

Performs periodic Integration through

K ^O _par

Optional additional feature to process ^eO

w

Reference variable,

y

Controlled variable,

d

disturbance

Note on terms in formulas:

lowercase letters designate signals in the time domain; Capital letters designate transfer functions or signals in the frequency domain.

Claims (13)

Method for controlling cyclic processes, eg. B. Regulation of the speed and smoothness of a reciprocating engine, comprising at least two successive transfer functions F ^O and I ^O characterized in that a cyclic control deviation (e ^O ) is determined, wherein for determining the cyclical control deviation (e ^O ) of the average of the actual Control deviation (e) from the immediately past, a period duration (Tp) wide time interval is added to at least one phase-shifted fundamental and / or harmonic of the actual control deviation (e), wherein the thus determined cyclic control deviation (e ^O ) by an algorithm with periodically integrating behavior is further processed to the manipulated variable (u) of the control method. A method 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. Method according to Claim 1 or Claim 2, characterized in that the controller according to the invention has a parallel branch (K _par ) which processes the control deviation proportionally and / or differentially or nonlinearly to a value which is added to the manipulated variable of the controller. A method according to claim 1, characterized in that the cyclic control deviation (e ^O ) by the discrete Fourier transform and the inverse discrete Fourier transform from the actual control deviation (e) is obtained (F ^O ). Method according to Claim 4, characterized in that frequency-selective phase shifts φ _n take place in the inverse discrete Fourier transformation. A method according to claim 1, characterized in that for the controller, the temporal period (T _p ) of the process to be controlled is specified, wherein in the discrete case, the period (T _c ) the integer multiple (R) of the sampling period (T). Method 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. Method according to one of the preceding claims, characterized characterized in that the algorithm is represented by a linear or nonlinear Difference equation in the time domain is displayed discretely. Method according to claim 8, characterized in that that the discrete algorithm through a discrete transfer function which is represented as a Z transformation of the difference equation gets where by the relationship between Z-transformation and Laplace transformation comes to a continuous presentation. A method 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 interpretation of the phase angle (φ _n ) is given. A method according to claim 3, characterized in that the parallel branch (K _par ) has PD behavior, and that the periodically integrating part behaves linearly. A method 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 method 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.