A new observer design method that allows for estimating the angular rates along a vehicle’s three principal axes is described. The observer uses measurements from a single two-axis angular rate sensor (gyro) and determines the rates for the third axis using a nonlinear observer. Unlike conventional approaches where the equations governing vehicle motion (Euler’s equations) are linearized and then an observer is constructed based on the linear model, this method does not require linearization of the system. Instead, a pseudo-linear representation is used. The pseudo-linear model is obtained by systematically decomposing a nonlinear system into linear and nonlinear terms. The nonlinear components are then redefined as an auxiliary set of state variables and/or inputs. This leads to an augmented linear system representation that is mathematically equivalent to the original nonlinear system. This method enables standard linear observer design techniques to be applied and develops observers that are capable of estimating the thirdaxis angular rates using measurements corresponding to the other two axes. The effectiveness of this approach is illustrated with an example. The case studied is the complete attitude rate determination and control of a spinning spacecraft. Computer simulation results show that the new approach provides excellent three-axis attitude control, yet requires angular rate sensors for only two axes.
Marcelo C. Algrain,
"Controlling three-axis attitude rates on a pointing system using nonlinear observer and two-axis measurements," Optical Engineering 36(4), (1 April 1997). https://doi.org/10.1117/1.601303