DE4020502A1 - Extrapolation of time varying measurement parameter - by deriving steady state value from instantaneous value, time derivative and differential quotient - Google Patents

Abstract

A method of extrapolating a time varying measurement parameter x(t) with the relationship of its first time derivative to a time invariant input parameter K y id defined by x(t)=(K y - x(t))/T, where T is a time constant, involves determining the steady state value xE. The steady state value is derived from an instantaneous value x/ of the parameter, its first derivative w.r.t. time and the differen-tial quotient of the first time derivative and the parameter, i.e.: xE=x1-x1(1/dx - dx). USE/ADVANTAGE - Rapid indication of steady state value, e.g. of temp . in heating process, irrespective of time constant.

Description

The invention relates to a method for extrapolation a time-varying measured variable x on a controlled system with compensation that is approximately of first order is and which is essentially dynamic through a Time constant T is characterized, to which a time constant input variable K y is applied and at between the output variable x (t), the input variable K y, the Time constant T and the first derivative of the output variable according to time (t) the relationship

consists.  

The start-up process of a regulation or control process is often associated with considerable difficulty since either a very careful and slow approach to the Control variable to the target value or a strong overshoot must be accepted. Such problems occur, for example, in the control or Control of electrically heated water heater as well even with room temperature controllers.

Electrically heated water heaters are generally with at least one heating coil of fixed and known power fitted. The switching intervals of the heating coil, that is, the periods of performance are included both of the heating temperature to be achieved as well depending on the amount of water flowing through per unit of time. The following applies:

where D _{m is} the flow rate, P _{m is} the power, ϑ _{d is} the temperature after part of the heating section, ϑ _{e is} the temperature before the first heating coil and c is the specific heat. The power to be supplied to the water until the target temperature ϑ _target is reached therefore arises

P = cD _m (ϑ _target - ϑ _e ).

Hence is

Immediately after switching on, the measured variable ϑ _d is still much smaller than the steady-state value ϑ _dE so that a much too high power P is calculated. If this power is supplied, the temperature can easily overshoot. It is known that the rate of change x of the measured value, based on the time constant T of the measured value acquisition, including a constant K, can be determined according to the following relationship:

where y is the manipulated variable.

This equation, which is also written in the form = f (x, y) is for y = const. geometrically as a straight line can be represented with the slope. The end point this falling straight line is the steady state value, that is = 0.  

The invention is based on the object of specifying a method for extrapolating a temporally changing measured value, in particular the temperature profile in an electric instantaneous water heater. This should enable us to make useful statements about the steady state ϑ _dE early on and regardless of the time constant T of the temperature sensor and ultimately about the switching intervals of the power output.

According to the invention the object is achieved in that the steady-state value x _{E of} the measured variable x (t) from a momentary value x 1 of the measured variable, the first derivative of the measured variable existing at the same time after the time 1 and the differential quotient of the first derivative of the measured variable x 1 and the measured variable ₁ is determined according to the following equation:

It is essential that by measuring K, x (t) and (x) from the increase in the steady state value for x with t → ∞ and = 0 can be calculated at a very early point in time regardless of the time constant T. It can be seen that a usable statement about the steady-state value x _{E is} available after a period of time that is approximately 25% of the compensation process plus a dead time.

According to a first advantageous embodiment of the method according to the invention, in an electrically heated instantaneous water heater with control of the power supply as a function of the inlet temperature ϑ _e , the target value of the outlet temperature and the temperature ϑ _d , which is supplied by a temperature sensor after a first section of the heating duct , the steady-state value ϑ _dE by forming the first derivative of the temperature _d and the differential quotient of the first derivative of the temperature _d and the measured temperature ϑ _d according to the equation

determined.

For this purpose, in particular a temperature sensor is provided within the flow range after about ¼ to ¹ / ₃ of the flow path. The water temperature ϑ _d reached at this point depends on the amount of water flowing through per unit of time, that is to say on the flow D _m , and thus also a measure of the flow D _m . The outlet temperature to be set ϑ _target can be set by changing the output of the subsequent heating coils with constant voltage U applied to the heating coil. To increase the outlet temperature, the output must be increased accordingly, i.e. voltage must be applied to the subsequent heating coils.

Advantageous developments of the invention are in the Subclaims are marked below along with the description of the preferred ones Execution of the invention shown in more detail with reference to the figures. It shows

Fig. 1 is a functional diagram of an electric continuous flow heater,

Fig. 2 shows the time course of the temperature, the electric voltage and the flow rate in an electric water heater,

Fig. 3, the parameter dependence of the temporal development of a measured variable,

Fig. 4 shows the dependence of the rate of change of a measured parameter of this measured variable,

Fig. 5 to Fig. 4 for the measured variable temperature in an electric water heater, and

Fig. 6 is a further illustration of the functional relationship between the rate of change of temperature, and this temperature.

The core of an electrical instantaneous water heater, shown in a highly schematic form in FIG. 1, is a multiplicity of heating coils 1, 2 and 3 which are used in a water flow region 4 . The water flowing in the direction of the arrow initially has the inlet temperature ϑ _e . When applied to the heating coils 1, 2 and 3 constant voltage U₁, U₂ and U₃, the water is gradually heated as it passes through the heating coils 1, 2 and 3 . A temperature sensor 6 for determining an intermediate temperature ϑ _{d is} arranged after part of the heating section. Another temperature sensor 5 in front of the heating coil 1 is used to determine the inlet temperature ϑ _e . For example, a constant voltage U 1 is applied to the first heating coil 1 . The power P _n is then output from this heating coil 1 . The output of the other heating coils is set by an electrical power control, not shown here, for example a vibration package control, so that the desired target outlet temperature ϑ _{target is} reached. This performance is determined from. Because of the long idle times within the heating system, the outlet temperature is not regulated, but determined via a control system in which all disturbance variables (flow, inlet temperature, mains voltage) are determined.

Fig. 2 shows in a first diagram of two possible waveforms for the measured temperature θ _d in function of time. In order to reach a certain outlet temperature ϑ _target , the required power must be determined according to the above equation and supplied to the heating coils. In the steady state this includes a value ϑ _dE at the measuring point of the temperature sensor 3 of the intermediate temperature. The aim is to implement this control process with as little time as possible and without excessive overshoot of the temperature to be set. After a dead time t _T caused by the system and inertia, the measured temperature ϑ _d increases exponentially. The time t₄ is required for this until the steady-state value ϑ _dE is reached. The inventive method now aims but from thereon to determine the steady-state value θ _dE before expiry of the period t₄ so that the power supply be adapted for a non described in this algorithm so θ _target before reaching this temperature θ _dE and thus the outlet temperature, that an overshoot of the outlet temperature beyond the desired value ϑ _{target is} avoided. As the ϑ _d / t diagram shows, by applying a tangent to the measurable temperature curve, a statement about the steady-state value ϑ _{dE can be} extrapolated after a certain period T. The period T is significantly smaller than t₄.

During the start-up process, a constant voltage U 1 is applied to the heating coil 1 . The voltage U 1 can only assume the value U 1 or by switching off the value zero.

A flow D _m according to the third diagram results from the measured values ϑ _d and ϑ _{e of} the temperature sensor. This means that when the start-up, a flow that is much too high is initially determined and used as the basis for the power calculation. Too much power is supplied to the heating system so that significant overshoot must be expected.

More diagrams shown in Fig. 3 show the time course of the controlled variable x at different but constant manipulated variables Y₁ and Y₂. The persistence value X _E1 depends on the Y₁ level and the persistence value X _E2 on the Y₂ level. Different time constants T 1 and T 2 do not influence the level of the steady-state value X _E1 or X _E2 , but do influence the time required to set the steady-state value X _E1 or X _E2 .

In order to achieve complete independence of the determination of the steady-state value from the time constant, the rate of change of the controlled variable, that is to say of the measured value, is represented as a function of this measured value. Such a family of curves for different manipulated variables Y₁ and Y₂ and different time constants T₁ and T₂ is shown in Fig. 4. It can be seen that the curves belonging to Y₁ for both T₁ and T₂ are directed to the steady-state value X _E1 and the curves belonging to Y₂ for both the T₁ and T₂ control the steady-state value X _E2 .

Fig. 5 shows the application of this representation to the measured variable ϑ _d in an electric instantaneous water heater . The rate of change of the measured temperature ϑ _d as a function of this temperature ϑ _d decreases linearly, starting from a maximum. At ϑ _d = 0, that is, at the point of intersection with the abscissa, the steady-state _value ϑ _dE1 for a heating coil power P₁ or ϑ _dE2 for a heating coil power P₂ is reached. As can be seen from FIG. 6, two measured values _d1 and _d2 are sufficient to determine the steady-state value ϑ _dE from the slope of the _d / ϑ _d straight line.

It is crucial that in the method according to the invention to determine the persistence value, no system-internal and parameters that change over time in an undefined manner, such as time constants are.

The invention is not restricted in its implementation to the preferred embodiment described above. Rather, a number of variants are conceivable which of the solution shown also in principle make use of different types.

Claims (3)

1. Method for extrapolation of a time-changing measured variable x on a controlled system with compensation, which is approximately of first order and which is characterized dynamically essentially by a time constant T, to which a temporally constant input variable K y is applied and in which between the Output variable x (t), the input variable K y, the time constant T and the first derivative of the output variable after the time (t) of the relationship consists, characterized in that the steady-state value x _{E of} the measured variable x (t) from a momentary value x₁ of the measured variable, the first derivative of the measured variable existing at the same time after the time ₁ and the differential quotient of the first derivative of the measured variable ₁ and the measured variable x₁ according the following equation is determined: 2. The method according to claim 1, characterized in that in an electrically heated water heater with control of the power supply as a function of the inlet temperature ϑ _e , the target value of the outlet temperature and the temperature ϑ _d by a temperature sensor after a first section of the heating duct is delivered, the steady-state value ϑ _dE by forming the first derivative of the temperature _d and the differential quotient of the first derivative of the temperature _d and the measured temperature ϑ _d according to the equation is determined. 3. The method according to claim 2, characterized in that the water temperature ϑ _{d is determined} after a partial distance which is approximately ¼ to ¹ / ₃ of the heating channel length.