Abstract:
In a method for regulating an excited oscillation of a system to a resonance case of the system, instantaneous values of the oscillating quantity are discretely recorded using one sampling frequency, and the sampling frequency is selected to be below twice a maximum frequency of the system. In addition, the following steps are provided: ascertaining an oscillation amplitude from the instantaneous values; regulating a control amplitude on the basis of the ascertained oscillation amplitude; specifying a control frequency on the basis of the control amplitude; generating a control oscillation in consideration of the control frequency; combining the oscillation amplitude and the control oscillation to form a control signal; and exciting the system in consideration of the control signal.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to a method for regulating an excited oscillation of a system to a resonance case of the system. 
         [0003]    2. Description of Related Art 
         [0004]    To excite oscillatory systems and to regulate them to a resonance case of the system, it is necessary to record the excited oscillations of the system. If digital techniques are used for this purpose, the oscillations are sampled in a discrete process. In order to counteract errors made during sampling, a sampling frequency is used that is substantially greater than the maximum frequency, in particular, greater than double the maximum frequency of the excited system. This approach is considered to be an application of the Nyquist theorem. It prevents oscillations from being sampled too slowly, whereby an effect can occur, which, when evaluated, suggests that an oscillation having a substantially lower frequency has been recorded, although this is not the case. This is generally referred to as aliasing. In particular, it is not possible in such cases to ascertain the actual frequency and phase relation of the sampled oscillation. The inherent drawback is that a constantly very high sampling frequency must be used, thereby resulting in substantial computational outlay for a recording device that is used. This substantial computational outlay is reflected in a high demand for chip surface area when the recording device is realized as an integrated circuit, and in a substantial power consumption. 
         [0005]    Regulating systems which employ the method can be used, in particular, for systems such as ESP (electronic stability program), ROM (roll-over mitigation), EAS (electronic active steering), ASC (active suspension control), SbW (steer by wire) and other vehicle stability applications. This is due to the fact that what are generally referred to as inertia sensors are used as rotation-rate sensors. These typically have at least one part, a component, that is set into oscillation in response to excitation and that produces a Coriolis effect in response to a rotation of the sensor. This allows a relative movement to be measured between the oscillating portion and the remaining rotation-rate sensor. Other fields of applications of such sensors include NC applications, such as navigation, man-machine interfaces, game consoles, and sport and medical fields. These sensors must meet stringent requirements, in particular, in terms of a substantial computing capacity, a high level of stability, a minimal chip surface area and a low power consumption. 
         [0006]    There is a need for a method which will reduce the computational outlay required for such a device and, in particular, thereby minimize the demand for chip surface area and reduce power consumption as well. 
       BRIEF SUMMARY OF THE INVENTION 
       [0007]    The present invention provides a method for regulating an excited oscillation of a system to a resonance case of the system, instantaneous values of the oscillating quantity being discretely recorded using one sampling frequency, and the sampling frequency being selected to be below twice a maximum frequency of the system, including the following steps: Ascertaining an oscillation amplitude from the instantaneous values, regulating a control amplitude on the basis of the ascertained oscillation amplitude, specifying a control frequency on the basis of the control amplitude, generating a control oscillation in consideration of the control frequency, combining the oscillation amplitude and the control oscillation to form a control signal, and exciting the system in consideration of the control signal. By employing the described method, the sampling frequency may be kept below twice the maximum frequency of the system, thereby making it possible to save a great deal of computing capacity since it will merely be necessary to record the oscillation amplitude. Given a realization as an integrated circuit, it is possible in this manner to economize on chip surface area and to minimize the power requirement of such a device. In spite of violating the Nyquist theorem, the functionality of the system is ensured by such a regulation as is applied by the method. In particular, it is provided for a digital sampling to be carried out. It is especially advantageous that the method regulate a frequency and a phase relation of the control signal. Thus, in the context of the method, two initially separate control paths are derived, which are merged. On the one hand, the control amplitude is regulated on the basis of the ascertained oscillation amplitude and, on the other hand, the control oscillation, preferably a normalized control oscillation, is regulated in the frequency, as well as in the phase relation thereof by the control amplitude. The combination of the control amplitude and the control oscillation yields the control signal which is used for exciting the system. This method is based on the requirement that the system be operated in its resonance case and that, in the resonance case, the control amplitude assume a specific, preferably known, value. Thus, the method according to the present invention concerns a resonance control which uses an amplitude control to monitor the control frequency and, in this manner, regulates the control oscillation, so that the entire control loop and thus the oscillating system are in the resonance case. 
         [0008]    Another refinement of the present invention provides for a spring-mass system to be used as a system. A spring-mass system has the advantage that its system response to an excitation is known and is able to be readily calculated. In addition, the quantities required for a calculation are able to be easily determined from the spring-mass system and measured. 
         [0009]    One refinement of the present invention provides for at least one component of an inertia sensor, in particular of a rotation-rate sensor, to be used as a system. A rotation-rate sensor typically has at least one component that is set into oscillation. In response to a rotation of the entire rotation-rate sensor, a Coriolis force acts on this component, whereby a relative rotational movement is induced between the component and the remaining rotation-rate sensor. Using a suitable sensor system, such as a capacitive and/or piezoelectric sensor system, for example, this rotational movement may be recorded and properly evaluated. Using this sensor system, the excited oscillation of the component of the rotation-rate sensor may likewise be measured and recorded in the form of instantaneous values. Since the components within rotation-rate sensors oscillate at a very high frequency, even a small reduction in the required sampling frequency results in a substantial improvement in computational outlay and in the power consumption needed for regulating the excited oscillation of the component of the rotation-rate sensor. Particularly when working with multiaxial sensor cores, thus rotation-rate sensors, which have a plurality of components oscillating in the direction of a plurality of spatial axes, the computational outlay is reduced by a multiplex operation. It is particularly advantageous to sample the instantaneous values using a capacitive micromechanical sensor system, since these types of sensors are already known and are frequently used. Thus, the already existing advantages of such a sensor system may be combined with the advantages of the method according to the present invention. Particularly in connection with rotation-rate sensors, a significant reduction in the power requirement is achieved in evaluation units, such as AsiCs, for example, of drive and detection circuits, for exciting the oscillation. In this context, the multiplex operation relates, in particular, to the use of a converter stage for a plurality of sensor axes. Moreover, better conditions are obtained for a multiplex operation of the converter stage for a plurality of sensor axes, such as, for example, larger time windows for switching operations due to the reduced sampling frequency. In addition, by regulating to the resonance case, it is ensured that the system is always operated at an energetic optimum, resulting in a high- or low-grade system. 
         [0010]    To ascertain the oscillation amplitude on the basis of the instantaneous values, another refinement of the present invention provides for a sinusoidal characteristic to be calculated for the instantaneous oscillation and for the amplitude of the sinusoidal characteristic to be used as the oscillation amplitude. In particular, to calculate the sinusoidal characteristic, it is provided in this case to interpolate between the instantaneous values. 
         [0011]    One refinement of the present invention provides for the control frequency to be regulated using the control amplitude as a regulating variable. The control amplitude is already known from the regulation of the control amplitude, which is why it is beneficial and simplifying to continue to use this value. The relationship between the control amplitude and the control frequency is derived from the need to regulate the system to a resonance case. 
         [0012]    Another refinement of the present invention provides for an extreme value of the control amplitude to be used as a setpoint value for the control amplitude. This extreme value may be ascertained in the preliminary stages by analysis and/or from measurements of the system behavior which indicate different control amplitudes. By specifying the resonance case, an extreme value is made available for the control amplitude that may be used as a setpoint value. The inference may also be made that when the control amplitude assumes the extreme value, the system is in the resonance case. 
         [0013]    Another refinement of the present invention provides that a minimum possible value of the control amplitude, which is required to maintain the oscillation of the system in the resonance case, be used as an extreme value. 
         [0014]    Yet another refinement of the present invention provides that a characteristic curve and/or a characteristic map be used to regulate the control amplitude to the extreme value. The use of a characteristic curve and/or of a characteristic map makes it possible to consider both linear, as well as non-linear behaviors of the system. In addition, desired regulation characteristics, such as transient reactions, may be specified in the preliminary stages. 
         [0015]    One refinement of the present invention provides that the characteristic curve assign a change in the control amplitude over time to a change in the control frequency over time. This presupposes that a relationship between the control amplitude and the control frequency is known. This relationship may be measured in the preliminary stages or be analytically determined and stored in the characteristic curve so that a recorded change in the control amplitude is readily assignable to a change in the control frequency. 
         [0016]    One refinement of the present invention provides that the characteristic map of the change in the control amplitude over time and a change in the frequency of the control oscillation over time be assigned to a change in the control frequency over time. The characteristic map has the same advantages as the characteristic curve. It is also advantageously possible that an inference regarding the control oscillation be included in the control. Thus, an additional variable is included that enhances the control accuracy of the method. 
         [0017]    Another refinement of the present invention provides that a sinusoidal oscillation or a square-wave oscillation be used as a control oscillation. The square-wave oscillation may be produced in a simple manner, for example, by switching an electrical voltage on and off. 
         [0018]    In accordance with another refinement of the present invention, a switch-on and/or switch-off control is provided that is only implemented by the method as needed. The advantage of this switch-on and/or switch-off control is that the power consumption may be additionally reduced, for example, in that a device for implementing the method is only used when it is needed. 
         [0019]    The present invention also provides a device for regulating an excited oscillation of a system to a resonance case of the system, in particular, for implementing the method described above, having a sampling device having a sampling frequency for recording instantaneous values of the oscillation, the sampling frequency being below twice a maximum frequency of the system; having an oscillation-amplitude sensing device which ascertains an oscillation amplitude from the instantaneous values; a control-amplitude regulating device, which regulates the control amplitude on the basis of the oscillation amplitude; a control-frequency regulating device which regulates a control frequency of a control oscillation on the basis of the control amplitude; an oscillator, which generates the control oscillation on the basis of the control frequency; a combining device, which generates a control signal from the control amplitude and the control frequency; and an actuator which excites the system in consideration of the control signal. 
         [0020]    Another refinement of the device provides that the system be an oscillating element, in particular, an oscillating frame of an inertia sensor, in particular of a rotation-rate sensor. 
         [0021]    Another refinement of the present invention provides that the actuator be a comb drive. Electrostatic comb drives are classified under micromechanics. The principle of operation thereof is based on an action of force that is generated between two plate elements having different electrical charges. 
     
    
     
       BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWING 
         [0022]      FIG. 1  shows a rotation-rate sensor having a device for regulating an excited oscillation. 
           [0023]      FIG. 2  shows an equivalent circuit diagram of the rotation-rate sensor having a device for regulating the excited oscillation. 
           [0024]      FIG. 3  shows a diagram including the excited oscillation, as well as instantaneous values and a sinusoidal characteristic. 
           [0025]      FIG. 4  shows the device for regulating the excited oscillation in a schematic representation. 
           [0026]      FIG. 5  shows a control-frequency regulating device in a schematic representation. 
           [0027]      FIG. 6  shows diagrams illustrating the response characteristic of the rotation-rate sensor, as well as a frequency response characteristic of the control amplitude. 
           [0028]      FIG. 7  shows a diagram illustrating the characteristics of the manipulated variable over the frequency. 
           [0029]      FIG. 8  shows a characteristic map. 
           [0030]      FIG. 9  shows a diagram illustrating an output signal of a decoder. 
           [0031]      FIG. 10  shows a transfer function of the rotation-rate sensor. 
           [0032]      FIG. 11  shows simulation results without the adaptation of a phase-change increment having a small absolute value. 
           [0033]      FIG. 12  shows simulation results without the adaptation of the phase-change increment having a large absolute value. 
           [0034]      FIG. 13  shows simulation results including adaptation of the phase-change increment between the large and small absolute value. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0035]      FIG. 1  shows a system  1  that is regulated by a control and measuring device  2 . System  1  is designed as a spring-mass system  3  in the form of an inertia sensor  4 . Inertia sensor  4  is a rotation-rate sensor which, in response to a rotation, outputs a measurement signal which indicates the rate of rotation. For this purpose, inertia sensor  4  has two sensor modules  6  which have a similar design and are coupled to one another via a spring  7 . Rotation-rate sensor  5  is rotated in the direction of an arrow  8 , for example, to produce the measurement signal. Each of sensor modules  6  has an oscillating element  9  in the form of an oscillating frame  10 . For the time segment needed to generate the measurement signal, oscillating element  9  may be excited to oscillate by actuators  11  in the form of comb drives  12 . The excitation is carried out alternately in the directions of arrows  13  and  14 . Displaceably configured in the direction of arrows  17  within oscillating elements  9  are detection elements  15  that interact with a capacitance-voltage transducer (not shown in  FIG. 1 ). Control and measuring device  2  is bidirectionally connected via a signal path  16  to inertia sensor  4 . 
         [0036]    In response to a rotation of inertia sensor  4  excited by actuators  11 , detection elements  15  are each deflected in the direction of one of arrows  17 , thereby inducing capacitance-voltage transducer to generate the measurement signal and transmit the same via signal path  16  to control and measuring device  2 . The actual rotation rate of inertia sensor  4  may be ascertained on the basis of this measurement signal. Oscillating elements  9  are excited by a regulation carried out by control and measuring device  2 , which, via signal path  16 , on the one hand, transmits a control signal to actuators  11  and, on the other hand, receives a return signal describing a position of the oscillating frame from actuators  11 , which also render possible a sensing of the oscillation. Thus, described control and measuring device  2  assumes the task of controlling the oscillation of oscillating elements  9 , as well as of recording the measurement signal which indicates the rotation rate of inertia sensor  4 . It is also possible (not illustrated) for detection element  15  to be equipped with actuators allowing it to be set into oscillation, thereby making possible superpositions between the deflection resulting from rotation of inertia sensor  4  and a fundamental oscillation, for example. 
         [0037]      FIG. 2  shows a part-sectional view of rotation-rate sensor  5  of  FIG. 1  in a schematic representation. Oscillating element  9  and detection element  15  are combined in one mass element  17 .  FIG. 2  exemplarily shows the configuration of one of sensor modules  6 . Mass element  17  is connected via two spring elements  18  to reference bearings  19 . Thus, inertia sensor  4  measures the rotation rate of reference bearing  19  relative to its surroundings. Signal path  16  is shown in two parts in  FIG. 2 . It is composed of a drive path  20  and a detection path  21 , which are both linked to control and measuring device  2 . Drive path  20  has a signal path  22  for the control signal which leads to a converter  23  that actuates actuator  11 . Actuator  11  excites mass element  17  alternately in the directions of double arrow  24 . A measuring element  25  measures the resulting deflection of mass element  17  and transmits this signal via an amplifier  26  and a signal path  27  to control and measuring device  2 . Thus, drive path  20  forms a closed control loop that includes control and measuring device  2  and mass element  17 . Detection path  21  has a signal path  28  which leads to a converter  29 . Converter  29  transmits a control signal arriving via signal path  28  to an actuator  30  which is able to deflect mass element  17  alternately in the directions of a double arrow  31 . Signal path  28 , converter  29 , and actuator  30  are optional. A measuring element  31 ′ measures the deflections of mass element  17  that are either in response to actuator  30  and/or to a rotation of inertia sensor  4 . The measurement signal derived therefrom is transmitted via an amplifier  32  and another signal path  33  to device  2 . 
         [0038]      FIG. 3  shows a diagram  34  having an abscissa  35  to which time t is assigned and an ordinate  36  to which an excited oscillation  37  is assigned. Within diagram  34 , excited oscillation  37  is shown as a sinusoidal curve  37 ′ that corresponds to the signal of measuring element  25 . Situated above sinusoidal curve  37 ′ is a sinusoidal characteristic  38  which has a lower frequency than sinusoidal curve  37 ′. Sinusoidal curve  37 ′ represents the oscillation of system  1  of  FIGS. 1 and 2 . Sampling oscillation  37  at equally spaced time intervals using a sampling frequency yields instantaneous values  39 . The sampling frequency is lower than twice a maximum frequency of system  1 , so that it is not possible to fully record oscillation  37 , and sinusoidal characteristic  38  is assumed self-evidently from instantaneous values  39 . To complete sinusoidal characteristic  38 , the intermediate values, which reside between instantaneous values  39 , may be calculated by interpolation from instantaneous values  39 . Thus, the procedure for recording sinusoidal curve  37 ′ using the low sampling frequency leads to a loss of information on the phase relation and frequency of excited oscillation  37 . The information on oscillation amplitude  40  of sinusoidal curve  37  remains, which is also correctly recorded in the sampling process using a low sampling frequency and corresponds to an amplitude  40 ′ of sinusoidal characteristic  37 . To implement a regulation of system  1  including a recording of oscillating quantity in the form shown in  FIG. 3 , the method employed must consider the information on phase relation and frequency of oscillation  37  for other purposes. 
         [0039]      FIG. 4  illustrates a device  41  for controlling system  1  of  FIG. 1 . System  1  is schematically shown in  FIG. 4  on the basis of actuators  11  and measuring elements  25  that form a sampling device  25 ′. Device  41  has a digital region  42 , a transitional region  43 , as well as an analog region  44 . Starting out from system  1  and its measuring elements  25 , signal paths  45  and  46  extend to an analog measuring device  47 . Analog measuring device  47  records the signals produced by measuring elements  25  and converts them into values of the oscillating quantity. In the case of capacitive measuring elements  25 , this may be accomplished by a measuring device  47  in the form of a capacitance-voltage transducer  47 ′. Measuring device  47  transmits the processed signal via a signal path  48  to an analog-digital converter  49 . The analog-digital converter ascertains instantaneous values  39  from the signal and transmits these via a signal path  50  to a control-amplitude regulating unit  51 . Control-amplitude regulating unit  51  has an oscillation-amplitude sensing device  52 , which ascertains the active oscillation amplitude from instantaneous values  39  and transmits it to a control-amplitude regulating device  53 . The control amplitude ascertained by control-amplitude regulating device  53  is transmitted via a signal path  54  to a combining device  55 . In addition, control-amplitude regulating unit  51  transmits the active control amplitude via a signal path  56  to a control-frequency regulating device  57 , which, on the basis of the control amplitude, regulates a control frequency and specifies the same to an oscillator  59  via a signal path  58 . From the control frequency, oscillator  59  generates a normalized control oscillation, i.e., an oscillation having a normalized amplitude that oscillator  59  transmits via a signal path  60  to combining device  55 . The control oscillation is realized as sinusoidal oscillation. In combining device  55 , the control amplitude is multiplied by the control oscillation, thereby yielding the control signal which is directed via a signal path  61  to a digital-analog converter  62 . Digital-analog converter  62  generates an analog control signal that is transmitted via a signal path  63  to actuators  11  of system  1 . Thus, a control loop  64 , which allows system  1  to be regulated on the basis of recorded amplitude  40 ′, is closed. Systems  1 , which are illustrated in  FIGS. 1 and 2 , are provided as system  1 . In addition,  FIG. 4  shows a switch-on and/or switch-off control  65 , which, via signal lines  66  and  67 , is able to switch off measuring device  47 , as well as analog-digital converter  49  and digital-analog converter  62 . This is preferably carried out when system  1  is designed as rotation-rate sensor  4  and no measurement of the rotation rate is to take place. This makes it possible to save additional energy. It is conceivable that a switch-on and/or switch-off control  65  is able to switch other components on and/or off. It is also conceivable to only switch off measuring device  47  and analog-digital converter  49 . In this case, the digital control signal is generated with a fixed amplitude and a fixed frequency. 
         [0040]      FIG. 5  shows control-frequency regulating device  57  of  FIG. 4 , to which the active control amplitude is fed via signal path  56  and which outputs the control frequency via signal path  58 . Control-frequency regulating device  57  has a test signal generator  66  which transmits its test signal via a signal path  67  to an amplifier  68 . The test signal is preferably an oscillating signal, however, it may also be a question of a jump function or a pulse function. The test signal is preferably generated in normalized form and may be adjusted in its characteristic via amplifier  68 . The amplified test signal is transmitted via a signal path  69  to a summing device  70 . Summing device  70  again receives a phase-modulation signal from another signal path  71  that is added to the amplified test signal. From this, a modulated test signal is derived that is transmitted via a signal path  72  to an output unit  73 . Output device  73  transmits the modulated test signal as a control signal via a signal path  74  to signal path  58 . In addition, via a signal path  75 , output device  73  transmits the control frequency to a differentiator  76  which ascertains a change Δx in the control frequency and transmits the same via a signal path  77  to a decoder  78 . Signal path  56  transmits the active control amplitude to a signal path  79  that leads to an input device  80 . Starting out from input device  80 , the control amplitude is transmitted via a signal path  81  to a differentiator  82  which ascertains a change Δy in the control amplitude over time and transmits the same via a signal path  83  to decoder  78 . Decoder  78  contains a characteristic map  102 . A change in the control frequency over time is assigned by characteristic map  102  to changes Δx and Δy. This change in control frequency is transmitted via a signal path  83  to an integrator  84  which integrates the change in the control frequency over time and transmits the signal via a signal path  85  to an amplifier  86 . A phase-change increment may be adjusted in amplifier  86  by adapting the amplification factor of amplifier  86 . It is particularly advantageous when the phase-change increment is adaptively matched in amplifier  86 . Amplifier  86  is linked via signal path  71  to summing device  70  and thus delivers the phase-modulation signal. 
         [0041]    Control-frequency regulating device  57  makes it possible for the control frequency to be regulated on the basis of the control amplitude and for the information on phase relation and the frequency of oscillation  37  to be indirectly considered to implement the regulation of system  1 . This is possible under the condition that system  1  is to be regulated for its resonance case. Thus, for this control, the principle is derived that a test signal is transmitted by characteristic map  102  to entire control loop  64 , and the test signal is modulated in such a way that the control amplitude is minimized, thus that it assumes a minimum possible value. Therefore, the minimized control amplitude forms the setpoint value. This results from the response characteristic of system  1  since it is designed as spring-mass system  3  and thus exhibits PT 2  response which includes a resonance case. 
         [0042]      FIG. 6  shows a diagram  87  and a diagram  88 . Diagram  87  has an abscissa  89  to which the frequency is assigned. In addition, diagram  87  has an ordinate  90  which describes the response characteristic of system  1 . Diagram  88  likewise has an abscissa  92 , to which the frequency is assigned, and an ordinate  92  which describes the control signal of control-amplitude regulating device  53 . Within diagram  87 , a curve  93  is shown which illustrates the response characteristic of system  1  over the frequency. Curve  93  has a maximum 94 which describes the resonance case of system  1 . In diagram  88 , a curve  95 , shown as a dashed line, describes the characteristic of the control signal of control-amplitude regulating device  53  over the frequency. Curve  95  exhibits inverse properties relative to curve  94 , so that a minimum  97 , thus an extreme value, is formed for the resonance case of system  1 . Two straight lines  96  describe a range around minimum  97 , thereby specifying a possible setting range  98  for the control amplitude. To the extent possible, the control amplitude should reside within this setting range  98  since the resonance case of system  1  is completely or almost completely derived therefrom. Thus, by adjusting the control amplitude to within this setting range, the control-frequency regulating device is able to determine that the control frequency resides in the resonance case of system  1 , both in phase and frequency. Curves  93  and  95  of  FIG. 6  are illustrated qualitatively. 
         [0043]      FIG. 7  shows a detail of curve  95  from  FIG. 6  in setting range  98 . On curve  95 , an active control frequency is denoted by a point  99 , a control frequency following the active control frequency by point  100 , and an available, desired control frequency by point  101 . 
         [0044]      FIG. 8  shows a characteristic map  102  which specifies the change in the control frequency over time on the basis of changes Δx and Δy. 
         [0045]      FIG. 9  shows a diagram  103  having an abscissa  104  which is assigned to time t and an ordinate  105  which is assigned to the output signal of decoder  78 . Within diagram  103 ; a curve  106  is shown which is a square-wave curve  107  that oscillates. 
         [0046]    The case illustrated in  FIG. 9  for the values that are output from characteristic map  102  exists when the control frequency is to be retained in point  101 . The control frequency of points  99  and  100  must be alternately assumed, whereby the oscillation of curve  106  results. 
         [0047]      FIG. 10  shows a response characteristic of system  1  in a part-sectional view in a diagram  108 . Diagram  108  has an abscissa  109 , to which the frequency is assigned, and an ordinate  110  to which the oscillation amplitude is assigned. Within diagram  108 , a curve  111  is shown which describes the response characteristic of system  1 . Curve  111  has a minimum  112  which represents the lowest possible amplitude of the excited oscillation of system  1  and thus indicates the resonance case. 
         [0048]      FIG. 11  shows simulation results for control loop  64  illustrated in  FIG. 4 .  FIGS. 11 through 13  each have diagrams  113 ,  114 ,  115  and  116 . Diagrams  113 ,  114 ,  115  and  116  each have an abscissa  117  which is assigned to time t. Diagram  113  has an ordinate  118  which is assigned to the control frequency. Diagram  114  has an ordinate  119  to which the transfer function of system  1  is assigned. Diagram  115  has an ordinate  120  which is assigned to the output value of decoder  78 , and diagram  116  has an ordinate  121  which describes the value of the phase-change increment of amplifier  86  of  FIG. 5 . A curve  122  illustrating the characteristic of the control frequency over time is plotted in diagram  113 . A curve  123 , which illustrates a characteristic of the value that the transfer function assumes over time, is shown in diagram  114 . A curve  124 , which shows the characteristic of the output signal of decoder  78 , is shown in diagram  115 . In diagram  116 , a curve  125  is shown that describes the characteristic of the phase-change increment over time. 
         [0049]      FIG. 11  shows simulation results that arise for the case that phase-change increment constantly has a low value (0.01 Hz). In this case, the resonance frequency of system  1 , here 16 kHz, is completely reached. This occurs only very slowly due to the small phase-change increment. Curve  122  is ramp-shaped and ascends linearly. On the other hand, curve  123  descends gradually in a linear fashion, and curve  124  constantly has the value one since the frequency is to continuously rise. Curve  125  is likewise constant over the entire displayed time segment since it is a question of a constant phase-change step. A control is obtained that optimally achieves the resonant frequency. 
         [0050]      FIG. 12  shows all the features of  FIG. 11 .  FIGS. 12 and 11  differ in the shapes of curves  122 ,  123 ,  124  and  125 . For the simulation results of  FIG. 12 , control loop  64  is adjusted in such a way that the phase-change increment is substantially greater than in  FIG. 11 , in this case 0.3 Hz. From this, it follows that curve  122  ascends very quickly in a first time segment  126  up to resonant frequency and subsequently oscillates around the resonant frequency. For curve  123 , it follows in first time segment  126  that it drops very quickly to its minimum, in this case—0.5—and remains at this minimum. In time segment  126  at the front, curve  124  is initially constant and allows the control frequency to rise. 
         [0051]    Following time segment  126  at the front, thus, after reaching the resonant frequency, the output signal of decoder  87  begins to oscillate in order to adjust the resonant frequency. Curve  125  likewise has a constant progression, as in  FIG. 11 , however, in this case with a value of 0.3 Hz. 
         [0052]    Thus, a very rapid control is obtained, which has a frequency ripple component after reaching the resonant frequency. 
         [0053]      FIG. 13  shows simulation results for control loop  64  whose phase-change increment is adapted.  FIG. 13  shows all features of  FIG. 11 .  FIGS. 13 and 11  differ in the shapes of curves  122 ,  123 ,  124  and  125 . The characteristic of curve  122  shows a first time segment  127  in which the control frequency rises slowly. First time segment  127  is followed by a second time segment  128  in which the control frequency ascends quickly up to the resonant frequency. Once the resonant frequency is reached, a third time segment  129  follows in which curve  122 , thus the control frequency, exhibits a transient response, and the control frequency optimally reaches the resonant frequency. In first time segment  127 , curve  123  likewise has a constant progression and falls to its minimum within the second time segment. Within this minimum, curve  123  remains for the entire third time segment  129 . The progression of curve  124  in the first and second segment  127  and  128  is constant. This means it produces a rise in curve  122 , thus in the control frequency. In third time segment  129 , the resonant frequency is reached by the control frequency, and the output signal of the decoder begins to oscillate, thereby inducing an oscillation of curve  124 . In first time segment  127 , curve  125  exhibits a constant progression. In second time segment  128 , the value for the phase-change increment increases and is subsequently constantly maintained at a higher value. From this, the rise in curve  122  is derived in second time segment  128 . Once the resonant frequency is reached by the control frequency in third time segment  129 , this is recognized by the adaptation, and, within third time segment  129 , the phase-change increment is made smaller and remains constant for the remainder of the third time segment. 
         [0054]    Adapting the phase-change increment makes it possible to implement a very fast regulating device that produces an optimal control result. Only small phase shifts occur when this regulation is used.