Resolvers are used widely as devices for detecting the rotational angle of rotary shafts employed in industrial equipment such as vehicles. Since resolvers are capable of operating even in operating environments where the temperature is in the vicinity of 150° C., they are particularly ideal as rotational angle detectors in the field of motor control.
A resolver is one type of transformer. When a winding on the input side is excited by an AC voltage, an AC output voltage is induced in a winding on the output side. The relationship between rotational angle and the input and output of a resolver is shown in FIG. 13. The waveforms synchronized to an excitation power supply are the actual outputs (sine output and cosine output) at the rotational angles of a rotor. It will be understood that if sampling is performed at the peaks of the waveform of the excitation power supply and each of the output values at the rotational angle are connected, the waveforms will take on the cosine and sine values of the rotational angles. The absolute rotational angle of the rotor can be determined from these cosine and sine values.
In an actual system, however, it is highly likely that the output of a resolver will contain external noise in view of the fact that the resolver is mounted on the shaft of a rotor of a motor or the like. If the output contains noise, error ascribable to noise will occur when the resolver output signal is subjected to an analog-to-digital conversion. The A/D converter itself exhibits conversion error as well. This makes it necessary to correct for error based upon the result of the A/D conversion.
An R/D converter serves as a device that digitizes and extracts a rotational angle from a resolver. However, since an R/D converter has a high unit cost and involves a greater amount of hardware, a rotational angle conversion method that does not rely upon an R/D converter has been sought.
Rotational angle in a resolver is found by applying an analog-to-digital conversion to the sine and cosine output signals of the resolver and to the excitation power supply and processing the results of this A/D conversion. This is achieved using an apparatus comprising a single-phase excited, two-phase output resolver, A/D converters on two or more channels and a microcomputer.
FIG. 14 illustrates a method described in the specification of Patent Document 1. The excitation power supply signal, sine output signal and cosine output signal of a resolver are sampled by an A/D converter (step S41), and the sine and cosine output signals are each subjected to a Fourier transform (steps S42, S43). Next, ¦Sin θ¦, ¦Cos θ¦ are calculated from the product of a Fourier series (steps S44, S45) and the quadrant is discriminated (step S46). Next, ¦Sin θ¦/¦Cos θ¦ is calculated (step S47) and a digital rotational angle is found from the quadrant and a table of an arc tan (tan−1) function (step S48). At steps S42 to S45, ¦Sin θ¦, ¦Cos θ¦ are obtained by Equations (1) to (6) below using results of A/D conversion applied to n-number of excitation power supply sampling values, n-number of sine output sampling values and n-number of cosine output sampling values at sampling points of the kind illustrated in FIG. 15.
                    SA1        =                              ∑                          k              =              1                        n                    ⁢                                          ⁢                      (                          sine              ⁢                                                          ⁢              output              ⁢                                                          ⁢              sampling              ⁢                                                          ⁢              value              ×              excitation              ⁢                                                          ⁢              power              ⁢                                                          ⁢              supply              ⁢                                                          ⁢              sampling              ⁢                                                          ⁢              value                        )                                              (        1        )            
                    SB1        =                              ∑                          k              =              1                        n                    ⁢                                          ⁢                      (                          sine              ⁢                                                          ⁢              output              ⁢                                                          ⁢              sampling              ⁢                                                          ⁢              value              ×              value              ⁢                                                          ⁢              shifted              ⁢                                                          ⁢              by              ⁢                                                          ⁢                              90                ∘                            ⁢                                                          ⁢              from              ⁢                                                          ⁢              excitation              ⁢                                                          ⁢              power              ⁢                                                          ⁢              supply              ⁢                                                          ⁢              sampling              ⁢                                                          ⁢              value                        )                                              (        2        )            ¦sin θ¦=√{square root over ((SA1)2+(SB1)2)}{square root over ((SA1)2+(SB1)2)}  (3)
                    CA2        =                              ∑                          k              =              1                        n                    ⁢                                          ⁢                      (                          cosine              ⁢                                                          ⁢              output              ⁢                                                          ⁢              sampling              ⁢                                                          ⁢              value              ×              excitation              ⁢                                                          ⁢              power              ⁢                                                          ⁢              supply              ⁢                                                          ⁢              sampling              ⁢                                                          ⁢              value                        )                                              (        4        )            
                    CB2        =                              ∑                          k              =              1                        n                    ⁢                                          ⁢                      (                          cosine              ⁢                                                          ⁢              output              ⁢                                                          ⁢              sampling              ⁢                                                          ⁢              value              ×              value              ⁢                                                          ⁢              shifted              ⁢                                                          ⁢              by              ⁢                                                          ⁢                              90                ∘                            ⁢                                                          ⁢              from              ⁢                                                          ⁢              excitation              ⁢                                                          ⁢              power              ⁢                                                          ⁢              supply              ⁢                                                          ⁢              sampling              ⁢                                                          ⁢              value                        )                                              (        5        )            ¦cos θ¦=√{square root over ((CA2)2+(CB2)2)}{square root over ((CA2)2+(CB2)2)}  (6)
According to a method described in Patent Document 2, a DC-component error possessed by an A/D converter is eliminated by performing sampling twice in one period of an excitation power supply and subtracting the two results of A/D conversions, as illustrated in FIG. 16. An integral is subsequently calculated from the results of A/D conversion and the digital angle is obtained.
According to a method described in the specification of Patent Document 3 and shown in FIG. 17, sampling is performed twice in succession at points bracketing the peaks of sine and cosine output signals of a resolver, values that do not fall within an allowable range are excluded and noise produced at the first or second sampling time is eliminated.
Furthermore, with a method that employs the method of least squares that is generally well known, a regression line is found from multiple items of sampled data, as shown in FIG. 18, results of an A/D conversion applied to sine and cosine output signals are substituted into the equation of the regression line and an error correction is performed. This method will be described with reference to the flowchart of FIG. 19. A sine output signal and a cosine output signal are sampled by an A/D converter (step S51) and data obtained as a result of the conversion is stored in memory (step S52). The equation of a regression line is calculated from data that has already been stored in the memory (step S53) and the latest result of conversion is substituted into the equation of this regression line (step S54). Correction values of ¦Sin θ¦, ¦Cos θ¦ are calculated from the result of substitution (step S55). Further, the coordinates of the center of ¦Sin θ¦, ¦Cos θ¦ are calculated (step S56). In which quadrant the found point belongs is discriminated (step S57), ¦Sin θ¦/¦Cos θ¦ is found (step S58) and the angle, namely the digital rotational angle, is calculated from the quadrant and the function Tan−1 (step S59).
[Patent Document 1]
JP Patent Kokai Publication No.11-118520A
[Patent Document 2]
JP Patent No.3408238
[Patent Document 3]
JP Patent Kokai Publication No. P2001-82981A