Abstract:
Methods and systems, utilizing simplified digital hardware, for measuring parameters needed for control of a system (referred to as a plant) such as a power supply or motor. In one embodiment, the system for measuring the desired parameters includes simplified digital hardware to implement the functionality of transfer function measurement in the plant.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority to U.S. Provisional Application No. 61/116,897 filed Nov. 21, 2008 entitled METHODS AND SYSTEMS FOR POWER SUPPLY ADAPTIVE CONTROL UTILIZING TRANSFER FUNCTION MEASUREMENTS which is incorporated herein in its entirety by reference. 
    
    
     BACKGROUND 
     These teachings relate generally to adaptive control, and in particular, to the measurement of desired system parameters needed for feedback or adaptive control. 
     Feedback control systems in general and for power supplies in particular, have performance and stability limitations caused by unknown component variations. To achieve high speed transient performance it is necessary to have an accurate measurement of several key parameters. In particular, in the case of power supplies, the output capacitance may be largely unknown. This is due to the fact, that the power supply load has capacitance and it is in parallel to power supply output capacitance. Commonly, the load capacitance is in the form of additional capacitance added in the load circuit to improve high frequency characteristics and is, thus, required. 
     Unfortunately, the unknown load capacitance and possibly other components with significant tolerances are common occurrences in power supplies. A similar situation can occur in motor control where the motor torque constant and the load inertia are generally not known precisely enough for high speed control. 
     To allow for compensation for these unknown parameters it is necessary to measure them. Once these parameters are measured, calculations or gains scheduling can be used to map the measured parameters to required controller gains. Thus, there is a need for simplified digital hardware that can be used to measure the desired parameters. 
     SUMMARY 
     In one embodiment, the system of these teachings includes a stimulus source and signal measurement means. In one instance, the signal measurement means can include one or more correlators. In one embodiment, the stimulus source can include a source of basis functions. In one instance, the basis functions can be sinusoidal functions. Other instances of basis functions, such as, for example, but not limited to, square waves or Walsh functions, are also within the scope of these teachings. 
     In another embodiment, the system of these teachings can also include a compensator component, one or more processors and computer usable media. In one instance, the computer usable media can include computer readable code embodied therein and the computer readable code can cause the one or more processors to process the results of the signal measurement means and adjust parameters of the compensator based on the processed results. 
     Other embodiments of the system of these teachings and the methods of these teachings are also disclosed. In one embodiment, the system of these teachings can include simplified digital hardware to implement the functionality of transfer function measurement in a power supply. Conventional components to implement the functionality of transfer function measurement are typically very expensive (typically in the range of US $10,000-30,000) and bulky. These teachings can enable transfer function measurement functionality to be included in the power supply at a modest cost (in one instance less than one cent when implemented in deep sub micron CMOS). In one embodiment, the method of these teachings for measuring these unknown parameters is based on utilizing simplified hardware of these teachings to measure steady state transfer function characteristics. These transfer function characteristics can then be related by conventional techniques to the unknown parameters of system. 
     In one embodiment, a switching power supply of the present teachings can include, but is not limited to including, a circuit including at least two reactive components. The circuit can provide an output voltage and can be switched from one output voltage state to another output voltage state. The system can further include a switching component. The switching component can be operatively connected to switch the circuit between switching states. The switching states can include both output voltage states. The system can still further include a driver component operatively connected to drive the switching component in order to cause switching between two of the switching states, and a compensator component operatively connected to receive an input control signal and parameters, and to provide the switching states to the driver component. The system can further include a signal generator providing sinusoidal basis signals having in phase and quadrature components as input to the switching power supply, and a correlator. The correlator can receive basis signals from the signal generator, and can receive a power supply signal from the switching power supply. The correlator can provide a correlation between the a power supply signal and one of the in-phase and quadrature components. The system can also include a processor and a computer readable medium. The computer readable medium can have a first computer readable code embodied therein causing the processor to obtain a transfer function based on the correlation, compute the parameters from the transfer function, and provide the parameters to the compensator. The power supply signal can optionally include an output power supply signal or an output power supply signal and an input power supply signal. The signal generator can optionally include an oscillator. The oscillator can include, but is not limited to including, a table of values providing the in-phase components and quadrature components and a counter that is updated when the table is accessed. The oscillator can access the values according to the updated counter. The oscillator can generate the in-phase components and quadrature components based on forward and backward Euler integrators. The correlator can include an accumulator that accumulates a product of two inputs. The computer readable code can cause the processor to store the transfer function in the computer readable medium, and can recall the transfer function based on pre-selected conditions. 
     In one embodiment, a controller for a system of the present teachings can include, but is not limited to including, a signal generator providing sinusoidal basis signals having in phase and quadrature components as input to the system, and a correlator. The correlator can receive the basis signals from the signal generator and can receive a system signal from the system. The correlator can provide a correlation between a system signal and one of the in-phase and quadrature components. The controller can further include a processor and a computer readable medium having a first computer readable code embodied therein causing the processor to obtain a transfer function based on the correlation, to compute parameters from the transfer function, and to provide the parameters to the system. The signal generator can include, but is not limited to including, an oscillator. The oscillator can include, but is not limited to including, a table of values providing the in-phase components and quadrature components, and a counter that is updated when the table is accessed. The oscillator can access the values according to the updated counter. The oscillator can optionally generate in-phase components and quadrature components based on forward and backward Euler integrators. The computer readable code can cause the processor to store the transfer function in the computer readable medium and recall the transfer function based on pre-selected conditions. The correlator can include, but is not limited to including, an accumulator that accumulates a product of two inputs. 
     In one embodiment, a method for obtaining parameters for adaptive control of a system can include, but is not limited to including, the step of providing, in a power supply, a multiplier component, an adder component, and a delay component to obtain a correlation between the system signal and one of in-phase and quadrature components of sinusoidal basis signals. The method can further include the steps of obtaining transfer function characteristics based on the correlation, and obtaining the parameters based on the transfer function characteristics. The system signal can optionally include an output system signal or an output system signal and an input system signal. The method can optionally include the step of generating the basis signals by an oscillator. The step of generating the basis signals can include, but is not limited to including, the steps of associating the in-phase and quadrature components of the basis signal with a table of values, updating a counter when the table is accessed, and accessing the values according to the updated counter. The method can further optionally include the step of generating the in-phase and quadrature components based on forward and backward Euler integrators, storing the transfer function characteristics in a computer readable medium, and recalling the transfer function characteristics based on pre-selected conditions. 
     For a better understanding of the present teachings, together with other and further needs thereof, reference is made to the accompanying drawings and detailed description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1   a  is a schematic block diagram of a system of these teachings including a hardware digital generator for generating a stimulus signal; 
         FIG. 1   b  is a schematic block diagram of a system of these teachings including a table look-up oscillator to generate a sinusoidal basis function; 
         FIG. 2  is a schematic block diagram of a system of these teachings including an oscillator generating a sinusoidal signal and its quadrature using forward and backward Euler integrators; 
         FIG. 3  is a schematic block diagram of a digital correlator of the present teachings including an accumulator; 
         FIGS. 4   a  and  4   b  are schematic block diagrams of the system of these teachings in which four digital correlators are shown; 
         FIG. 4   c  is a schematic block diagram of a system of these teachings in which a possible partitioning between hardware and software is shown; 
         FIG. 5  is a schematic block diagram of the method for capacitance extraction of these teachings; and 
         FIG. 6  is a schematic block diagram of an alternate method for capacitance extraction of these teachings. 
     
    
    
     DETAILED DESCRIPTION 
     An exemplary embodiment is described below in order to better illustrate the system of these teachings. The exemplary embodiment uses a buck converter topology. However the methods of these teachings are applicable to any generic converter of buck, boost, or buck-boost, forward, fly-back, SEPIC, cuk, or other type. With some of these other types of converters, many switch states are possible. For example, in the buck-boost topology, the switch states are buck, boost, buck-boost, short across the inductor, and open. With the buck topology, the switch states are charging, discharging, and tri-state. The method and systems of these teachings are also applicable to other systems such as, but not limited to, motor control systems. 
     In one embodiment, the measurement is performed by injecting a signal into the power supply in a manner that stimulates the unknown power supply components. The input and output of the power supply network is then measured. In one instance, the inputs and outputs of the power supply network under question are measured by using correlation. Mathematically this is the projection of the signal on to a known function. These known functions are termed basis functions. By knowing the coefficient multiplying (also referred to as the size of) each of these basis functions in the original signal, the original signal can be reconstructed by using the measured projections as scale factors. If the known functions are harmonically related sinusoids, the result is a Fourier series. It should be noted that other series expansions in terms of other basis functions are also within the scope of these teachings. It should also be noted that one skilled in the art will recognize the relationship between a series expansion in the discrete representation and an integral representation in the continuous case. 
     In one embodiment of these teachings, a single pair of orthogonal signals is used for correlation of the input and output. The projections are the gains of the basis components at the basis functions frequency. This technique provides the averaging needed to reduce or effectively eliminate noise and load current sensitivity. To simplify the analysis of the measurements, it is possible to use a sinusoidal stimulation. (Sinusoids are eigenfunctions of linear systems and the input and outputs are then of the same form). Other inputs can be used, for example a square wave or Walsh functions. These can simplify the hardware at the expense of increased algorithmic complexity. 
     Referring now to  FIG. 1   a , in one embodiment, the system of these teachings can include, but is not limited to including, hardware digital generator  23  (also referred to as oscillator  23 ) that can generate a sinusoidal stimulus  45  to the external power supply network. Correlators  19  can perform cross correlation between power supply network input and output terminals and sinusoid stimulus  45  and its quadrature. Correlations  17 , the output of correlators  19 , represent the complex signals of the input and output signals. The transfer function can be calculated as the ratio of the output signal to the input signal. 
     Referring now to  FIG. 1   b , to generate the required sinusoidal and quadrature inputs, oscillator  23 A can be used. Oscillator  23 A can include, but is not limited to including, table  42  of values providing said in-phase components and quadrature components, and counter  41  that is updated when table  42  is accessed. Oscillator  23 A can access the values according to the updated counter. Oscillator  23 A, can be implemented in a variety of ways, table  42  with sinusoidal values accessed cyclically by counter  41  being one of the ways. 
     Referring now to  FIG. 2 , a second method of generating a sinusoidal signal and its quadrature includes providing oscillator  23 B that generates in-phase components and quadrature components based on forward and backward Euler integrators. The phases of the forward and backward integrators cancel, and this network rings at its resonant frequency with minimal damping. The initial condition of the cosine integrator determines the peak amplitude. The frequency of oscillation is determined by the gains. The gain value should be the resonant frequency in rads/sec multiplied by the sampling period. 
     Referring now to  FIG. 3 , digital correlator  19  can be, in one instance, accumulator  43  that accumulates the product of its two inputs. 
     Referring now to  FIGS. 4   a  and  4   b , four digital correlators  19  ( FIG. 4   b ) can be used. One pair of correlators can be used to measure the input and another pair can be used to measure the output signal projections onto the two sinusoidal basis functions. Oscillator  23  ( FIG. 4   a ) and four digital correlators  19  ( FIG. 4   b ) can be, but aren&#39;t limited to being, implemented in hardware. The resulting four values  47  are then processed by complex division  49 . The division algorithm may either be implemented in hardware or in software. Typically, the system processor that is responsible for mapping the measured parameters and the compensator gains also performs the division function. The system can include a stimulus source, oscillator  23  ( FIG. 4   a ), and signal measurement means, the four correlators  19  ( FIG. 4   b ). Other embodiments, such as the embodiment shown in  FIG. 1   a , can include at least one correlator. 
     Referring now primarily to  FIG. 4   c , the switching power supply of the present teachings can include, but is not limited to including a circuit including at least two reactive components. The circuit can provide an output voltage and can be switched from one output voltage state  11  to another output voltage state  11 . The switching power supply can further include at least one switching component. The switching component can be operatively connected to switch the circuit between at least two switching states  31 . Switching states  31  can include output voltage states  11 . The switching power supply can still further include driver component  12  operatively connected to drive the switching component in order to cause switching between switching states  31 , and compensator component  29  that can be operatively connected to receive input control signal  33  and parameters  32 , and can provide switching states  31  to driver component  12 . The switching power supply can even still further include signal generator  23  that can provide sinusoidal basis signals  21  having in phase and quadrature components as input to the switching power supply, and at least one correlator  19  that can receive basis signals  21  from signal generator  23 . Correlator  19  can receive power supply signal  25  from the switching power supply, and can provide at least one correlation  17  between power supply signal  25  and one of the in-phase and quadrature components. The switching power supply can still further include processor  13 , and computer readable medium  15  having computer readable code embodied therein causing processor  13  to obtain transfer function  38  based on correlation  17 , compute parameters  32  from transfer function  38 , and provide parameters  32  to compensator component  29 . Power supply signal  25  can optionally include an output power supply signal or an output power supply signal and an input power supply signal. The computer readable code can optionally cause processor  13  to store transfer function  38  in computer readable medium  15 , and recall transfer function  38  from computer readable medium  15  based on pre-selected conditions. 
     Continuing to refer to  FIG. 4   c , a controller for a system can include, but is not limited to including, signal generator  23  that provides sinusoidal basis signals  21  having in phase and quadrature components as input to the system, and correlator  19  that can receive basis signals  21  from signal generator  23 . Correlator  19  can receive system signal  25  from the system, and can provide correlation  17  between system signal  25  and one of the in-phase and quadrature components. The controller can also include processor  13 , and computer readable medium  15  that includes computer readable code that causes processor  13  to obtain transfer function  38  based on correlation  17 , compute parameters  32  from transfer function  38 , and provide parameters  32  to the system. Signal generator  23  can optionally include oscillator  23 A ( FIG. 1   b ) that can include table  42  ( FIG. 1   b ) of values providing the in-phase components and quadrature components, and counter  41  ( FIG. 1   b ) that can be updated when table  42  ( FIG. 1   b ) is accessed. Oscillator  23 A ( FIG. 1   b ) can access the values according to the updated counter. Signal generator  23  can also optionally include oscillator  23 B ( FIG. 2 ) that generates in-phase components and quadrature components based on forward and backward Euler integrators. The computer readable code can optionally cause processor  13  to store transfer function  38  in computer readable medium  15 , and recall transfer function  38  from computer readable medium  15  based on pre-selected conditions. Correlator  19  can optionally include accumulator  43  ( FIG. 3 ) accumulating a product of two inputs. 
     Continuing to still further refer to  FIG. 4   c , a possible partitioning between hardware and software is shown. Oscillator  23  and correlators  19  can be implemented in hardware and the complex division can be implemented in system microprocessor  13 . System microprocessor  13  can then use resulting parameters  32  to adjust compensator  29 . These adjustments can be made by using traditional closed loop analysis techniques that are implemented in the microprocessor  13 . Alternatively, the result of these analysis techniques for different measurements can be stored in memory  15  and recalled based on capacitance or other measurements. System  100  can include stimulus source basis signal  21  and signal measurement means correlators  19 . System  100  can also include processor  13  (shown here and referred to as a microprocessor) and computer usable medium (for example, memory  15 ) having computer readable code that causes processor  13  to process the results (for example, correlation  17 ) from the signal measurement means (correlators  19 ) in order to obtain parameters  32 , and to provide those parameters  32  to compensator  29  in order to adjust compensator  29 . In another embodiment, the processed results can be stored in computer usable medium (for example, memory  15 ) and the computer readable code causes processor  13  to recall the processed results based on predetermined conditions. 
     Continuing to even still further refer to  FIG. 4   c , the result of each correlator  19 , correlation  17 , is: 
             corr   =       ∑     i   =   0     NM     ⁢       basis   ⁡     (   i   )       ⁢     signal   ⁡     (   i   )                 
When the basis functions are orthogonal sinusoids and the measured signal is sinusoidal, the signal is
 
signal( wnTsi/N )= A  sin( wnTsi/N )+ B  cos( wnTsi/N )
 
Each pair of correlators  19 , for sinusoidal signals, is:
 
                 [           NM   2         0           0         NM   2           ]     ⁡     [         A           B         ]       =     [             ∑     i   =   0     NM     ⁢       sin   ⁡     (     wnTsi   /   N     )       ⁢     signal   ⁡     (     wnTsi   /   N     )                       ∑     i   =   0     NM     ⁢       sin   ⁡     (     wnTsi   /   N     )       ⁢     signal   ⁡     (     wnTsi   /   N     )                 ]           
Thus, the in phase and quadrature correlators are proportional to the complex signal amplitude. Note, the summing interval is chosen to be M cycles of the stimulus signal so the signals are orthogonal and the diagonal terms are zero. Since ratios are of interest (transfer function, impedance, etc.), the proportionality constant cancels.
 
     Continuing to still further refer to  FIG. 4   c , a method for obtaining parameters  32  for adaptive control of a system can include, but is not limited to including, the step of providing, in a power supply, at least one multiplier component  61  ( FIG. 3 ), at least one adder component  43  ( FIG. 3 ), and at least one delay component  63  ( FIG. 3 ) to obtain at least one correlation  19  of at least one system signal  25  with one of in-phase and quadrature components of sinusoidal basis signals  21 . The method can also include the steps of obtaining transfer function characteristics based on correlation  19 , and obtaining parameters  32  based on the transfer function characteristics. System signal  25  can optionally include an output system signal or an output system signal and an input system signal. The method can optionally include the step of generating basis signals  21  by oscillator  23 . The step of generating basis signals  21  can include, but is not limited to including, the steps of associating the in-phase and quadrature components of basis signals  21  with table  42  ( FIG. 1   b ) of values, updating counter  41  ( FIG. 1   b ) when table  42  ( FIG. 1   b ) is accessed, and accessing the values according to the updated counter. The step of generating basis signals  21  can include, but is not limited to including, the step of generating the in-phase and quadrature components based on forward and backward Euler integrators. The method can optionally include the steps of storing the transfer function characteristics in computer readable medium  15 , and recalling the transfer function characteristics from computer readable medium  15  based on pre-selected conditions. 
     Referring now to  FIG. 5 , an embodiment of the method for capacitance extraction is shown. In this method the transfer function reciprocal is measured and real part  51  is used to calculate load capacitance  53  assuming a known inductance. Capacitance  53  is given by: 
             C   =         1   -     real   ⁡     (     duty   /   vout     )           Lwn   2       =       1   -     real   ⁡     (       (       I   1     +     ⅈ   ⁢           ⁢     Q   1         )     /     (       I   2     +     ⅈ   ⁢           ⁢     Q   2         )       )           Lwn   2               
It can be seen in  FIG. 5  that stimulus  45  is injected into the feedback loop reference. It is also possible to inject stimulus  45  after compensator  29 . Depending on the frequency and closed loop bandwidth either method may be used.
 
     Referring now to  FIG. 6 , another embodiment of the method for capacitance extraction is shown. In this embodiment, the capacitor admittance is measured and imaginary part  55  is used to calculate load capacitance  53 . Capacitance  53  is given by: 
             C   =         imag   ⁡     (       ⅈ   ⁡     (   ind   )       /     v   ⁡     (   cap   )         )       wn     =       imag   ⁡     (       (       I   1     +     ⅈ   ⁢           ⁢     Q   1         )     /     (       I   2     +     ⅈ   ⁢           ⁢     Q   2         )       )       wn             
Another embodiment of the system of these teachings can include a synthesizable digital logic description of the block diagrams in  FIGS. 4   a  and  4   b , excluding the complex division calculation. The complex division calculations can be done in processor  13  ( FIG. 4   c ).
 
     It should be noted that, although the systems and methods have been described for the exemplary embodiment of the power supply, the systems and methods of these teachings can be applied to the control of other systems besides power supplies, for example, but not limited to, motor control. Although these teachings have been described with respect to various embodiments, it should be realized these teachings are also capable of a wide variety of further and other embodiments within the spirit and scope of these teachings.