DE102022116485A1 - Method for vibration-free, precise control - Google Patents

Abstract

The invention relates to a method for controlling a controlled variable (y) of a system, wherein the system shows a system-specific and reproducible step response to a step function, and wherein the reaction of the controlled variable (y) follows a manipulated variable (u) in a predictable manner, and wherein the Controlled variable (y) is recorded with a measuring element as the actual value (ym). The invention is characterized by evaluating the recorded actual value (ym) according to the following rules: a) if the recorded actual value (ym) is within a predetermined distance (s) as a threshold value from a setpoint (w), then there is no control intervention in the system, b) if the recorded actual value (ym) lies outside a previously determined distance (s) as a threshold value from a setpoint (w), then a control intervention is carried out Setting a manipulated variable us, whereby the amplitude of the manipulated variable (us) as continuous compensation for the external disturbance (d) acting on the controlled system is proportional to the distance of the recorded actual value (ym) to the threshold value, whereby this exceedance is determined by a computational simulation previous control interventions in the system-specific step response are taken into account.

Description

The invention relates to a method for controlling a controlled variable of a system, wherein the system shows a system-specific and reproducible step response to a step function, and wherein the reaction of the controlled variable follows a manipulated variable in a predictable manner, and wherein the controlled variable is recorded as an actual value using a measuring element.

To control physical systems, so-called PID controllers are usually used, which derive a control strategy from various actual value data of the system recorded from a series of measured values in order to constantly regulate the system to be controlled using a manipulated variable. PID controllers as such have proven themselves in practice and the mathematical description of a PID controller, which can be mathematically described by a transfer function as a differential equation, is well understood. The disadvantage of known PID controllers is, on the one hand, that the strategy for manually setting control parameters for the proportional element, for the integral element and for the differential element is not very simple and not intuitively obvious. As a result, many PID controllers regulate with control parameters set far from the ideal state. Even a computer-aided setting of a PID controller often does not lead to the ideal state of the entire control loop, since the system parameters, such as the system-specific step response (e.g. time course of an actual variable) of the system in response to a sudden change in the manipulated variable, are not involved in determining the ideal control parameters or, if they do occur, they can only be determined empirically in the control loop. On the other hand, it is known that the ideal state of the parameterization of a PID controller is close to a parameterization that tends to oscillate. A controller set (parameterized) in this way can be disturbed by external influences, so that the system to be controlled together with its step response behavior and the initially ideally parameterized controller form an oscillating circuit. As a result, the controlled variable varies over time around a center point. Depending on the type of system to be controlled, this residual oscillation can be ignored because it is subcritical. An example of this would be temperature control for a swimming pool. The swimming pool as a system to be controlled has a long follow-up time when regulating the temperature, the step response is very flat, but the variation in temperature of less than 1°C is insignificant. If the temperature oscillates with this small amplitude, it is irrelevant. Other systems that have a rather shorter follow-up time and must be set precisely can be operating parameters for an internal combustion engine or correction parameters for additional magnetic field stabilization in a magnetically shielded room. The correction of the magnetic field by a current in a coil has a short follow-up time and even the smallest variations in the magnetic field strength in the magnetically shielded room can have a significant influence on the results of the experiments carried out in the magnetically calmed room. Examples of this are studies on living bodies or basic physics experiments. The extremely sensitive and low-noise SQUID magnetic field detectors (SQUID; super conducting quantum interference device) and OPMs (OPM; optically pumped magnetometer) used in such experiments require that regulation of the local magnetic field in the laboratory arrangement should be so constant that Noise on the actual value, caused by different sources in the control loop, is not negligible. If a conventional PID controller were used here to constantly regulate the magnetic field of the laboratory arrangement, the PID controller parameterized ideally and close to the oscillation state, together with the system to be controlled, would be stimulated to oscillate by the noise of the recorded actual value. It is therefore desirable to have a control method or a controller that does not tend to oscillate, but still regulates very precisely.

The object of the invention is therefore to provide a method for controlling a system and a corresponding controller which regulates very precisely without any tendency to oscillate.

The object according to the invention is solved by a method with the method features according to claim 1. Further advantageous embodiments of the method are specified in the subclaims to claim 1. A corresponding controller is specified in claims 10 and 11.

According to the idea of the invention, it is provided that the step response of the system to be controlled, such as the change in a physical parameter in response to a control intervention in the form of a step function of a manipulated variable, is anticipated. The control algorithm therefore provides for the control intervention to be simulated in terms of time and calculation, taking into account the actual step response behavior of the entire system. A control intervention only takes place if a recorded actual value lies outside a threshold value interval. The threshold value interval is centered around the setpoint or reference variable. The threshold value interval is formed by an upper and lower threshold with a distance from the setpoint value called the threshold value. The threshold value interval prevents intervention in the system if no intervention is necessary. This is the case when the noise on the Changes caused by the actual value are not significant and/or the change is so small that it cannot be compensated for with sufficiently small steps due to the hardware structure of the system. If the actual value leaves the threshold value interval, the significant change in the system can be predictably compensated for using a step response function based on knowledge of the final system change. Due to the time course of the system's step response behavior, when determining whether there is a further significant correctable external change in the system state, all compensations previously triggered by the control and not yet completed must be taken into account when deciding whether to intervene again. This can be done in different ways. One possibility is to adapt the actual value measured by the measuring element; another equivalent embodiment is to define the threshold value range consisting of a constant component and a dynamic component, depending on the previous system interventions. By means of quick, periodic queries to check whether the threshold value has been exceeded, significant external disturbances are continuously compensated for in minimal steps after they occur. The controlled variable is thereby kept within the dynamic threshold value with only minor exceedances. If the hardware is viewed as given, the smallest standard deviation of the controlled variable for the existing hardware is achieved by a minimum, and therefore optimal, constant threshold value for this hardware version. Its size results from the requirement to minimize the statistically occurring system interventions caused by noise and the requirement that the smallest possible system change does not lead to the opposite threshold being exceeded. If the smallest possible system state change is not negligible compared to the noise, it is advantageous to round the manipulated variable change proportional to the threshold value exceedance to the next highest integer multiple of the smallest possible system state change in order to respond to even the smallest significant system changes.

Because the time delay of the system response to all compensations made is taken into account when querying whether the threshold value is exceeded, the controlled system is not fed back in the classic sense of control technology and is therefore not prone to control oscillations. Due to the quick periodic query after a threshold value has been exceeded, the manipulated variable changes caused by the controller are correspondingly small. If a large change in the manipulated variable occurs suddenly, this is a measured value outlier. In order to reduce the effects of outliers, the system intervention can be limited by introducing a maximum permitted actuator change. If it is a one-time outlier, the maximum permitted and executed actuator change is reversed at the next query time. If the outlier is a step-shaped change, e.g. due to a spontaneous change in the electrical contact resistances in the control loop, the setpoint is approached with a ramp whose slope results from the ratio of the maximum control value change to the query time interval. Possible overshoots after the ramp or switching up and down in the event of a single outlier are a result of the system response and do not build up to a control oscillation.

All parameters for determining the constant threshold value, all properties of the system required by the controller to calculate the compensation for recognized significant correctable system changes caused by external disturbances on the system and the prediction of the system reaction to a control intervention that has taken place can be determined on the uncontrolled system.

The constant portion of the threshold value is calculated from the noise on the actual value and the smallest possible control intervention in the system. Both can be determined by measurements on the uncontrolled system. For this purpose, the system response function is measured for small steps (in the order of magnitude of the threshold value or the smallest possible control intervention). The determination is possible on an uncontrolled system by periodically switching the manipulated variable back and forth on the actuator (triggered signal). By averaging, taking the sign of the steps into account, the step response function for the smallest steps can be determined with appropriate precision, regardless of the course of the external disturbances affecting the system during the measurement. The asymptotic limit value of the step response function is used to calculate the change to be set at the actuator in order to compensate for the actual value change above the threshold value observed in the last query period.

The standard deviation of the noise can be determined from the signal amplitude in the frequency spectrum above the highest interference frequency that still needs to be adjusted or by determining the signal amplitude of the high-pass filtered actual value of the uncontrolled system with a corner frequency corresponding to the highest frequency of the external interference that still needs to be adjusted.

If the time intervals between the threshold value violation queries are short, the manipulated variable changes caused by the controller are correspondingly small. It is possible to measure the actual value via a low-pass filter in the signal path of the measuring element as an electronic filter and/or in the way of recording the actual value as a digital filter in order to reduce the increase in noise on the actual value caused by a high bandwidth. It is also possible to record the actual value via one or more bandpass filters in the signal path of the measuring element as an electronic filter and/or in the way of recording the actual value as a digital filter in order to suppress frequencies and frequency ranges that should not be subject to regulation in the actual value.

• 1 eine Skizze zur Verdeutlichung einer Sprungfunktion und einer Sprungantwort,
• 2 eine Skizze zur Verdeutlichung der Messung eines verrauschten Istwertes auf einer Sprungantwortfunktion,
• 3 eine Skizze zur Verdeutlichung des Zusammenhangs einer Gaußverteilung und dem Rauschen eines Signales,
• 4 eine Skizze zur Verdeutlichung, dass eine kleine zeitlich begrenzte Störgröße n(t) durch eine dynamische Schwelle auf einer Sprungantwortfunktion erkannt wird.
• 5 eine Skizze zur Verdeutlichung der Regelstrategie,
• 6 ein Flussdiagramm zur Verdeutlichung der Funktion des erfindungsgemäßen Verfahrens zur Regelung in Ausführungsform „angepasster Istwert“,
• 7 ein Flussdiagramm zur Verdeutlichung der Funktion des erfindungsgemäßen Verfahrens zur Regelung in Ausführungsform „dynamischer Schwellwert“.

The invention is explained in more detail using the following figures. It shows:

• 1 a sketch to illustrate a step function and a step response,
• 2 a sketch to illustrate the measurement of a noisy actual value on a step response function,
• 3 a sketch to illustrate the connection between a Gaussian distribution and the noise of a signal,
• 4 a sketch to illustrate that a small, time-limited disturbance n(t) is detected by a dynamic threshold on a step response function.
• 5 a sketch to clarify the control strategy,
• 6 a flowchart to illustrate the function of the method according to the invention for control in the “adapted actual value” embodiment,
• 7 a flowchart to illustrate the function of the method according to the invention for control in the “dynamic threshold” embodiment.

In 1 The connection between a step function and various possible step responses y ₁ (t), y ₂ (t), y ₃ (t), y ₄ (t) and y ₅ (t) of any system is shown. The step function us(t) can be the switching on of an actuator by an actuating signal u(t), such as a heater for a system to be heated or adjusting a current through a coil to compensate for a change in the magnetic field. The jump function us(t) is assumed to be instantaneous, i.e. like a real step function. A system reacts to this step function with a slightly delayed step response y(t). An example of this: When a heating element is energized, it gradually heats up and releases its own heat to a heat reservoir that needs to be regulated. It takes time for the heater and reservoir to reach equilibrium. The temperature of the heat reservoir asymptotically approaches a new final temperature. Depending on the power of the heater and the size of the reservoir, the entire system can follow more quickly, for example y ₁ (t) or follow more slowly, for example y ₂ (t) or y ₃ (t).

There are also systems that quickly follow the step function us(t) and even tend to overshoot, for example y ₄ (t) and y ₅ (t). The type of expression of the step response y(t) has a strong influence on the control behavior and thus on the achievable stability of the controlled variable y(t).

In 2 is a sketch to illustrate the measurement of a noisy actual value y _m (t). The actual value y _m (t), namely the value of the step response y(t) at a defined time t after the edge of a step function at time t ₀ , is further superimposed with a noise signal n(t). The noise is defined here by a function n(t) and is independent of the level of the step function. The measurement signal y _m (t) of the actual actual value y(t) is determined by superimposition with the noise signal n(t), so that the measured value y _m (t) at time t is still y(t) + n(t) amounts. The noise interval, which is centered around the actual actual value y(t), is described here by a dynamic upper and lower threshold value depending on the standard deviation of the noise σ _n . If the smallest possible system change is negligible compared to the noise, this dynamic threshold range can be used to make a decision about a control intervention. In practice and from theoretical considerations it has been shown that the optimal minimum constant threshold value component (without the dynamics due to the step response) for the upper and lower thresholds is s _const = k _n . σ _n + LSS/2 with LSS (lowest step size) as the lowest possible value of the step function, and with k _n = 3 is to be set. The choice of k _n = 3 means that if there is approximately white noise, a system intervention is decided in 0.3% of cases if there is no external disturbance. This is a compromise because a higher k _n degrades the accuracy of the controlled variable, while a smaller k _n varies the controlled variable unnecessarily due to the more frequent statistical system interventions with different signs.

In 3 It shows what relationship exists in the case of approximately white noise between a noise signal n(t) and a Gaussian distribution G, or normal distribution. The Gaussian distribution G, a bell curve, describes a binomial distribution. A binomial distribution is a probability, expressed by p, that this value will be taken. The probability p for the mean in the center of the bell curve G is the highest. The probability p decreases with distance from the mean. For a noise signal n(t), centered around a value y(t), shown here vertically, there are approximately ⅔ of all values ever measured are within the limits of the standard deviation σ _n . For 3·σ _n, 99.7% of all values are within the limits.

In 4 is shown what a signal curve in a controller could look like when adjusting from far outside the adjusted state. A time-dependent actual value y(t) as a controlled variable is superimposed on a noise signal n(t) and cannot be separated from it and is measured by the measuring element as y _m (t). The control strategy in this example specifies that the interval s _const around y _m (t) should be ±3·σ _n , in which the controller will not make any further control intervention. LSS (lowest step size) is assumed to be negligible compared to σ _n . The course of y(t) shown here is the expected course of the actual value y(t) as a controlled variable as a step response to a previous step function u _s (t). A “dent” in the actual value curve for y(t) can be seen approximately in the middle. This dent can be described by y(t) + d(t), with d(t) as the disturbance at time t. Because the disturbance d(t) is added to the actual signal y(t) as a controlled variable, the noise signal n(t) also shifts. At some points it falls below the limits of the expected actual signal as a controlled variable y(t) - s _const . These could be outliers or an actual trend. The trend can be recognized more reliably by forming a moving average, but forming a moving average leads to an additional time delay. If you react immediately to any exceeding of the predetermined limits without averaging, this minimizes the time delay and thus also the deviations that occur between the controlled variable and the setpoint.

In 5 is shown what a signal curve y(t) with a small external disturbance d(t) in the middle of the figure could look like. At the beginning of the time interval shown, the actual value y(t) as a controlled variable is equal to the setpoint w. A noise signal n(t) is superimposed on the actual value and cannot be separated from it. The dashed lines mark the area between the upper threshold w+s _const and lower threshold ws _onst , here corresponding to 3σ _n of the noise signal n(t) with negligible LSS compared to σ _n . If the measured actual value y _m (t) is the sum of the actual actual value y(t) plus the noise signal n(t) in this interval, the controller will not carry out any control intervention. Approximately in the middle of the curve of y(t) a “dent” can be seen in the actual value curve y(t). This dent can be described by y(t) + d(t). The sum signal y _m (t) = y(t) + d(t) + n(t) falls below the lower constant threshold ws _const at some points. Individual measuring points that fall below the threshold could be static exceedances due to noise or an actual trend. The trend can be recognized more reliably by forming a moving average, but forming a moving average leads to a tracking error. It is also possible to react to each individual value and thus react more quickly to the disruption. The system interventions due to statistical noise-related threshold values being exceeded are averaged out. Due to their statistical nature, they do not lead to an escalating control oscillation. By reacting early to a significant change in the controlled variable, a temporal constancy of the actual value y _m (t) can be achieved with the control switched on, i.e. the standard deviation of the actual value y _m (t), close to the standard deviation of the noise σ _n , which is achieved with a classic PID is not reachable.

In 6 a diagram of a control loop in the embodiment of the “adjusted actual value” control method is shown. The control loop includes the controlled system, which is influenced by a disturbance variable d(t). The controlled variable y(t) to be kept at the setpoint w by the control is detected by a measuring element (detector) and fed to the controller as the actual value y _m (t). The actual value y _m (t) is subject, among other things, to uncertainty due to a noise signal n(t) with the standard deviation σ _n . In this embodiment of the control method according to the invention, the recorded actual value y _m (t) is adjusted by the compensation delay C _comp (t), which takes into account the outstanding actual value changes due to previous compensation processes based on the expected system responses calculated by the control algorithm. If the actual value y _m (t) falls below or exceeds a constant threshold value s _const after adjustment by C _comp (t), a change in the manipulated variable is carried out.

The change in the manipulated variable is effected by the controller via an actuator, whereby the actuator has a direct effect on the controlled variable of the controlled system. Within the controller surrounded by dashed lines there is a previously determined parameterization of a measured controlled system response. This parameterization, which contains the asymptotically approximated value for t=∞, influences the calculated change in the manipulated variable to compensate for the significant and correctable exceedance of the manipulated values that has occurred. The parameterized time course of the controlled system response and the stored history of control interventions that have taken place are used to calculate C _comp (t) to adapt the actual value to control interventions that have already taken place.

The constant threshold s _const must be a compromise between two opposing requirements be determined. A small value reduces the standard deviation of the controlled variable y(t), while a value that is too small increases the number of control interventions caused by the noise n(t) on the actual value y _m (t). If the standard deviation σ _n of the noise is negligible compared to the smallest possible value for a change in the system state LSS, s _const must not be less than the value of LSSj2. A general good compromise for choosing s _const is s _const = k _{n *} σ _n + LSS/2 with k _n =3. For this value of k _n , with approximately white noise, in 0.3% of all queries after the threshold value has been exceeded, a control value change caused by the noise occurs, regardless of the size of C _comp (t).

In 7 a diagram of a control loop of the “dynamic threshold” embodiment is shown. The control loop includes the controlled system, which is influenced by a disturbance variable d(t). The controlled variable y(t) to be kept at the setpoint w by the control is detected by a measuring element (detector) and fed to the controller as the actual value y _m (t). The actual value y _m (t) is subject, among other things, to uncertainty due to a noise signal n(t) with the standard deviation σ _n . In this embodiment of the control method according to the invention, the recorded actual value y _m (t) is compared with a dynamic threshold value s (t). The dynamic threshold value s(t) consists additively of a constant component s _const and a dynamic component C _comp (t). The dynamic component C _comp (t) is calculated from changes in the controlled variable that have not yet been made due to previous compensation processes based on the expected system response calculated by the control algorithm. If the actual value y _m (t) falls below or exceeds the dynamic threshold value s(t), a change in the manipulated variable is carried out.

The constant threshold s _const must be set as a compromise between two opposing requirements. A small value reduces the standard deviation of the controlled variable y(t), while a value that is too small increases the number of control interventions caused by the noise n(t) on the actual value y _m (t). If the standard deviation σ _n of the noise is negligible compared to the smallest possible value for a change in the system state LSS, s _const must not be less than the value of LSSj2. A general good compromise for choosing s _const is s _const = k _{n *} σ _n + LSS/2 with k _n =3. For this value of k _n , with approximately white noise, in 0.3% of all queries after the threshold value has been exceeded, a control value change caused by the noise occurs, regardless of the size of C _comp (t).

REFERENCE SYMBOL LIST

Ccomp(t)

Compensation delay

d(t)

Disturbance variable

G

Gaussian distribution

p

probability

kn

integer

LSS

smallest possible system state change

n(t)

Rush

sconst

constant threshold

s(t)

dynamic threshold

σn

Standard deviation

t

Time

u(t)

Control signal

us(t)

manipulated variable

umax

maximum manipulated variable

w

Setpoint

y(t)

controlled variable

ym(t)

actual value

Claims (11)

Method for controlling a controlled variable (y) of a system, - where the system shows a system-specific and reproducible step response to a step function, and - where the reaction of the controlled variable (y) follows a manipulated variable (u) in a predictable manner, and - where the controlled variable (y) is recorded with a measuring element as the actual value (y _m ), characterized by evaluating the recorded actual value (y _m ) according to the following rules: a) if the recorded actual value (y _m ) is within a predetermined distance (s) as a threshold value of a setpoint (w), then there is no control intervention in the system, b) if the recorded actual value (y _m ) lies outside a previously determined distance (s) as a threshold value from a setpoint (w), then a control intervention is carried out Setting a manipulated variable (u _s ), whereby the amplitude of the manipulated variable as continuous compensation for the external disturbance (d) acting on the controlled system is proportional to the distance of the recorded actual value (y _m ) to the threshold value, whereby previous control interventions are determined when this exceedance is determined be taken into account by a computational simulation of the system-specific step response. Procedure according to one of the Claims 1 , characterized by the omission of taking into account the step response of previous controlled variable interventions, since the control is only intended to compensate for slow external disturbances compared to the query intervals and the expected manipulated value response after a control intervention in the system during a query interval has already occurred with sufficient accuracy. Procedure according to one of the Claims 1 , characterized by reducing the effects of outliers by introducing a maximum permitted actuator change (u _max ). Procedure according to one of the Claims 1 , characterized by forming a constant threshold value s _const derived from the noise (n(t)) around the actual value (y), whereby in the case of approximately white noise, this threshold value is formed by a standard deviation σ _n multiplied by a constant factor k _n , and where the standard deviation is determined by determining the signal amplitude from the frequency spectrum of the actual value (y _m ) of the controlled variable (y) above the highest frequency of the external disturbance that still needs to be controlled. Procedure according to Claim 4 , characterized by forming a constant threshold value (s _const ) by additionally adding a constant, preferably according to the following scheme $$s_{cOnst}=k_n\ast {\sigma }_n+LSS/2$$

with LSS (lowest step size), the lowest possible value for a change in the system state, which is determined by an element of the system to be controlled. Procedure according to Claim 5 , characterized by rounding the manipulated variable (u) to the next highest integer multiple of LSS, so that in particular the smallest possible system change is effected when the threshold values are exceeded, which are smaller than LSS. Procedure according to one of the Claims 1 until 6 , characterized by forming a moving average of the recorded actual values (y _m ) to identify an actual value trend Procedure according to one of the Claims 1 until 7 , characterized by detecting the actual value (y _m ) via a low-pass filter in the signal path of the measuring element, the low-pass filter being an electronic filter and/or a digital filter. Procedure according to one of the Claims 1 until 7 , characterized by detecting the actual value (y _m ) via one or more bandpass filters in the signal path of the measuring element, the bandpass filter being an electronic filter and/or a digital filter. Controller for controlling a controlled variable of a system, comprising - at least one actuator, at least one measuring element and - a controller unit for controlling the actuator depending on an actual value (y _m ) of the system to be controlled recorded by the measuring element, characterized in that the controller unit detects the Actual values (y _m ) are evaluated according to the following rules for controlling the at least one actuator: a) if the recorded actual value (y _m ) is within a predetermined distance (s) as a threshold value from a setpoint (w), then a control intervention is made in the system waives b) if the recorded actual value (y _m ) lies outside a predetermined distance (s) as a threshold value from a setpoint (w), then a control intervention is effected by setting a manipulated variable (u _s ), whereby the amplitude of the The manipulated variable as continuous compensation for the external disturbance (d) acting on the controlled system is proportional to the distance between the recorded actual value (y _m ) and the threshold value, with previous control interventions being taken into account by a computational simulation of the system-specific step response when determining this exceedance. regulator Claim 10 , characterized in that a low-pass filter and/or one or more band-pass filters are arranged in the signal path of the measuring element in order to suppress frequencies and frequency ranges that should not be subject to regulation in the actual value (y).

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