1 Error Reduction of 2DOF Gimbal Gyros Using LQG/LTR Controller H.Torab 1 , M. Farrokhi 1,2 1 Department of Electrical Engineering 2 Center of Excellence for Power System Automation and Operation Iran University of Science and Technology Tehran 16486 - IRAN htorab@ee.iust.ac.ir , farrokhi@iust.ac.ir Abstract—In this paper, the dynamic equations and error reduction of 2DOF gimbal gyros are investigated. One of the major error sources in such gyros is the gimbal lock, which causes major errors and losing one degree of freedom. This error source is eliminated in this paper using a permanent magnet motor as the torquer. Moreover, using an LQG/LTR controller will guarantee the closed-loop system stability. In addition, effects of other error sources such as the drift, the measurement noise and the nutation are eliminated or reduced. Using the proposed method, one can easily measure the output angular rates using multiplication of the measured input voltage of the torquer and the system scale factor. Key Words: 2DOF gimbal gyro, gyroscope feedback control, LQG/LTR control, gimbal lock, INS 1. INTRODUCTION Inertial sensors such as gyroscopes are important parts of Inertial Navigation Systems (INS) that measure vehicle angular rate or deflection angle. Therefore, even a slight error in gyro outputs could lead to serious errors and malfunction of the system and results in severe system performance degradation. Hence, it is very important to detect and remove the faults effects in gyros. Mechanical gyros are the first and very important types of gyros, which have many applications with their various types. There are two important types of mechanical gyro: 1) rate gyros and 2) displacement or free gyros, which measure the angular rate and the deflection angle of the vehicle, respectively. These gyros exist in single and two Degree-of-Freedom. The most important type of the mechanical gyros is the Dynamically Tuned Gyro (DTG) and gimbal gyro. Gimbal gyros could be used as the rate gyro or the free gyro; DTGs are usually used as the free gyro to measure the deflection angle. Single DOF (SDOF) gyros have been widely studied in the literatures. Although various algorithms have been developed to investigate the faults in gyros and INS, few results dealt with specific faults and sometimes the faults are left undefined or are only handled based on very simplified assumptions. In [1] a robust Kalman filter is applied to eliminate some faults. However, the fault characteristics are not described from an engineering point of view. In [2] and [3] the gyro failures are classified as the hard and soft failures. The hard failures are modeled by zeroing out the corresponding rows in the measurement matrix while the soft failures are simulated by either adding biases or increasing the variance of the noise at the gyro outputs. Zhang and Jiang [4] have adopted a similar formulation for hard gyro failures in their investigation of fault-tolerant control systems; later they continue their research on analysis of various faults sources in rate gyros [5]. Due to the fact that there is no noticeable research on 2DOF mechanical gyroscopes, this remains already an open problem in the control and INS literatures. In this paper, dynamic equations and error reduction of such gyros are investigated. By designing a suitable controller and using a permanent magnet motor as the torquer, the effects of the bias and drift errors and measurement noise are reduced. The advantages of this methodology are eliminating the gimbal lock phenomenon and disturbances, and reducing the effect of other common faults such as nutation and noises. The gimbal lock is a major error source, which occur in 2DOF gyros and can cause loosing one degree of freedom. In this way, the measured angular rates are obtained form the product of the measured torquer input voltage and the system scale factor. In this paper, an LQG/LTR controller, which involves a Kalman filter and an LQR controller, is used to guarantee the stability of the closed-loop system and reduce the effects of disturbances and measurement noises. One of the main advantages of the proposed method is that it can be easily implemented. This paper is organized as follows. Section 2 shows how to obtain nonlinear equations of the 2DOF gimbal gyro, followed by linearization about the zero equilibrium point, which provides linear state-space equations of the gyroscope. In Section 3, the control structure and the system scale factor is investigated. Section 4 defines important error resources of gyroscope. Section 5 provides simulation results of the closed-loop system, where failures are also considered. Section 6 concludes the paper. Notations: The following notations are used in this paper: (X , Y , Z): inertial coordinate axis (x , y , z ): moving (body) coordinate axis s w : speed of spinning w : angular velocity of gyroscope W : angular velocity of vehicle w & : angular acceleration