Patent GB-864776-A (GB)
Title: Improvements in or relating to servo-resolver apparatus for effecting co-ordinate conversions
IPC: G06G7/22
Filed: 1957-07-16
Abstract: 864,776. Electric analogue calculating. SOC. ALSACIENNE DE CONSTRUCTIONS MECANIQUES. July 16, 1957 [July 23, 1956], No. 22557/57. Class 37.  A servo-resolver device converting rectangular to spherical co-ordinates comprises a pair of input circuits connected to a resolver unit and receiving voltages respectively representing rectangular co-ordinates, a pair of output circuits connected to the resolver unit, a shaft rotationally servo-driven under control of a voltage from one of the output circuits to adjust the resolver unit; such shaft being capable of occupying two positions of stable equilibrium corresponding to two angles differing by # radians for each combination of inputs, and means for automatically and continuously rotating such shaft towards that one of the two positions which it can reach by rotation through 7T an angle not greater than - radians. 2 In a servo-operated resolver apparatus (Fig. 1, not shown) for converting Cartesian co-ordinates x, y, z of a point referred to an origin into spherical co-ordinates D = distance, G = bearing and S = elevation, the analogue voltages of Y = r sin G and X = r cos G, where r = I cos S are applied to energize a first resolver whose drive shaft is rotated by a servomotor through angle G<SP>1</SP> to produce output analogue voltages given by (1) D cos S cos (G<SP>1</SP>- G) = x cos G<SP>1</SP> + Y sin G<SP>1</SP> = r<SP>1</SP> - cos (G<SP>1</SP>- G<SP>1</SP>). (2) - D cos S sin (G - G) _ - x sin G<SP>1</SP> + Y cos G<SP>1</SP> = # 1  = -r sin (G<SP>1</SP>- G<SP>1</SP>) wherein # 1  is fed back to control the servo system so that at balance G = G<SP>1</SP> = G<SP>1</SP> Œ2k# and r<SP>1</SP> = r > 0. Analogue voltages of Z = D sin S and r<SP>1</SP> are fed to a second resolver whose drive shaft is rotated by a servomotor through angle S<SP>1</SP> to produce output analogue voltages given by (3) D<SP>1</SP> =   r<SP>1</SP> cos S<SP>1</SP> + Z sin S<SP>1</SP> =  D[cos   S 1  cos   S   cos   (G 1  -   G 1 )   +   sin   S 1  sin   S]   =  D[cos (S<SP>1</SP>- S) - 2 cos S<SP>1</SP> sin 2(G1 - G /2) (4) #2 = - r<SP>1</SP> sin S<SP>1</SP> + Z cos S<SP>1</SP> = D[- sin S<SP>1</SP> cos S cos (G<SP>1</SP> - G<SP>1</SP>) + cos S<SP>1</SP> sin S] = D[- sin (S<SP>1</SP> - S) + 2 sin S<SP>1</SP> cos S sin <SP>2</SP>(G<SP>1</SP>-G/2) wherein # 2  is fed back to control the second servomotor so that at balance S<SP>1</SP> = Sand D<SP>1</SP> = D>O. As the co-ordinate point intersects the z axis, G changes abruptly by # and S passes through a # maximum or minimum value Œ-, so that r 2 passes through zero. The error angle (Gl - G) reaches a high value, due to the inertial lag of the servomotor which cannot follow sufficiently rapidly the variations of G\ so that voltage r<SP>1</SP> is negative while G<SP>1</SP>- G > #/2 and corresponding dynamic errors are produced in S<SP>1</SP> - S and D<SP>1</SP> - D. [Equations 1-4.] These dynamic errors are avoided in an improved servo resolver system (Fig. 2) according to the invention, wherein for given input parameters the resolver shaft may be driven into two positions of stable equilibrium separated by an angle #; the shaft automatically adopting at balance that position of equilibrium which is # reached by a rotational angle of less than -. 2 The zero point of the G<SP>1</SP> rotation is therefore electrically displaced by angle # by changing the signs of the voltages from the resolver at the instant at which the angle G varies abruptly by #; i.e. when the voltage (5) x cos G<SP>1</SP>+ y sin G<SP>1</SP> = r cos (G<SP>1</SP>- G) changes sign through zero. In Fig. 2, resolver R 1  receiving inputs Y = r sin G, X = r cos G is rotated through angle G <SP>1</SP> by servomotor M 1  in response to a control signal # 1  to produce outputs r<SP>1</SP>, # 1  according to equations (1), (2) of which the first is applied to a sign detector which may comprise an amplifierrectifier-valve-operated relay circuit (Figs. 3, 4, not shown) operative to change over the sign or phase sense of the first and second outputs of the resolver at a sufficient negative value of # r<SP>1</SP> = r cos (G<SP>1</SP> - G) i.e. when / G<SP>1</SP> - G / > -, 2 so that the zero point of the G<SP>1</SP> rotation is shifted electrically through # radians, equivalently to the physical rotation of shaft G<SP>1</SP> by #, thus reducing the dynamic error (G<SP>1</SP>- G<SP>1</SP>) # from a value exceeding - to a value less than 2 # -. When the voltage r cos (G<SP>1</SP> - G) swings 2 positively, the sign inverters are restored, the effect being similar to a further rotation of the shaft by #. The latter thus has two stable positions at which G<SP>1</SP> = G or G<SP>1</SP> = G + #; of which that position is chosen to reach which the shaft must revolve by < #/2. The two positions are equivalent so far as output voltages are concerned ; the voltage representing r<SP>1</SP> being supplied together with the voltage representing z to a second servo-operated resolver as above whose rotation represents S at balance and which then develops an output signal representing D. Servomotor M 1  may drive a second resolver R 1 1, reponsive to voltages representing Cartesian co-ordinates v, u to develop outputs which are correspondingly reversible in polarity by other sign reversers controlled by the above Œ α = a<SP>1</SP> #relay circuit so that Œ #=b<SP>1</SP>.