The bell-shaped vibratory angular rate gyro (abbreviated as BVG) is a novel shell vibratory gyroscope, which is inspired by the Chinese traditional bell. It sensitizes angular velocity through the standing wave precession effect. The bell-shaped resonator is a core component of the BVG and looks like the millimeter-grade Chinese traditional bell, such as QianLong Bell and Yongle Bell. It is made of Ni43CrTi, which is a constant modulus alloy. The exciting element, control element and detection element are uniformly distributed and attached to the resonator, respectively. This work presents the design, analysis and experimentation on the BVG. It is most important to analyze the vibratory character of the bell-shaped resonator. The strain equation, internal force and the resonator's equilibrium differential equation are derived in the orthogonal curvilinear coordinate system. When the input angular velocity is existent on the sensitive axis, an analysis of the vibratory character is performed using the theory of thin shells. On this basis, the mode shape function and the simplified second order normal vibration mode dynamical equation are obtained. The coriolis coupling relationship about the primary mode and secondary mode is established. The methods of the signal processing and control loop are presented. Analyzing the impact resistance property of the bell-shaped resonator, which is compared with other shell resonators using the Finite Element Method, demonstrates that BVG has the advantage of a better impact resistance property. A reasonable means of installation and a prototypal gyro are designed. The gyroscopic effect of the BVG is characterized through experiments. Experimental results show that the BVG has not only the advantages of low cost, low power, long work life, high sensitivity, and so on, but, also, of a simple structure and a better impact resistance property for low and medium angular velocity measurements.
A bell-shaped vibratory angular rate gyro, which is inspired by the Chinese traditional bell, is a kind of axisymmetric shell resonator gyroscope. Its sensitive element is a vibratory-like Chinese traditional bell, using a piezoelectric element on the wall of the vibrator to detect the standing wave's precession to solve the input angular rate. This work mainly studies the circuit system of a bell-shaped vibratory angular rate gyro. It discusses the process of circuit system design, analysis and experiment, in detail, providing the foundation to develop a bell-shaped vibratory angular rate gyro. Since the bell-shaped resonator's curved structure has the characteristics of large noise in the piezoelectric signal and large harmonics, this paper analyzes its working and signal detection method, then gives the whole plan of the circuit system, including the drive module, the detection module and the control loop. It also studies every part of the whole system, gives a detailed design and analysis process and proves part of the circuit system using digital simulation. At the end of the article, the test result of the circuit system shows that it can remove the disadvantages of the curved structure having large noise in the piezoelectric signal and large harmonics and is more effective at solving the input angular rate.
The tactical missile autopilot design process is detailed from a backstepping control perspective. Wherein, two autopilot topologies are proposed, i.e. the angle of attack (AOA) autopilot and acceleration autopilot. The nonlinear missile longitudinal dynamics is dealt with firstly to meet the strict feedback form. Control parameters of AOA autopilot are introduced in turn and required to be positive real numbers during the recursive process, however, act with some combination form in the final law. Thus a set of new parameters is presented to simplify the expression and disclose the conservatism of the aforementioned autopilot design. The results show that the positive real requirement on AOA autopilot parameters during step by step design has an unfavorable effect on closed loop system performance. An acceleration autopilot as a tracking problem is then set up and developed. On the one hand, the derivative of measured acceleration containing much noise is included in the law, which is thus not benefit to practical implementation. On the other hand, it's hard to transform the design parameters in the control formula into a compact form similar to the case of AOA autopilot. Two control gains, i.e. k 1 and k 2 , are determined on the basis of step and sine command tracking. The results show that k 1 affects mainly system steady state error, and k 2 affects mainly response speed. Moreover, k 1 is bounded and its upper bound has less relevance with k 2 . Compared with the traditional linear three-loop acceleration topology, the nonlinear acceleration autopilot based on a backstepping approach exhibits excellent tracking performance and robustness. In spite of good performance, the application of nonlinear autopilot is limited owing to a lack of physical meaning and complex engineering implementation. Actually, the exact mathematical model including aerodynamics and unconventional control strategy of an advanced missile could hardly be obtained from wind tunnel testing data or software simulation. Both linear and nonlinear autopilots could stabilize a static unstable missile. Through the control usage analysis, it can be concluded that actuator resource is the crucial factor in controlling a static unstable missile 12 .
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