ANGULAR RATE COORDINATE TRANSFORMER

• US 3,660,648 A
• Filed: 10/15/1969
• Issued: 05/02/1972
• Est. Priority Date: 10/15/1969
• Status: Expired due to Term

• Current Assignee: Northrop Corporation
• Original Assignee: Jack Kuipers
• Inventors: Kuipers, Jack
• Primary Examiner(s): Morrison, Malcolm A.
• Assistant Examiner(s): Dildine, Jr., R. Stephen
• Application Number:
  US04/866,637
• Time in Patent Office: 930 Days
• Field of Search: 235/150.25,150.27,186,189
• US Class Current: 708/811
• CPC Class Codes: G06G 7/22 for evaluating trigonometric functions; for conversion of co-ordinates; for computations involving vector quantities trigonometric computations using simultaneous equations G06G7/34 for computations in the complex plane; G06G7/20, G06G7/28 take precedence

Abstract

Apparatus for converting signals representing rates of change of the angular position of a body with respect to its own axes to Euler angle rates of change utilizing three resolvers and two feedback paths so as to avoid practical difficulties equivalent to the '"'"''"'"''"'"''"'"'gimbal-lock'"'"''"'"''"'"''"'"' problem in the gyroscope art.

Claims

1. Coordinate transformer apparatus for obtaining Euler angle rates of change with respect to predetermined reference axes from signals representing the component angular rates of change of angular position of a body measured along three orthogonal axes fixed with respect to said body, said apparatus comprising first resolver means receiving two signals representing vector components which in turn represent the angular rates of change of said body about two of said body axes, said first resolver means being continuously set to resolve said signals representing vector components one of which is oriented with respect to said reference axes and the other one of which is an intermediate output component, second and third resolver means connected to each other and to said first resolver means for receiving inputs, said second and third resolver means being set to resolve said inputs into output components, feedback means connected to said second and third resolver means so as to receive said output component therefrom, summing means connected to and providing input for said second and third resolver means, said summing means being supplied with an input signal representing said angular rate of change of said body about said third body axis, said feedback means being connected to and operable to provide a further electrical signal to said summing means which after summing with said input signal to said summing means and resolution in said second resolver means will result in the output component from one of said second and third resolver means being zero or essentially zero.

2. The combination according to claim 1 wherein said feedback means comprises two feedback paths.

3. Coordinate transformer apparatus for obtaining Euler angle rates of change with respect to predetermined reference axes from signals representing the component angular rates of change of position of a body measured along three orthogonal axes fixeD with respect to said body, said apparatus comprising three resolvers, each said resolver being capable of providing two output signals representing Euler angular rates of change corresponding to applied input signals representing angular rates of change, feedback means connected from the output to the input sides of two of said three resolvers for modifying input signals to said two of said three resolvers, each said input signal including the sum of the integral of the Euler angle output rates of each of said two resolvers and a separate one of said angular rates of change, and means for providing as an input to the third of said resolvers signals which are a function of the angular rate output of one of said two resolvers, said angular rate output of one of said two resolvers being determined by the angular rate of said body, whereby the input to the third of said resolver is essentially zero when said body is not subjected to an angular rate.

4. In coordinate transformer apparatus for converting first, second and third body angular rate input signals into first, second and third Euler angle output signals respectively, the combination of:

first, second and third resolvers, each said resolver being capable of receiving first and second input signals and a reference signal and producing first and second output signals according to the equations X X cos theta + or - y sin theta Y y cos theta + or - x sin theta where x is the amplitude of a first input signal to each resolver y is the amplitude of a second input signal to each resolver, X is the amplitude of a first output signal from each resolver, Y is the amplitude of a second output signal from each resolver, and theta is the amplitude of a reference signal;

first and second summers, each capable of receiving first and second input signals and producing an output signal according to the equation A B - C where A is a summer output signal amplitude B is a first summer input signal amplitude, and C is a second summer input signal amplitude;

an integrator having an input and an output terminal;

two amplifiers each having an input and an output terminal;

means for applying said first and second body angular rate input signals to said first resolver;

means for applying said third body angular rate input signal to said first summer;

means for applying the first output signal from said first resolver and the output of said first summer as input signals to said second resolver;

means for applying the second output signal from said first resolver as an input signal to said second summer;

means for applying the first output signal from said second resolver and the output of said second summer as input signals to said third resolver;

means for applying the second output signal from said second resolver as an input signal to said integrator input terminal;

means for applying the signal from the output terminal of said integrator as an input signal to said first amplifier;

means for applying the signal from the output terminal of said first amplifier as a second input signal to said first summer;

means for applying the output signal from said second amplifier, as a second input signal to said second summer;

means for applying the signal from the output terminal of said integrator as the reference signal to said third resolver;

means for applying the second output signal from said third resolver as an input signal to the input terminal of said second amplifier, whereby said first output signal from said third resolver, the signal from the output terminal of said second amplifier, and the signal from the output terminal of said first amplifier constitute said first, second and third Euler angle output signals, respectively;

first feedback means for applying said third Euler angle output sIgnal to said first resolver as said reference signal applied thereto; and

second feedback means for applying said second Euler angle output signal to said second resolver as said reference signal applied thereto.

5. Coordinate transformer apparatus comprising:

first, second and third resolvers, each having first and second input terminals, a reference terminal, and first and second output terminals for transforming signals received at said input terminals and said reference terminal into signals at said output terminals according to the equations;

X x cos theta + y sin theta Y Y cos theta - x sin theta where x and y are proportional to the amplitudes of signals received respectively and said first and second input terminals, theta is proportional to the amplitude of a signal received at said reference terminal, and X and Y are proportional to the amplitudes of signals produced respectively at said first and second output terminals;

first and second summers, each having first and second input terminals and an output terminal for transforming signals received at said input terminals into a signal at said output terminal according to the equation C A - B where A and B are proportional to the amplitudes of signals received respectively at said first and second input terminals; and

C is proportional to the amplitude of the signal produced at said output terminal;

first and second amplifiers, each having an input and an output terminals; and

first, second, third and fourth integrators, each having an input and an output terminal;

wherein said resolver, summer, amplifier and integrator terminals are connected in circuit as follows;

said first resolver first output terminal to said second resolver first input terminal;

said first resolver second output terminal to said second resolver first input terminal;

said first summer output terminal to said second resolver second input terminal;

said second resolver second output terminal to said first integrator input terminal;

said second resolver first output terminal to said third resolver first input terminal;

said second summer output terminal to said third resolver second input terminal;

said third resolver first output terminal to said second integrator input terminal;

said third resolver second output terminal to said second amplifier input terminal;

said first integrator output terminal to said first amplifier input terminal and to said third resolver reference terminal;

said first amplifier output terminal to said fourth integrator input terminal and to said first summer second input terminal;

said second amplifier output terminal to said third integrator input terminal and to said second summer second input terminal;

said third integrator output terminal to said second resolver reference terminal; and

said fourth integrator output terminal to said first resolver reference terminal.