METHOD OF DETERMINING DELIVERY FLOW OR DELIVERY HEAD

Abstract

A torque required to achieve the modulated reference speed or adjustment of a modulated torque and the actual speed of the centrifugal pump is determined. Then a model speed is calculated with the aid of a mathematical pump-motor model simulating the behavior of the centrifugal pump within a hydraulic system as well as a disturbance signal from a deviation of the model speed from the actual speed of the centrifugal pump. Then a correction signal is determined by integrating the product of the disturbance signal and a sine or cosine signal with a multiple of the excitation frequency over at least one period of the excitation signal. Finally, at least one model parameter of the pump-motor model is determined as a function of the correction signal and the flow rate and/or the head is calculated using the adapted pump-motor model.

Claims

1. A method of determining the delivery flow and/or the delivery head of a speed-controlled centrifugal pump, wherein a reference speed or a torque of the centrifugal pump is acted upon by a periodic excitation signal of a specific excitation frequency to achieve a modulated setpoint speed, the method comprising the steps of: a. determining and adjusting a torque required to achieve the modulated reference speed or adjustment of the modulated torque, b. determining the actual speed of the centrifugal pump, c. calculating a model speed with the aid of a mathematical pump-motor model simulating the behavior of the centrifugal pump within a hydraulic system, d. calculating at least one disturbance signal from a deviation of the model speed from the actual speed of the centrifugal pump, e. determining at least one correction signal by integrating the product of the disturbance signal and a sine or cosine signal with a multiple of the excitation frequency over at least one period of the excitation signal, f. adapting at least one model parameter of the pump-motor model as a function of the correction signal, and g. calculating the flow rate and/or the head using the adapted pump-motor model.

2. The method according to claim 1, wherein the pump-motor model comprises at least a first equation in integral form for calculating the flow rate and a second equation in integral form for calculating the model speed, and these two equations are repeatedly cyclically evaluated.

3. The method of claim 2, wherein the first equation is used in the following integral form: $\begin{array}{cc}{Q}_{mdl}=\frac{1}{L_{hyd}}{\int }_0^t\left(\left(a{\omega }^2-b{Q}_{mdl}\omega -c{Q}_{mdl}^2\right)-R_{hyd}{Q}_{mdl}^2-H_{static}\right)\mathrm{dt}\mathrm{or}& G11\end{array}$ $\begin{array}{cc}{Q}_{mdl}\left(k+1\right)=Q_{mdl}\left(k\right)+\frac{1}{L_{hyd}}\left(\left(a{\omega }^2\left(k\right)-b{Q}_{mdl}\left(k\right)\omega \left(k\right)-c{Q}_{mdl}^2\left(k\right)\right)-R_{hyd}{Q}_{mdl}^2\left(k\right)-H_{static}\left(k\right)\right).Math.\Delta t& G11\end{array}$ where Q.sub.mdl the flow rate of the centrifugal pump, ω a speed or rotational frequency of the centrifugal pump (ω=2πn), a, b, care parameters that describe the hydraulic pump map (H(Q, ω)) by means of pump curves, R.sub.hyd the hydraulic resistance of the hydraulic system, L.sub.hyd the hydraulic inductance of the hydraulic system Hstatic is a geodetic head, k is a discrete time and Δt is the time interval between one time k and the next time k+1.

4. The method according to claim 2 wherein the first equation (G11) is used in the form of the following two partial equations (G11a, G11b) which are calculated repeatedly one after the other: $\begin{array}{cc}{H}_{mdl}=a{\omega }^2-b{Q}_{mdl}\omega -c{Q}_{mdl}^2& G11a\end{array}$ $\begin{array}{cc}{Q}_{mdl}=\frac{1}{L_{hyd}}{\int }_0^t\left(H_{mdl}-R_{hyd}{Q}_{mdl}^2-H_{static}\right)\mathrm{dt}\mathrm{or}& G11b\end{array}$ $\begin{array}{cc}{H}_{mdl}\left(k\right)=a{\omega }^2\left(k\right)-b{Q}_{mdl}\left(k\right)\omega \left(k\right)-c{Q}_{mdl}^2\left(k\right)& G11a\end{array}$ $\begin{array}{cc}{Q}_{mdl}\left(k+1\right)=Q_{mdl}\left(k\right)+\frac{1}{L_{hyd}}\left(H_{mdl}\left(k\right)-R_{hyd}{Q}_{mdl}^2\left(k\right)-H_{\mathrm{static}}\left(k\right)\right).Math.\Delta t& G11b\end{array}$ where H.sub.mdl is the delivery head of the centrifugal pump. Q.sub.mdl the flow rate of the centrifugal pump, ω a speed or rotational frequency of the centrifugal pump (ω=2πn), a, b, care parameters that describe the hydraulic pump map (H(Q, ω)) by means of pump curves, R.sub.hyd the hydraulic resistance of the hydraulic system, L.sub.hyd the hydraulic inductance of the hydraulic system, Hstatic a geodetic head k is a discrete time and Δt is the time interval between one time k and the next time k+1.

5. The method according to claim 2, wherein the second equation is used in the following integral form: $\begin{array}{cc}{\omega }_{\mathrm{mdl}}=\frac{1}{J}{\int }_0^t\left(T_{mot}-\left(a_t{Q}_{mdl}\omega -b_t{Q}_{mdl}^2-c_t\frac{Q_{mdl}^3}{\omega }+v_i{\omega }^2+v_s\omega -I\frac{dQ}{dt}\right)+T_D\right)\mathrm{dt}\mathrm{or}& G12\end{array}$ $\begin{array}{cc}{\omega }_{mdl}\left(k+1\right)={\omega }_{mdl}\left(k\right)+\frac{1}{J}\left(T_{mot}\left(k\right)-\left(a_t{Q}_{mdl}\left(k\right)\omega \left(k\right)-b_t{Q}_{mdl}^2\left(k\right)-c_t\frac{Q_{mdl}^3\left(k\right)}{\omega \left(k\right)}+v_i{\omega }^2\left(k\right)+v_s\omega \left(k\right)-I\frac{Q\left(k\right)-Q\left(k-1\right)}{\Delta t}\right)+T_D\left(k\right)\right).Math.\Delta t& G12\end{array}$ where T.sub.mot the mechanical torque of the motor (motor torque) of the centrifugal pump, T.sub.D the calculated disturbance signal in the form of a moment (disturbance moment), Q.sub.mdl the flow rate of the centrifugal pump, ω.sub.mdl the model speed or rotational frequency of the centrifugal pump (ω=2πn), ω a speed or rotational frequency of the centrifugal pump (ω=2πn), a.sub.t, b.sub.t, c.sub.t are parameters describing the static torque map (T(Q, ω)) of the pump by means of torque curves, ν.sub.i a quantity describing the friction between impeller and medium ν.sub.s a quantity describing the friction in the bearing J the mass inertia of the rotating components of the centrifugal pump (impeller, shaft, rotor), The mass inertia of the pumped medium in the impeller, k is a discrete time and Δt is the time interval between one time k and the next time k+1.

6. The method according to claim 2 wherein the second equation is used in the form of the following two partial equations (G12a, G12b) which are calculated successively, cyclically repeated: $\begin{array}{cc}{T}_{mdl}=a_t{Q}_{mdl}\omega -b_t{Q}_{mdl}^2-c_t\frac{Q_{mdl}^3}{\omega }+v_i{\omega }^2+v_s\omega -I\frac{dQ}{dt}& G12a\end{array}$ $\begin{array}{cc}{\omega }_{mdl}=\frac{1}{J}{\int }_0^t\left(T_{mot}-T_{mdl}+T_D\right)\mathrm{dt}\mathrm{or}& G12b\end{array}$ $\begin{array}{cc}{T}_{mdl}\left(k\right)=a_t{Q}_{mdl}\left(k\right)\omega \left(k\right)-b_t{Q}_{mdl}^2\left(k\right)-c_t\frac{Q_{mdl}^3\left(k\right)}{\omega \left(k\right)}+v_i{\omega }^2\left(k\right)+v_s\omega \left(k\right)-I\frac{Q\left(k\right)-Q\left(k-1\right)}{\Delta t}& G12a\end{array}$ $\begin{array}{cc}b{\omega }_{mdl}\left(k+1\right)={\omega }_{mdl}\left(k\right)+\frac{1}{J}\left(T_{mot}\left(k\right)-T_{mdl}\left(k\right)+T_D\left(k\right)\right).Math.\Delta t& G12\end{array}$ where T.sub.mdl a pump torque of the centrifugal pump T.sub.mot the mechanical torque of the motor (motor torque) of the centrifugal pump, T.sub.D the calculated disturbance signal in the form of a moment (disturbance moment), Q.sub.mdl the flow rate of the centrifugal pump, ω.sub.mdl the model speed or rotational frequency of the centrifugal pump (ω=2πn) , ω a speed or rotational frequency of the centrifugal pump (ω=2πn), a.sub.t, b.sub.t, c.sub.t are parameters describing the static torque map (T(Q, ω)) of the pump by means of torque curves, ν.sub.i a quantity describing the friction between impeller and medium ν.sub.s a quantity describing the friction in the bearing J the mass inertia of the rotating components of the centrifugal pump (impeller, shaft, rotor), Idis the mass inertia of the pumped medium in the impeller, k is a discrete time and Δt is the time interval between one time k and the next time k+1.

7. The method according to claim 1, wherein the difference between the model speed and the actual speed is fed to a controller containing at least one integral component, the output signal of this controller forming the disturbance signal or the disturbance signal being formed by multiplying the output signal of this controller by the actual speed.

8. The method according to claim 1, wherein in step d. a first disturbance signal and a second disturbance signal are determined by supplying the difference between the model speed and the actual speed to a controller containing at least one integral component, and the output signal of this controller forms the first disturbance signal and the second disturbance signal is formed by multiplying the output signal of this controller by the actual speed.

9. The method according to claim 1, wherein two or more correction signals are determined from the disturbance signal or from each of the disturbance signals from the disturbance signal or from each of the disturbance signals, and each correction signal is used to adapt in each case a specific model parameter of the pump-motor model.

10. The method according to claim 1, wherein the model parameter is the hydraulic resistance of the system or the parameter, and in step e. the sine or cosine signal is used which is in phase with the excitation signal.

11. The method according to claim 8, wherein the hydraulic resistance is adjusted in dependence of a first correction signal formed from the second disturbance signal and/or that the parameter is adjusted in dependence of a first correction signal formed from the first disturbance signal.

12. The method according to claim 1, wherein the model parameter is the mass inertia of the centrifugal pump or the hydraulic inductance of the system and in step e. that sine or cosine signal is used which is 90° out of phase with the excitation signal.

13. The method at least according to claim 8, wherein the mass inertia of the centrifugal pump is adjusted as a function of a second correction signal formed from the second disturbance signal, and/or in that the hydraulic inductance of the system is adjusted as a function of a second correction signal formed from the first disturbance signal.

14. The method according to claim 1, wherein the adaptation of the model parameter is carried out using a controller containing an integral component, to which the correction signal is supplied, the controller output signal being multiplied by an initial value for the model parameter to obtain the adjusted model parameter.

15. A centrifugal pump having a centrifugal pump, an electric motor driving it and control electronics for controlling with or without feedback the electric motor, wherein the control electronics are set up to carry out the method according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWING

[0090] Further features, characteristics, effects and advantages of the invention will be explained in more detail below with reference to examples or embodiments and the accompanying figures. The reference signs contained in the figures retain their meaning from figure to figure. In the figures, reference signs always denote the same or at least equivalent components, areas, directions or locations. In the drawing:

[0091] FIG. 1 is a schematic representation of a centrifugal pump within a closed hydraulic system;

[0092] FIG. 2 is a signal flow diagram of a first embodiment of the method according to the invention with singular model parameter adjustment;

[0093] FIG. 3 is a signal flow diagram with an embodiment of the pump-motor model 9 in FIG. 2;

[0094] FIG. 4 is an embodiment of the disturbance controller 10 in FIG. 2;

[0095] FIGS. 5-8 show different versions of the parameter controller 12 in FIG. 2;

[0096] FIG. 9 is a signal flow diagram of a second embodiment of the method according to the invention with singular model parameter adjustment and missing actual speed feed to the pump-motor model 9;

[0097] FIG. 10 is a signal flow diagram with an embodiment of the pump-motor model 9a in FIG. 9 with internal use of the model speed;

[0098] FIG. 11 is a signal flow diagram of a third embodiment of the method according to the invention comprising a multi-model parameter adaptation and a single disturbance variable on the output side of the disturbance controller 10;

[0099] FIG. 12 is a signal flow diagram of a fourth embodiment of the method according to the invention with multi-model parameter adaptation and two disturbance variables on the output side of the disturbance controller 10a;

[0100] FIG. 13 is an embodiment of the disturbance controller 10a in FIG. 12; and

[0101] FIG. 14 is a signal flow diagram showing an embodiment of the pump-motor model 9b in FIGS. 11 and 12 with multi-model parameter fitting.

SPECIFIC DESCRIPTION OF THE INVENTION

[0102] FIG. 1 shows a purely schematic representation of a centrifugal pump 3, 4 within a closed hydraulic system 1 in which the centrifugal pump 3, 4 circulates a fluid. The hydraulic system 1 may be, for example, a heating system or a cooling system for buildings, although for simplicity system components such as a heating source or chiller, heat exchanger, hydraulic separator, valves, etc. are omitted. However, the hydraulic system 1 comprises a piping network 2 extending from the centrifugal pump 3, 4 to a number of consumers (flow), such as radiators, heating circuits of a floor heating system or cooling circuits of a cooled ceiling and extending from these consumers back to the centrifugal pump 3, 4 (return). In this case, the centrifugal pump 3, 4 is intended to convey a heat transfer medium, such as water, to the consumers. Control valves, such as thermostatic valves or electrothermal actuators, are associated with these consumers to adjust the flow rate through the respective consumer or through a group of consumers. Due to the varying degree of opening of these control valves, the hydraulic load 5 to be served by the centrifugal pump 3, 4 changes according to the demand from the consumers, which for simplicity is symbolized in FIG. 1 by a single, but variable hydraulic resistance R.sub.hyd. It describes the slope of the so-called pipe network parabola of the hydraulic system 1, generally also called system characteristic curve or system curve.

[0103] It should be noted that the hydraulic system may equally be an open system, as in the case of a borehole pump, a sewage-lift station or a drinking-water pressure-boosting system.

[0104] The centrifugal pump 3, 4 comprises a centrifugal pump 4 together with an electric motor drive and pump or control electronics 4 for controlling with or without feedback the electric motor that are also set up for carrying out the method according to the invention. The electric motor may, for example, be a three-phase, permanently excited, electronically commutated synchronous motor. The control electronics 4 comprise a frequency converter for setting a specific speed of the electric motor. In operation, the centrifugal pump 4 generates a differential pressure between its suction and discharge sides, also referred to as head H.sub.real that, depending on the hydraulic resistance R.sub.hyd of the pipe network 2 connected to the centrifugal pump 4, results in a flow rate Q.sub.real.

[0105] A signal flow diagram illustrating the sequence of a first embodiment of the method according to the invention for determining the current delivery head H.sub.real and/or the current delivery flow Q.sub.real as accurately as possible by calculation is shown in FIG. 2. The method can be roughly divided into six process sections I to VI that are explained individually below. The process sections I to IV basically take place simultaneously and are repeatedly executed cyclically one after the other as a result of their program-technical processing by software in the control electronics 4, in particular at the clock speed of a processor not shown in the control electronics 4 on which the process according to the invention runs.

[0106] In the first process section I, a periodic excitation of the hydraulic system 1 takes place. In this embodiment, this takes place by applying a periodic excitation signal f.sub.A of a specific excitation frequencyω.sub.A to a reference rotational speed n.sub.0 of the centrifugal pump 3, 4 to obtain a modulated set rotational speed n.sub.soll and thus to modulate the actual rotational speed n.sub.real of the centrifugal pump 3, in particular to cause it to fluctuate periodically. It should be noted at this point that in various places in the figures the rotational frequencyω is used instead of the rotational speed n that due to the relationshipω=2π n does however correspond to the rotational speed and is understood to be synonymous with it, which is why in the following we refer generally to the “rotational speed ω.”

[0107] The periodic excitation f.sub.A has the effect of modulating the differential pressureΔ p of the centrifugal pump 3 or its delivery head H.sub.real proportional thereto that, depending on the modulation amplitude and frequency, results in a signaling response of the hydraulic system 1 that in turn is reflected in the torque required to set the modulated setpoint speed n.sub.soll, and also in the electrical power consumption of the centrifugal pump, from which the delivery flow Q can be determined. This basic principle is described in U.S. Pat. No. 10,184,476, to which reference is hereby made.

[0108] The reference speed no can be an externally specified speed for the centrifugal pump 3, 4 or a speed determined internally in the control electronics 4. It can, for example, originate from a characteristic curve control upstream of the speed control that, for example, sets the delivery head H as a function of the delivery flow Q according to a defined characteristic curve in the so-called HQ diagram, or result from an automatic control that sets the delivery head H as a function of other criteria, e.g. the change in delivery flow dQ/dt.

[0109] For example, the excitation signal f.sub.A can be a sinusoidal signal of the form f.sub.A=n.sub.1.Math.sin(ω.sub.A.Math.t), where n.sub.1 is the excitation amplitude and ω.sub.A is the excitation frequency. However, the excitation need not be sinusoidal. Another periodic waveform such as a square wave, trapezoidal wave, triangular wave, sawtooth wave or shark fin waveform are also possible. The periodic excitation of the system 1 or application of the excitation signal f.sub.A to the reference speed no is done by superimposition in an adder 6, to which the reference speed no and the excitation signal f.sub.A are each supplied in terms of signals. The output variable of this adder 6 is the modulated reference speed n.sub.soll=n.sub.0+n.sub.1.Math.sin(ω.sub.A.Math.t). This forms the input variable for the second process step II.

[0110] In this second method section II, the motor control 7 known per se is carried out for setting the modulated setpoint speed n.sub.soll, for example using a vectorial, in particular field-oriented control. Since the actual speed ω.sub.real is the controlled variable in this case, it is directly available from the field-oriented control, either based on a measurement by means of an encoder, by evaluating the voltage induced back into the stator coils by the rotor magnetic field (back EMF) or based on a calculation using a known algorithm for sensorless speed control. The motor control 7 comprises at least one speed controller 8, to which the modulated reference speed n.sub.soll is fed and which determines the torque T.sub.mot required to achieve the modulated reference speed n.sub.soll as a function of the deviation of the actual speed ω.sub.real from the reference speed n.sub.soll or, of course, ω.sub.soll. The actual speed ω.sub.real is thus also an input variable of the speed controller 8. The speed controller 8 may, for example, be a P, PI or PID controller, in which case the torque T.sub.mot is the manipulated variable. It can also be a PI-R controller that has a resonance component at the excitation frequency ω.sub.A to achieve the lowest possible control deviation.

[0111] The determined torque T.sub.mot is then adjusted by the motor control 7 on the drive of the centrifugal pump 3 that in FIG. 2 forms a physical system component. Depending on this torque T.sub.mot, a corresponding (actual) speed ω.sub.real of the centrifugal pump 3 results that then generates a delivery head H.sub.real and, depending on the load 5 in the form of the hydraulic resistance R.sub.hyd, a corresponding delivery flow Q.sub.real. The determined actual speed ω.sub.real, is fed to the speed controller 8 to determine the deviation from the set speed n.sub.soll and to adjust the torque T.sub.mot. Such a motor control 7 is known per se.

[0112] According to the invention, the determined torque To is further fed to a mathematical pump-motor model 9 which simulates the hydromechanical behavior of the centrifugal pump 3. This is a third section III of the method according to the invention and is part of a model-based operating point determination device 13 that is implemented in the control electronics 4 and is set up to determine the delivery head H.sub.mdl and/or the flow rate Q.sub.mdl of the centrifugal pump 3 from the pump-motor model 9. In control terms, this pump-motor model 9 represents a so-called observer which ideally enables observation of all state variables of the centrifugal pump 3, i.e. also non-measurable state variables. In particular, the pump-motor model 9 enables an estimation of the actual head H.sub.real, the actual flow Q.sub.real and the actual speed ω.sub.real in the form of their respective model quantities H.sub.mdl, Q.sub.mdl and ω.sub.mdl, it also being referred to as the model speed ω.sub.mdl.

[0113] One embodiment of the pump-motor model 9 is illustrated in FIG. 3. It comprises a system of equations based on a first differential equation G11a, G11b and a second differential equation G12a, G12b, each of which is transformed into an integral form to form a first and a second integral equation to simplify their calculation. The first integral equation Eq1a, Eq1b is based on a hydraulic differential equation describing a pressure balance in system 1 expressed in head. It forms a volumetric flow equation since it allows the calculation of the flow rate Q.sub.mdl. The second integral equation Eq2a, Eq2b is based on a hydromechanical differential equation describing a torque balance in system 1 considering friction losses. It forms a velocity equation since it allows the calculation of the model speed ω.sub.mdl. The two integral equations are calculated successively in a discrete-time manner using forward Euler integration.

[0114] To simplify the evaluation of the two integral equations, they are each divided into a static first partial equation G11a, G12a (secondary equation) and a dynamic second partial equation G11b, G12b (main equation) that has the integral form. In this case, the first partial equation G11a, G12a and then the second partial equation G11b, G12b are each calculated in terms of signal technology, whereby the result of the solution of the respective first partial equation G11a, G12a is used for the calculation of the respective second partial equation G11b, G12b, as is made clear below with reference to FIG. 3, which is why the first partial equations can be regarded as secondary equations to the second partial equations that in turn form the main equations due to their integral form.

[0115] In total, the system of equations thus consists of the following four subequations G11a, G11b, G12a, G12b, where the first two subequations G11a, G11b form a set describing the first integral equation, and the second two subequations G12a, G12b form a set describing the second integral equation. In the discrete-time implementation, the partial equations are as follows

[00019]$\begin{array}{cc}{H}_{mdl}\left(k\right)=a{\omega }^2\left(k\right)-b{Q}_{mdl}\left(k\right)\omega \left(k\right)-c{Q}_{mdl}^2\left(k\right)& G11a\end{array}$$\begin{array}{cc}{Q}_{mdl}\left(k+1\right)=Q_{mdl}\left(k\right)+\frac{1}{L_{hyd}}\left(H_{mdl}\left(k\right)-R_{hyd}{Q}_{mdl}^2\left(k\right)-H_{static}\left(k\right)\right).Math.\Delta t& G11b\end{array}$$\begin{array}{cc}{T}_{mdl}\left(k\right)=a_t{Q}_{mdl}\left(k\right)\omega \left(k\right)-b_t{Q}_{mdl}^2\left(k\right)-c_t\frac{Q_{mdl}^3\left(k\right)}{\omega \left(k\right)}+v_i{\omega }^2\left(k\right)+v_s\omega \left(k\right)& G12a\end{array}$$\begin{array}{cc}{\omega }_{mdl}\left(k+1\right)={\omega }_{mdl}\left(k\right)+\frac{1}{J}\left(T_{mot}\left(k\right)-T_{mdl}\left(k\right)+T_D\left(k\right)\right).Math.\Delta t& G12b\end{array}$

where

[0116] H.sub.mdl the delivery head to be determined H.sub.mdl of the centrifugal pump 3,

[0117] Q.sub.mdl the flow rate of the centrifugal pump 3 to be determined,

[0118] ω a speed or rotational frequency of the centrifugal pump (ω=2πn) ,

[0119] ω.sub.mdl the model speed of the centrifugal pump 3, [0120] a, b, c are parameters that describe the hydraulic pump map (H(Q, ω)) by means of pump curves,

[0121] R.sub.hyd is the hydraulic resistance of the hydraulic system 1,

[0122] L.sub.hyd the hydraulic inductance of the hydraulic system 1 and

[0123] H.sub.static is a geodetic head,

[0124] T.sub.mdl the theoretical pump torque of the centrifugal pump 3 to be calculated,

[0125] T.sub.mot the mechanical torque of the motor (motor torque) of the centrifugal pump,

[0126] T.sub.D a calculated disturbance signal in the form of a moment (disturbance moment),

[0127] a.sub.t, b.sub.t, c.sub.t are parameters describing the static torque map (T(Q, ω)) of the centrifugal pump 3 by means of torque curves,

[0128] ν.sub.i a quantity describing the friction between impeller and medium,

[0129] ν.sub.s a quantity describing the bearing friction,

[0130] J the mass inertia of the rotating components of the centrifugal pump 3 (impeller, shaft, rotor), and

[0131] k is a discrete time and

[0132] Δt is the time interval between one time k and the next time k+1.

[0133] In the first partial equation G11a of the first integral equation, further pressure terms can be considered, if necessary, to further adapt the pump-motor model 9 to reality. Furthermore, in the first partial equation G12a of the second integral equation G12 further terms (e.g. for friction) can be considered if necessary.

[0134] The pump-motor model 9 in FIG. 3 comprises three function blocks 9.1, 9.2, 9.3. In the second function block 9.2 the main equation G11b of the first integral equation (volume flow equation) is evaluated. Furthermore, in the third function block 9.3, the main equation G12b of the second integral equation (velocity equation) is evaluated. The second and third function block 9.2, 9.3 are preceded by the first function block 9.1, in which the two secondary equations G11a, G12a (pressure and torque characteristics) of the integral equations are evaluated. The functional summary of the calculation of these two partial equations G11a, G12a in the first function block 9.1 is done here because both partial equations G11a and G12a need the actual speedω and the flow rate Q to be calculated. However, the partial equations G11a and G12a could just as well be calculated in separate function blocks in terms of signal technology.

[0135] The first partial equation G11a of the first integral equation (volume flow equation) describes the speed-dependent relationship between flow rate Q and head H, or more precisely the pump characteristic diagram, i.e. for each speed co the dependence of the head H on the flow rate Q, this relationship being referred to as the pump curve Hω(Q). Along such a pump curve Hω the speed w is constant. All pump curves Hω form the pump map H(ω, Q). The pump characteristic diagram H(ω, Q) is usually measured at the factory and specified in the technical documentation of a centrifugal pump 3. The model parameters a, b, c that mathematically describe the pump curve H(ω, Q), are therefore known.

[0136] To calculate the model quantity H.sub.mdl by means of the partial equation G11a in the first function block 9.1, the speedω and the flow rate Q are required. In the embodiment according to FIGS. 2 and 3, the speedω is provided as the actual speed ω.sub.real is provided by the motor control unit 7 or fed to the first function block 9.1. The calculated feed flow Q.sub.mdl from the output of the second function block 9.2 is used as the feed flow Q and is also supplied to the first function block 9.1, wherein the feed flow Q.sub.mdl is zero at the start of the process or a defined initial value is used. The calculated model variable H.sub.mdl is output at the output of the first function block 9.1 and thus also forms the delivery head to be determined in accordance with the invention H.sub.mdlwhich is output at the output of the pump-motor model 9 as the first output variable.

[0137] In addition, the calculated delivery head model variable H.sub.mdl is transferred to the second function block 9.2, in which it is used to calculate the delivery flow Q.sub.mdl by means of the second partial equation G11b of the first integral equation. For the evaluation of this partial equation G11b, the hydraulic resistance R.sub.hyd, the hydraulic impedance L.sub.hyd, the current flow rate Q.sub.mdl and the geodetic head Hstatic are also required.

[0138] The second partial equation G11b of the first integral equation is based on the hydraulic differential equation:

[00020]$H\left(n,Q\right)=R_{hyd}{Q}^2+L_{hyd}\frac{dQ}{dt}+H_{static}$

that describes the system characteristic curve of the pipeline network 2 or the hydraulic system 1 that depends significantly on the position/degree of opening of the valves on the consumer side, i.e. on the hydraulic resistance R.sub.hyd.

[0139] The geodetic head H.sub.static is the minimum head H that must be reached in order for a flow (Q>0) to be possible at all. In closed hydraulic systems, i.e. those pipe networks in which the pumped medium circulates, such as in a heating or cooling system, the geodetic head H.sub.static is zero and can be neglected in this case. In the case of an open system, the geodetic head H.sub.static can, for example, be measured or specified on the pump electronics 4 of the centrifugal pump by a user.

[0140] The hydraulic resistance R.sub.hyd and the hydraulic impedance L.sub.hyd are initially unknown, since these parameters are part of the user's hydraulic system 1 that the pump manufacturer does not know. The hydraulic inductance L.sub.hyd, together with the volume flow, is a measure of the kinetic energy stored in the flowing water mass. Provided that the system is not changed structurally, the hydraulic impedance L.sub.hyd consequently does not change either. In the embodiment according to FIGS. 2 and 3, it can be determined by a simple estimation. In contrast, the hydraulic resistance R.sub.hyd changes dynamically during operation of the system 1 as a function of the demand of the consumers, in particular the heating or cooling demand, i.e. as a function of the position of the control valves on the consumer side which adjust the volume flow through the consumers. However, when the valves close completely, the inductance L.sub.hyd also changes.

[0141] In the first embodiment, the hydraulic resistance R.sub.hydis a model parameter of the pump-motor model 9 which is dynamically adapted according to the invention. It is repeatedly redetermined by a parameter controller 12 and fed to the pump-motor model 9, more specifically to the second function block 9.2, to be used in partial equation Eq1b. Since the hydraulic resistance R.sub.hyd is unknown at the beginning of the process, any initial value can be used for R.sub.hyd. This is because during the procedure its value is corrected by the parameter controller 12 towards the real value, as will be explained further below.

[0142] The volumetric flow value Q to be used in equation G11b is the volumetric flow value that is valid at the current point in time k. Partial equation G11b can thus be evaluated and the new volumetric flow Q.sub.mdl(k+1) can be determined. It thus represents the output signal of the second function block 9.2 as well as the second output variable of the pump-motor model 9.

[0143] The first part G12a of the second integral equation (velocity equation) describes the speed-dependent relationship between torque T and flow rate Q. It is therefore basically a torque equation. Like partial equation Eq. 1a, it requires the current rotational speed wand the current flow rate Q(k). As explained for the individual equation G11a, the speedω is the actual speed supplied by the motor control 7 to the first function block 9.1 ω.sub.real and as the current delivery flow Q the delivery flow Q.sub.mdl(k+1) from the output of the second function block 9.2 last calculated with partial equation G11b is used.

[0144] The term ν.sub.iω.sup.2 in partial equation Eq. 2a describes the friction between impeller and medium, the term ν.sub.sω describes the bearing friction losses resulting from the bearing of the pump or motor shaft. Both quantities ν.sub.i and ν.sub.s can be determined at the factory by measuring the centrifugal pump and are therefore known. Furthermore, the term

[00021]$I\frac{dQ}{dt}$

describes the moment of inertia of the medium in the impeller. Due to the comparatively small amount of pumped medium in the impeller, the term is comparatively small and can be neglected.

[00022]$I\frac{dQ}{dt}$

is comparatively small and can be neglected.

[0145] The model parameters a.sub.t, b.sub.t and c.sub.t describe the physical relationship between the torque T, flow Q and speed win other words the torque map T(ω, Q) of the centrifugal pump 3 formed from the individual torque curves Tω (Q), whereby the speedω is constant along a torque curve Tω (Q). Since, as previously stated, each pump is measured by the manufacturer and its hydraulic and hydromechanical pump characteristics are known to the manufacturer, the model parameters a.sub.t, b.sub.t and c.sub.t are also known per se. In the present example, the model parameter c.sub.t is a value that can change with time. Its initial value can also be determined at the factory by measuring the centrifugal pump 3.

[0146] The calculated model quantity T.sub.mdl is also output at the output of the first function block 9.1 and transferred to the third function block 9.3, in which it is used to calculate the model speed ω.sub.mdl by means of the second partial equation G12b of the second integral equation. For the evaluation of this partial equation G12b, the moment of inertia J, the motor torque T.sub.mot and the value of a disturbance torque T.sub.D are also required that exists in the event of a deviation of the model speed from the actual speed, i.e. is greater than zero in terms of amount. The moment of inertia J of the rotating components (shaft, rotor, impeller) of the centrifugal pump 3 can also be determined at the factory by measuring the centrifugal pump 3 or calculated from design data. The motor torque T.sub.mot is fed to the pump-motor model 9 or the third function block 9.3 by the motor control 7. Furthermore, the disturbance torque T.sub.D is determined by a disturbance controller 10 and is also fed to the pump-motor model 9 or the third function block 9.3.

[0147] Partial equation G12b can thus be evaluated and the model speed ω.sub.mdl determined. It thus represents the output signal of the third function block 9.3 as well as the third output variable of the pump-motor model 9.

[0148] The equations of the pump-motor model 9 are continuously calculated repeatedly, in particular depending on the clock rate of the processor of the control electronics 4 on which this calculation is performed. In this process, a new flow rate value Q.sub.mdl (k+1) or speed value ω.sub.mdl (k+1) is calculated in each clock cycle from the flow rate value Q.sub.mdl or speed valueω.sub.mdl used in the previous clock cycle.

[0149] With the aid of the pump-motor model 9 (observer) the actual speed of the centrifugal pump 3 is estimated as the model speedω.sub.mdl and fed to a disturbance controller 10 that also receives the actual speedω.sub.real of the centrifugal pump 3. The disturbance controller 10 forms a fourth process section IV, compare FIG. 2. The disturbance controller 10 forms a fourth process section IV, compare FIG. 2. It first determines whether and to what extent there is a deviation of the model speed ω.sub.mdl from the actual speedω.sub.real and determines a disturbance signal T.sub.Dfrom this deviation. In this respect, the disturbance controller 10 forms a disturbance signal calculation unit. It is responsible for setting or controlling the model speedω.sub.mdl so that it corresponds to the actual speed ω.sub.real.

[0150] A first embodiment of the disturbance controller 10 is shown in FIG. 4. It comprises a subtractor 14 which calculates the deviation (ω.sub.real−ω.sub.mdl) of the model speedω.sub.mdl from the actual speedω.sub.real of the centrifugal pump 3, 4. This part of the disturbance controller 10, together with the pump-motor model 9, can be understood as a “torque observer,” because a deviation of the model speedω.sub.mdl from the actual speedω.sub.real means a deviation of the model 9 from reality, which manifests itself in a disturbance torque that in turn is responsible for the speed deviation. Furthermore, the disturbance controller 10 comprises a controller 15 having an integral component that is here a PID controller. The calculated deviation or speed difference is fed to this controller 15 and integrated based on the integral component. The physical quantity of the controller output is defined by the connected manipulated variable, so that the controller output signal (manipulated variable of the controller) physically corresponds to a torque.

[0151] In the first embodiment of the disturbance controller 10, the controller output signal directly forms the disturbance signal T.sub.D that can accordingly be regarded as the disturbance torque T.sub.D. If the speedsω.sub.mdl, ω.sub.real, differ, then the pump-motor model 9 does not match reality. Thus, the disturbance controller 10 may also be referred to as a “disturbance observer,” The disturbance torque T.sub.D accelerates the model speed ω.sub.mdl when it is less than the actual speed ω.sub.real, and brakes the model speed ω.sub.mdl when it is greater than the actual speed ω.sub.real. In this way, the disturbance signal T.sub.D compensates for a deviation of the pump-motor model 9 from reality. Such a deviation can, for example, be caused by inaccurate parameter values, but can also be due to external disturbances, such as torque fluctuations due to particles or bubbles in the pumped medium or due to changing bearing friction.

[0152] The PID controller 15 of the disturbance controller 10 is initialized with the value 0. If the speedsω.sub.real and ω.sub.mdl are identical, their deviation is zero and the disturbance signal T.sub.D(disturbance torque) is constant or also zero at the beginning of the process. If there is a negative deviation between the speeds ω.sub.mdl and ω.sub.real i.e. that the actual speedω.sub.real lags behind the model speed ω.sub.mdl, the disturbance signal T.sub.D falls. This can be interpreted to mean that in reality a disturbance torque (braking torque) is acting, as a result of which the centrifugal pump 3 actually has a lower speed ω.sub.real than it is estimated by the pump-motor model 9. In other words, losses (e.g. friction losses/bearing wear, higher hydraulic resistance, higher inertia force, etc.) act in reality.) that are not taken into account in the (idealized) pump-motor model 9, so that the pump-motor model 9 overestimates the model speed ω.sub.mdl. If there is a positive deviation between the speeds ω.sub.mdl and ω.sub.real, i.e. that the model speedω.sub.mdl is estimated to be lower than the actual speed ω.sub.real, the disturbance signal T.sub.D increases steadily as a result of the I component of the controller 15. A too low model speed ω.sub.mdl can be present if the pump-motor model 9 models the centrifugal pump 3, 4 together with the connected system 1 too lossy, if necessary overadjusted.

[0153] The disturbance signal T.sub.D is then fed to an evaluation unit 11 and evaluated therein, which represents a fifth process section V. The evaluation unit 11 according to FIG. 2 is set up to determine a correction signal T.sub.D1 sin from the interference signal T.sub.D. This is done in such a way that the interference signal T.sub.D is first multiplied by a sinusoidal signal whose frequency corresponds to the multiple of the excitation frequency ω.sub.A, i.e. the fundamental frequency of the excitation signal fA(t). The product thus formed is then integrated over at least one period T of the excitation signal f.sub.A to obtain the correction signal T.sub.D1 sin. Mathematically, this is a sinusoidal transformation. The correction signal T.sub.D1 sin can thus be determined as follows:

[00023]$T_{D1sin}=\frac{1}{T}{\int }_t^{t+T}{T}_D\left(t\right).Math.\sin \left({\omega }_{A}t\right)dt$

[0154] The correction signal T.sub.D1 sin is then fed to a parameter controller 12 that is set up to carry out an adjustment of a model parameter as a function of the correction signal T.sub.D1 sin. In the embodiment according to FIG. 2, the model parameter to be adjusted is (only) the hydraulic resistance R.sub.hyd of the pipe network 2.

[0155] A first embodiment of the parameter controller 12 is shown in FIG. 5. It comprises a controller 17 with integral component to which the correction signal T.sub.D1 sin is fed. The controller 17 is implemented here as a PID controller. The output signal of this controller 17 represents a correction factor K. The controller 17 is initialized with the value 1 as one of the first steps of the method, so that the correction factor K initially has the value 1. The parameter controller 12 further comprises a multiplier 19 which multiplies the correction factor K by an initial value of the model parameter R.sub.hyd. Consequently, if the correction factor K=1, the initial value is not corrected so that the model parameter R.sub.hyd is equal to the initial value. If the correction signal T.sub.D1 sin is zero, the correction factor K remains unchanged. If the correction signal T.sub.D1 sin is greater than zero, the correction factor K is increased as a result of the integral component of the controller 17. If the correction signal T.sub.D1 sin is less than zero, the correction factor K is decreased as a result of the integration of the correction signal T.sub.D1 sin. The model parameter R.sub.hyd is consequently dynamically adapted, in particular “controlled with feedback,” by the parameter controller 12, the correction factor K indicating as a manipulated variable the extent of the deviation of the model parameter R.sub.hyd from the initial value.

[0156] The correction factor K thus generally makes it possible to obtain further information about the centrifugal pump 3, 4 or the pipeline network 2, such as information about ageing/wear of the centrifugal pump 3, deposits on the impeller (clogging) or a fault in the pipeline network. This makes it possible to monitor the condition of the centrifugal pump 3, 4. If the correction factor K exceeds or falls below a predetermined limit value, an error message, a warning and/or maintenance notice can be issued.

[0157] The parameter controller 12 may further comprise a correction factor limitation 18 which limits the correction factor K to an upper and/or lower limit value, for example to the upper value 5 or to the lower value ⅕, so that the permissible range of values for the model parameter to be adjusted is at most five times and one fifth of the initial value. The correction factor limiter 18 is thus located signal-wise between the controller 17 and the multiplier 19. The correction factor limiter 18 prevents the model 9 from moving too far away from the real system, for example, due to temporarily incorrect measured values. If, for example, the flow rate Q=0, the resistance R.sub.hydwould have to be infinitely large. This means that this condition would never be reached by integration. Conversely, it would then also take a very long time to return from infinity to another operating point. However, since the result does not change significantly at very low volume flows, it makes sense to limit the resistance R.sub.hyd. It can also be assumed for other model parameters that they can only change within a certain range. Otherwise, there may be another error, e.g. a measurement error.

[0158] Further, the parameter controller 12 may include a linearization unit 20 such that the parameter controller 12 exhibits the same behavior for increase as for decrease and the disturbance signal TD1 sin becomes proportional to the change in flow rate.

[0159] The model parameter R.sub.hyd, adjusted if necessary by the parameter controller 12, is then fed to the pump-motor model 9. The pump-motor model 9 then uses the adjusted model parameter in the second function block 9.2 to calculate the delivery flow Q.sub.mdl.

[0160] FIGS. 9 and 10 show a second embodiment of the pump-motor model 9a. It differs from the first embodiment in that no actual speed ω.sub.real is fed to the pump-motor model 9a from the motor control 7. Instead, the model speed ω.sub.mdl calculated internally in the previous cycle is used in the pump-motor model 9a for the individual equations G11a, G12a, for which the output of the third function block 9.3 is fed back to the input of the first function block 9.1, see FIG. 10. This is possible because the disturbance controller 10 is able to compensate very well for any speed error.

[0161] The individual sections I-VI of the method according to the invention, which can also be regarded as functions, are summarized once again in the following table:

TABLE-US-00001 Procedure sec. Function block Function I Speed Periodic excitation of a reference specification speed II Motor control Speed control and determining actual speed and torque III Pump-motor Calculation/observation of speed, head model and flow rate IV Fault Calculating a disturbance signal; controller controller with high bandwidth, or a bandwidth of at least one decade above the excitation frequency; ensures that model speed corresponds to actual speed V Evaluation Calculating one or more correction unit signals from the disturbance signal VI Parameter Model parameter adjustment as a controller function of the correction signal

[0162] This method improves the accuracy of the flow rate and/or head determination, since any disturbance torque T.sub.D is counteracted by the disturbance controller 10 and the subsequent parameter adjustment in the parameter controller 12, thereby reducing the noise in the flow rate and/or head signal compared to the prior art approach. Thus, the signal quality can be improved or a lower excitation amplitude than in the prior art can be used for the excitation signal while maintaining the quality, or a subsequent smoothing by filtering can be reduced, so that a faster reaction of the centrifugal pump 3, 4 to system state changes or disturbances in the hydraulic pipeline network 2 can take place. As a result of the adjustment of the model parameter during operation of the pump 3, 4, any inaccuracies in the pump-motor model 9 are also compensated for, which may be due to a scattering of the model parameters in series production and/or wear due to ageing, for example of the bearings of the centrifugal pump 3.

[0163] In principle, only the hydraulic resistance R.sub.hyd needs to be tracked to determine the flow rate Q, at least if the other model parameters are known from a measurement, estimate, calculation, etc., since R.sub.hyd is the only dynamically variable parameter. Nevertheless, the hydraulic resistance R.sub.hyd could also be determined in another way and fed to the pump-motor model 9. The method according to the invention is thus not limited to tracking the hydraulic resistance R.sub.hyd with the evaluation unit 11 and the parameter controller 12. Rather, a single other parameter can also be tracked, such as the moment of inertia J, the hydraulic impedance L.sub.hyd or the parameter c.sub.t. In the case of the moment of inertia J, the parameter controller 12 in FIG. 2 or 9 is formed by the moment of inertia controller 12′ from FIG. 6, in the case of the hydraulic impedance L.sub.hyd by the impedance controller 12″ from FIG. 7 and in the case of the parameter c.sub.t by the c.sub.t controller 12″′ from FIG. 8. In each of these three cases, the evaluation unit 11 also outputs a different correction signal, as will be explained below.

[0164] However, to improve the accuracy of the flow rate determination, in particular also in case of series dispersion (model parameters for different pumps of the same series may differ due to manufacturing and tolerances) as well as over the several years of operation of the centrifugal pump 3, 4, i.e. in case of ageing effects, the above-described further parameters of the pump-motor model 9 can be tracked in addition to the hydraulic resistance. It is then also possible to obtain further information about, for example, the wear of the pump 3, 4.

[0165] FIG. 11 shows a third variant of the method according to the invention. It differs from the first and second variants essentially in that the evaluation unit 11a receives the actual speedω.sub.real and calculates several correction signals, whereby each correction signal can be used to adjust a single model parameter, so that a number of model parameters of the pump-motor model 9b corresponding to the number of correction signals can be adjusted simultaneously. In this regard, each correction signal is calculated in a correction signal calculation unit 11.1, 11.2, all of which are part of the evaluation unit 11a. From the actual speed ω.sub.real, the evaluation unit 11a can calculate a second disturbance signal P.sub.D. Further, the evaluation unit 11a may calculate one or more correction signals from both the first disturbance signal T.sub.D and this second disturbance signal P.sub.D respectively.

[0166] The evaluation unit 11a according to FIG. 11 is set up to perform a discrete sine/cosine transformation of the disturbance signal T.sub.D or disturbance torque T.sub.D at the fundamental frequencyω.sub.A of the excitation signal f.sub.A(t). On the one hand, by integrating the product of the disturbance signal T.sub.D and a sinusoidal signal with the this fundamental frequencyω.sub.A, a first correction signal T.sub.D1 sin which represents an active component (or real component) and is in phase with the excitation signal f.sub.A (t), and a second correction signal T.sub.D1 cos which represents a blind part (or imaginary part) and is orthogonal to the excitation signal f.sub.A (t). In addition, the DC component T.sub.D0 of the disturbance signal T.sub.D can be calculated as a third correction signal. These three correction signals can be used to adapt three parameters of the pump-motor model 9b, since they would disappear in a non-faulty model. Mathematically, the three correction signals can be T.sub.D1 sin, T.sub.D1 cos, T.sub.D0 can be represented by the following integrals, each of which is calculated in one of the correction signal calculation units 11.1, 11.2:

[00024]$T_{D1sin}=\frac{1}{T}{\int }_t^{t+T}{T}_D\left(t\right).Math.\sin \left({\omega }_{A}t\right)\mathrm{dt}{T}_{D1cos}=\frac{1}{T}{\int }_t^{t+T}{T}_D\left(t\right).Math.\cos \left({\omega }_{A}t\right)\mathrm{dt}{T}_{D0}=\frac{1}{T}{\int }_t^{t+T}{T}_D\left(t\right)dt$

[0167] In the same way even further frequencies can be excited and evaluated. One receives thereby per frequency nω.sub.At two further correction signals T.sub.Dn sin, T.sub.Dn cos from the first interference signal T.sub.D that can be calculated in corresponding correction signal calculation units 11.1, 11.2:

[00025]$T_{Dnsin}=\frac{1}{T}{\int }_t^{t+T}{T}_D\left(t\right).Math.\sin \left(n{\omega }_{A}t\right)\mathrm{dt}{T}_{Dncos}=\frac{1}{T}{\int }_t^{t+T}{T}_D\left(t\right).Math.\cos \left(n{\omega }_{A}t\right)dt$

[0168] These can be used to track two other model parameters.

[0169] As already mentioned, the evaluation unit 11a is further set up to calculate a second disturbance signal P.sub.D and to perform a discrete sine/cosine transformation of this second disturbance signal P.sub.D at the fundamental frequency of the excitation signal f.sub.A (t). For this purpose, the product of the first disturbance signal or the disturbance torque T.sub.D and the actual speed ω.sub.real is first calculated that represents a power P.sub.D=T.sub.D.Math.ω.sub.real which can be referred to as “disturbance power” in analogy to the disturbance torque T.sub.D.

[0170] Alternatively to the calculation of the second disturbance signal P.sub.D in the evaluation unit 11a, this calculation can be performed in the disturbance controller 10a. FIGS. 12 and 13 illustrate such an embodiment variant. Thus, the actual speed does not have to be supplied to the evaluation unit. As can be seen from FIG. 13, the disturbance controller 10a used in FIG. 12 in this case additionally comprises a multiplier 16 which multiplies the output signal of the controller 15, i.e. the disturbance torque T.sub.D, by the actual speed ω.sub.real and thus provides a disturbance power P.sub.D at its output. The disturbance torque T.sub.Dis then the first disturbance signal T.sub.D and the disturbance power P.sub.D is the second disturbance signal P.sub.D, both of which are transferred by the disturbance controller 10a to the evaluation unit 11a so that it does not have to calculate the second disturbance signal P.sub.D.

[0171] From the second disturbance signal P.sub.D, the evaluation unit 11a calculates, by integrating the product of the second disturbance signal P.sub.D and a sinusoidal signal having this fundamental frequencyω.sub.A, a fourth correction signal P.sub.D1 sin which represents an active part (or real part) and is in phase with the excitation signal f.sub.A (t), and a fifth correction signal P.sub.D1 cos representing a blind part (or imaginary part) and being orthogonal to the excitation signal f.sub.A (t). In addition, the DC component P.sub.D0 of the second disturbance signal P.sub.D can be calculated as the sixth correction signal. Thus, three further correction signals P.sub.D1 sin, P.sub.D1 cos, P.sub.D0 can be determined by forming the following integrals, which is performed in each case in one of the correction signal calculation units 11.1, 11.2:

[00026]$P_{D1sin}=\frac{1}{T}{\int }_t^{t+T}{P}_D\left(t\right).Math.\sin \left(\omega t\right)\mathrm{dt}{P}_{D1cos}=\frac{1}{T}{\int }_t^{t+T}{P}_D\left(t\right).Math.\cos \left(\omega t\right)\mathrm{dt}{P}_{D0}=\frac{1}{T}{\int }_t^{t+T}{P}_D\left(t\right)dt$
with P.sub.D=T.sub.D(t).Math.ω.sub.real(t)

[0172] In the same way, further frequencies can be excited and evaluated. One receives thereby per frequency nω.sub.At two further correction signals P.sub.Dn sin, P.sub.Dn cos from the second interference signal P.sub.D

[00027]$P_{Dnsin}=\frac{1}{T}{\int }_t^{t+T}{P}_D\left(t\right).Math.\sin \left(n{\omega }_{A}t\right)\mathrm{dt}{P}_{Dncos}=\frac{1}{T}{\int }_t^{t+T}{P}_D\left(t\right).Math.\cos \left(n{\omega }_{A}t\right)dt$

which can be used to track two additional model parameters.

[0173] Of course, the evaluation unit 11a does not necessarily have to calculate all the above-described correction signals. Rather, this can be done as required and desired.

[0174] The correction signals T.sub.D1 sin, T.sub.D1 cos, P.sub.D1 sin, P.sub.D1 cos, T, P.sub.D0D0 etc. calculated by the evaluation unit 11 are then fed to the parameter controller 12a that is set up to adjust one model parameter per correction signal. This is done in single parameter controllers 12.1, 12.2, etc., each of which is supplied with a particular correction signal. Thus, six model parameters can be adjusted simultaneously by this parameter controller 12a. The parameter controller 12 thus consists, more precisely, of a number of individual parameter controllers 12.1, 12.2, each of which may have a structure as in FIG. 5, 6, 7 or 8, and each of which specifies a model parameter. In FIG. 5 this is the hydraulic resistance R.sub.hyd, in FIG. 6 the inertia J of the rotating components of the centrifugal pump 3, in FIG. 7 the hydraulic impedance L.sub.hyd and in FIG. 8 the model parameter c.sub.t. The parameter controller 12 in FIG. 5 differs from the other parameter controllers 12′, 12″, 12″′ of FIGS. 6 to 8 only in that it has a linearisation unit 20. In addition, each parameter controller 12, 12′, 12″, 12″′ has a controller 17, 17a, 17b, 17c with an integral component which, for example, can be as a PID controller, a multiplier 19, 19′, 19″, 19″′ for multiplying the respective correction factor K, K.sub.a, K.sub.b, K.sub.c by the corresponding initial value of the respective model parameter R.sub.hyd, J, L.sub.hyd, c.sub.t, and optionally a correction factor limiter 18, 18′, 18″, 18′″. The operation of each parameter controller 12, 12′, 12″, 12′″ is as previously described with respect to the first embodiment.

[0175] In principle, each individual correction signal can be used for the tracking of a model parameter. However, it should be noted that signals which represent an active component, i.e. signals which are in phase with the excitation of the pump speed—i.e. the sinusoidal signals in the case of sinusoidal excitation—adjust those model parameters which predominantly act on the active power. This is the case with the hydraulic resistance R.sub.hyd and the model parameter c.sub.t, which is why the parameter controllers 12, 12″ are fed the correction signals T.sub.D1 sin and P.sub.D1 sin for these model parameters in FIGS. 5 and 8. However, it does not matter which of these parameter controllers 12, 12″′ receives the correction signal T.sub.D1 sin and which receives the correction signal P.sub.D1 sin. The correction signal supply can be interchanged to this extent.

[0176] In contrast, those correction signals which represent reactive power, i.e. are 90° out of phase with the excitation of the pump speed, i.e. the previously mentioned correction signals T.sub.D1 cos and P.sub.D1 cos, should adapt such model parameters which predominantly influence the reactive power. This is the case with the inertia J and the hydraulic impedance L.sub.hyd, which is why the parameter controllers 12′, 12″ are supplied with the correction signals T.sub.D1 cos and P.sub.D1 cos for these model parameters in FIGS. 6 and 7. Again, it does not matter which of these parameter controllers 12′, 12″ receives the correction signal T.sub.D1 cos and which receives the correction signal P.sub.D1 cos. The correction signal supply can also be interchanged in this respect.

[0177] Experiments have shown that the following assignment of the correction signals T.sub.D1 sin, T.sub.D1 cos, P.sub.D1 sin, P.sub.D1 cos, T.sub.D0, P.sub.D0 to the model parameters is advantageous: [0178] T.sub.D1 sin to adjust the model parameter R.sub.hyd [0179] T.sub.D1 cos to adjust the model parameter L.sub.hyd [0180] P.sub.D1 sin to adjust the model parameter c.sub.t [0181] P.sub.D1 cos to fit the model parameter J [0182] T.sub.D0 to adjust the model parameter ν.sub.s [0183] P.sub.D0 to adjust the model parameter ν.sub.i

[0184] However, other combinations are also possible. According to this assignment, the individual correction signals can be fed to that single parameter controller 12.1, 12.2, etc. which adjusts the correspondingly assigned model parameter.

[0185] The output signals of the single parameter controllers 12.1, 12.2, etc., i.e. the adjusted model parameters, are then made available to the pump-motor model 9b, whose signal flow diagram FIG. 14 shows. The pump-motor model 9b can then use these new values of the model parameters to calculate the model speedω.sub.mod, the flow rate Q.sub.mdl and the head H.sub.mdl. For this purpose, the model parameter c.sub.t is fed to the first function block 9.1, the two model parameters R.sub.hyd and L.sub.hyd are fed to the second function block 9.2 and the model parameter J is fed to the third function block 9.3, within each of which the new model parameter values are then used in the corresponding partial equations G11b, G12a, G12b.

[0186] It should be noted that the above description is given by way of example only for purposes of illustration and in no way limits the scope of protection of the invention. Features of the invention indicated as “may,” “exemplary,” “preferred,” “optional,” “ideal,” “advantageous,” “optionally,” “suitable” or the like are to be regarded as purely optional and likewise do not limit the scope of protection that is defined exclusively by the claims. To the extent that the above description recites elements, components, process steps, values or information having known, obvious or foreseeable equivalents, such equivalents are embraced by the invention. Likewise, the invention includes any changes, variations or modifications to embodiments that involve the substitution, addition, alteration or omission of elements, components, process steps, values or information, so long as the basic idea of the invention is maintained, regardless of whether the change, variation or modification results in an improvement or deterioration of an embodiment.

[0187] Although the above description of the invention mentions a plurality of physical, non-physical or procedural features in relation to one or more specific example of the invention, these features may also be used in isolation from the specific example of the invention, at least to the extent that they do not require the mandatory presence of further features. Conversely, these features mentioned in relation to one or more specific embodiment may be combined with each other and with further disclosed or non-disclosed features of shown or non-shown embodiments as desired, at least to the extent that the features are not mutually exclusive or do not lead to technical incompatibilities.