DE102016111065A1 - Control method with model-based anti-windup - Google Patents

Abstract

The invention relates to a control method with model-based anti-windup in which the control variable is subject to a manipulated variable limitation (2) and thus, limited in terms of their maximum, limited manipulated variable (ulim) for the controlled system is effective, the control variable determined by the controller (uc) and the limited manipulated variable (ulim) is supplied to the anti-windup algorithm (6). There is a parameter identification (4) of the controlled system (3) on the basis of which the parameters for the model of the controlled system (3) are estimated. These parameters are supplied to the anti-windup algorithm (6) in an adaptation branch (5), so that an adaptation of the model used in the anti-windup algorithm (6) takes place on the basis of the parameters currently determined by the parameter identification (4).

Description

Technical area

The invention relates to an adaptive controller, which takes into account the influence of limited in terms of their control variable actuators.

Commonly known are control methods in which a distance is controlled to a desired value, wherein a controller generates at its output on the basis of a determined control deviation a manipulated variable, which is set via a corresponding actuator to the controlled system. In classic linear control methods, it is assumed in the controller design that the manipulated variable is unlimited and that the manipulated variable determined in the control method can be ideally implemented in terms of amplitude and dynamics by the actuator. However, real actuators are always limited in terms of dynamics and amplitude. It is known below to (ideal) controller design to determine a control variable limit of the actuator and taken into account in the Regelagorithmus by z. For example, as the simplest form for PID controllers, the integrator values are frozen when the setting limit is reached in order to prevent so-called windup of the controller. Furthermore, it is generally known to use adaptive controller whose control parameters are changed during runtime of the controller by z. B. a parameter identification during operation takes place. It is also known to use a route model to perform an anti-windup method. This form is also referred to as a model-based anti-windup. The shape of the anti-windup structure influences the regulator input and output based on the deviation between the ideal and the real manipulated variable. Below is an adaptive controller will be described, which takes into account a track model in the anti-windup method and an improved signal behavior in unknown control systems or parameter variants routes z. B. has at parameter drift.

The term windup is to be described in the context of the patent application as a, caused by a manipulated variable limitation, misconduct of the control loop.

State of the art

From the Japanese patent application JP 2005-092267 A For example, a control method with an anti-windup algorithm using a reference model is known.

Object of the invention

The invention has for its object to provide an improved control method with an anti-windup algorithm.

Solution of the task

The object is achieved by a control method according to claim 1. Advantageous developments emerge from the subclaims.

Advantages of the invention

The control method with model-based anti-windup is based on a known structure in which a reference variable r a controller 1 is specified and determined on this a manipulated variable u _c and thus from the controlled system 3 returned controlled variable y / x results. The manipulated variable is subject to a manipulated variable limitation 2 and is thus limited in terms of its maximum, so that the limited manipulated variable u _lim for the controlled system 3 takes effect. The manipulated variable u _c determined by the controller and the limited manipulated variable u _lim become an anti-windup algorithm 6 fed, which is a model of the controlled system 3 contains and based on the feedback controlled variable at the controlled system output x / y, by the controller ( 1 ) certain manipulated variable (u _c ) and the limited manipulated variable (u _lim ), a controller coefficient (u _aw ) and a line coefficient (y _aw / x _aw ) is determined, wherein the controller coefficient (u _aw ) of the determined by the controller manipulated variable (u _c ) is subtracted and the distance _coefficient (y _aw / x _aw ) to that from the controlled system ( 3 ) recirculated controlled variable (y / x) is added. There is a parameter identification ( 4 ) of the controlled system ( 3 ), in that the limited manipulated variable (u _lim ) and the returned controlled variable at the controlled system output (x / y) of the parameter identification ( 4 ) are supplied and by means of known estimation method z. For example, the method of least squares the parameters for the model of the controlled system ( 3 ) to be appreciated. These parameters are inventively in an adaptation branch ( 5 ) the anti-windup algorithm ( 6 ), so that an adaptation of the anti-windup Algorithm ( 6 ) model currently used by the parameter identification ( 4 ) parameter is determined. According to the invention, the model of the anti-windup algorithm ( 6 ), so that a self-adjusting anti-windup method is provided and adjustments to unknown routes or due to variations of the route by parameter drift z. B. by aging effects, etc. can be done independently.

Advantageously in accordance with the invention, the parameter estimation of the distance model for the anti-windup algorithm can be isolated from the controller ( 1 ) respectively. Is this also an adaptable controller 1 a direct estimation of the controller parameters can be made by passing through the controller ( 1 ) determined manipulated variable (u _c ) and / or the limited manipulated variable (u _lim ), the feedback controlled variable at the controlled system output (x / y) and possibly the output of a reference model, such. B. in the model reference control, are evaluated on a goods criterion and therefrom via an optimization method, a parameter adaptation of the controller. Alternatively, the parameter identification ( 4 ) of the controlled system ( 3 ) are used for the adaptation. So for the anti-windup algorithm ( 6 ) estimated parameters of the controlled system 3 are thus usable for the controller data.

In an advantageous embodiment, the controller ( 1 ) a model of the controlled system ( 3 ) z. B. in the form of a model reference control. Which through the parameter identification ( 4 ) of the controlled system ( 3 ) estimated parameters can be used as model parameters of the controller ( 1 ) used model of the controlled system ( 3 ) be used.

drawings

Show it:

1 a schematic view of the control method with model-based anti-windup algorithm in a block diagram and

2 an application of the control method for a throttle valve

1 shows a block diagram of the control method. Here, the basic operation is explained below by way of example. A reference variable r is at the input of a regulator 1 this set as a setpoint. The regulator 1 , which is preferably an adaptive controller and in a possible embodiment, without consideration of the setting limits according to a classical design method z. B. Pole placement o. Ä. Is designed, generates at its output a manipulated variable u _c . As described, the manipulated variable constraints at the beginning of the controller design need not be considered, as these are subsequently followed by an external anti-windup algorithm 6 is taken into account. The existing in real actuators / actuators manipulated variable limitation is in the figure with 2 designated. The manipulated variable limit 2 causes the controller not to exceed the setting limit 1 determined manipulated variable u _c for the controlled system 3 becomes effective, but a limited manipulated variable u _lim at the input of the controlled system 3 is applied. At the output of the controlled system 3 is the control variable measurable, which is usually referred to by notation with x or y. Subsequently, both names y / x are used equally in the application. An external anti-windup algorithm 6 generates a controller coefficient u _aw and a path coefficient y _aw / x _aw . The controller coefficient u _aw is determined by the controller 1 subtracts the determined manipulated variable u _c and gives the unlimited manipulated variable u, which is at the input of the manipulated variable limit 2 is applied. The path coefficient y _aw / x _aw is added to the feedback controlled variable y / x, so that the modified controlled variable y _uss / x _us , which is the input of the controller 1 is switched on for comparison with the reference variable r. From the difference of the unlimited manipulated variable u and the limited manipulated variable u _lim , a manipulated variable difference Δu is formed, the input of the anti-windup algorithm 6 is. The limited manipulated variable u _lim and the returned controlled variable x / y are input of a parameter identification 4 , which estimates a track model or its parameters and this the anti-windup algorithm 6 and possibly the controller 1 provides. The parameter estimate for the controller 1 can also be done by a separate estimation method - not shown. This is the controller 1 z. B. adapted according to a quality criterion in terms of its parameters. But he can, as in the 1 shown its parameters from the estimation method of parameter identification 4 Respectively. In a further embodiment, the controller 1 contain a separate line model, as is known for model following rules, the parameters of this model being for the controller 1 used in the same way as for the anti-windup algorithm 6 be used.

mit dem Differentialoperator s dargestellt, dessen Zustandsraumdarstellung durch

gegeben ist, die im Allgemeinen als Streckenbeschreibung mit ẋ = Ax + Bu mit Erweiterungen durch Nichtlinearitäten beschrieben werden kann. Die Paramater r_i und z_i stellen dabei die Parameter des linearen Anteils der Regelstrecke dar. Der nichtlineare Anteil der Strecke, der z. B. durch Arbeitspunktabhängigkeit entstehen kann, besteht aus den bekannten vom Streckenausgang abhängigen Funktionen fi(y) und den dazugehörigen Parametern θ_i. Die vom Regler ermittelte Stellgröße u ergibt sich zu

, wobei P ^(s), L ^(s), M ^, K ^_aw und θ ^_i Reglerparameter sind, die aus den geschätzten Parametern der Strecke berechnet werden. Im Folgenden sind die Parameter P ^(s), L ^(s), M ^, K ^_aw zur Vereinfachung ohne Dach über dem Parameter verwendet. Das Dach kennzeichnet dabei lediglich die Parameter hinsichtlich ihrer Herkunft aus der Streckenschätzung. Die Verwendung ohne Dach als P, L, M, K_aw erfolgt synonym und kennzeichnet den identischen Parameter. An exemplary detailed mathematical description of the method is given below. The controlled system ( 3 ) is assumed in this case as a system of 2nd order and is determined by the mathematical model

represented by the differential operator s whose state space representation by

which can generally be described as a route description with ẋ = Ax + Bu with extensions by nonlinearities. The paramaters r _i and z _i represent the parameters of the linear component of the controlled system. The nonlinear component of the system, which, for B. can arise due to operating point dependence, consists of the known dependent on the distance output functions fi (y) and the associated parameters θ _i . The manipulated variable u determined by the controller is given by

, where P ^ (s), L ^ (s), M ^, K ^ _aw and θ ^ _{i are} controller parameters calculated from the estimated parameters of the route. In the following, the parameters P ^ (s), L ^ (s), M ^, K ^ _{aw are used} for the sake of simplicity without a roof over the parameter. The roof characterizes only the parameters with regard to their origin from the route estimation. The use without roof as P, L, M, K _aw is synonymous and identifies the identical parameters.

berechnen, wobei es sich bei den Streckenparametern in R(s) und Z(s) um geschätzte Streckenparameter handelt. Die gewünschte Dynamik des Regelkreises und des Anti-Windup Systems werden dabei durch R_d(s) = s² + r_d2s + r_d1 bzw. R_d,aw = s² + r_a2s + r_a1 angegeben. Die Schätzung der Streckenparameter erfolgt auf Grundlage eines linear parametrischen Modells, wie z. B.

R(s) = s² + r₂s + r₁ Z(s) = z₁ Λ(s) = 2 und kennzeichnet die Ordnung der Regelstrecke.
und eine Schätzung der Streckenparameter θ ^_p mit bekannten Schätzalgorithmen, vorzugsweise mit der Methode der kleinsten Quadrate vorzunehmen, ist diese im Folgenden in kontinuierlicher Version dargestellt ist

The controller parameters can be excluded from the regulations

calculate, where the route parameters in R (s) and Z (s) are estimated route parameters. The desired dynamics of the control circuit and the anti-windup system are carried R _d (s) = s ² + r s + r _{d1 d2} or R _{d, aw} = s ² + r _a2 + r s _a1 indicated. The estimation of the route parameters is based on a linear parametric model, such. B.

R (s) = s ² + r ₂ s + r ₁ Z (s) = z ₁ Λ (s) = 2 and marks the order of the controlled system.
and making an estimation of the line parameters θ ^ _p with known estimation algorithms, preferably with the method of least squares, this is shown below in a continuous version

ergeben.The anti-windup system can be described by the desired dynamics with the following equations:

result.

2 shows a schematic an equivalent circuit diagram of an electrically operated throttle valve DK. The electric actuator, which is shown here as motor M, is driven by a voltage u_m. Its inductance L and the resistor R are shown symbolically. A mechanical coupling of the engine M to a transmission allows the adjustment of the throttle valve, which is arranged rotatably on the transmission output on an output shaft.

wobei Jmech die Trägheit des mechanischen Systems, φ .. die Winkelbeschleunigung, φ . die Winkelgeschwindigkeit, Ts das nichtlineare Rückstellmoment der Feder, dmech die mechanische Dämpfung, Km die Motorkonstante und ng die Übersetzung des Getriebes beschreibt. Die zeitveränderliche Spannung u_m wird durch eine PWM mit Tastgrad τ und der konstanten Netzsspannung U über u_m = tau·U eingestellt. Somit kann die Systembeschreibung der Drosselklappe umgeschrieben werden in (s² + d / Js)φ = 1 / J(τ + θ T / tpf_tp(φ)) , mit der Zustandsraumbeschreibung

, deren Parameter gegeben sind durch

The rotation counteracts a spring and symbolically a friction T_fric is taken into account. Furthermore, the mechanical system has an inertia J _DK . The rotation of the throttle valve DK is as Rotation angle φ drawn. An equation of motion of the throttle valve DK is described by the following differential equation

where Jmech is the inertia of the mechanical system, φ .. the angular acceleration, φ. the angular velocity, Ts the nonlinear restoring moment of the spring, the mechanical damping, Km the motor constant and ng the gear ratio. The time-variable voltage u_m is set by a PWM with duty cycle τ and the constant mains voltage U via u_m = tau · U. Thus, the system description of the throttle valve can be rewritten in (s ² + d / Js) φ = 1 / J (τ + θ T / tpf _tp (φ)) , with the state space description

whose parameters are given by

überführt werden, wobei R(s) = s^2 + d/J·s, Z(s) = 1/J und umax = 1.The angle phi_lh describes the emergency air position of the throttle valve, in which the spring characteristic of the throttle valve changes abruptly. On one side of the emergency air position, a spring of rigidity k1 is prestressed with the moment T01 and on the other side a spring with the rigidity k2 is prestressed with the moment T02. The function in ftp is the Heaviside function. The throttle model can now in the more general form

where R (s) = s ^ 2 + d / J * s, Z (s) = 1 / J and umax = 1.

Verwendet werden. Die gewünschten Pole des Systems, die durch die Nullstellen der Polynome R_d(s) = s² + r_d2s + r_d1 bzw. R_d,aw = s² + r_a2s + r_a1 gegeben sind, können dabei frei gewählt werden. Die Berechnung der Verstärkung M erfolgt, um die statische Verstärkung von Eins des geschlossenen Regelkreises zu gewährleisten.For this general description can now again the calculation rule for the controller parameters

Be used. The desired poles of the system, by the zeros of the polynomials R _d (s) = s ² + r _{d 2} s + r _d1 and R _{d, aw} = s ² + r _a2 s + r are given _a1, can be freely chosen become. The calculation of the gain M is done to ensure the static gain of unity of the closed loop.

The procedure for the AntiWindup algorithm follows accordingly

als geschätzter Streckenparameter z1.With

as estimated route parameter z1.

QUOTES INCLUDE IN THE DESCRIPTION

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

Cited patent literature

• JP 2005-092267 A [0004]

Claims (4)

Control method with model-based anti-windup, in which a reference variable (s) is assigned to a controller ( 1 ) and this on the basis of one of the controlled system ( 3 ) feedback variable (y / x) a manipulated variable (u _c ) is determined, wherein the manipulated variable of a manipulated variable restriction ( 2 ) and thus a, limited in terms of their maximum, limited manipulated variable (u _lim ) is effective for the controlled system, wherein the controller determined by the manipulated variable (u _c ) and the limited manipulated variable (u _lim ) the anti-windup algorithm ( 6 ), which is a model of the controlled system ( 3 ) and based on the feedback controlled variable at the controlled system output (x / y), which is controlled by the controller ( 1 ) determined manipulated variable (u _c ) and the limited manipulated variable (u _lim ) a controller coefficient (u _aw ) and a section coefficient (y _aw / x _aw ) determined, the controller coefficient (u _aw ) of the determined by the controller manipulated variable (u _c ) and the distance _coefficient (y _aw / x _aw ) to that from the controlled system ( 3 ) feedback variable (y / x) is added and the controller ( 1 ) at its input, characterized in that a parameter identification ( 4 ) of the controlled system ( 3 ), wherein the limited manipulated variable (u _lim ) and the feedback control variable at the controlled system output (x / y) is applied and based on the parameters for the model of the controlled system ( 3 ) and these parameters in an adaptation branch ( 5 ) the anti-windup algorithm ( 6 ), so that an adaptation of the in the anti-windup algorithm ( 6 ) model currently used by the parameter identification ( 4 ) parameter is determined. Control method according to claim (1), characterized in that the controller ( 1 ) is adaptable with respect to its control parameters, whereby a direct estimation of the controller parameters from the controller ( 1 ) determined control variable (u _c ) and / or the limited manipulated variable (u _lim ), the feedback controlled variable at the controlled system output (x / y) and / or the output of a reference model, via a goods criterion or the parameters of the parameter identification ( 4 ) of the controlled system ( 3 ) are used for the adaptation. Control method according to one of the preceding claims, characterized in that the controller contains a model of the controlled system in the form of a model reference control and by the parameter identification ( 4 ) of the controlled system ( 3 ) estimated parameters as model parameters of the controller ( 1 ) used model of the controlled system ( 3 ) be used. Control method according to one of the preceding claims, characterized in that the controlled system ( 3 ) by means of a general route description with ẋ = Ax + Bu; the description is supplemented by a manipulated variable limitation and, taking the nonlinearities into consideration, yields by way of example equation (1)

where the matrix A contains the model state, sat u _max the manipulated variable limit and the sum Σ the operating point-dependent non-linear components and the manipulated variable u

according to the rule of law of Eq. 2, where P ^ (s), L ^ (s), M ^, K ^ _aw, and θ ^ _{i are} governor parameters determined based on estimated track parameters and the parameter estimate based on the system linear parametric model

and an estimate of the line parameters θ ^ _p with known estimation algorithms, preferably carried out with the method of least squares, in its continuous form with

is overwritten, so for the the controller parameters

the function R _d (s) = s ² + r _d2 s + r _d1 the desired dynamics of the closed loop and R _{d, aw} = s ² + r _a2 s + r _a1 Describes the desired dynamics of the anti-windup algorithm, so that the parameters of the anti-windup algorithm out

result.

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