Abstract
In this paper, a robust sliding mode control (SMC) based on backstepping technique is studied for a microgyroscope in the presence of unknown model uncertainties and external disturbances using adaptive fuzzy compensator and fractional calculus. At first, the dynamic of microgyroscope is transformed into analogically cascade system to guarantee the application of backstepping design. Then a novel fractional differential sliding surface is proposed which integrates the capacities of the fractional calculus and SMC. In order to reduce the chattering in SMC, a fuzzy logical system is utilized to approximate the external disturbances. In addition, fractional order adaptive laws are derived to estimate the damping and stiffness coefficients and angular velocity online based on Lyapunov stability theory which also guarantees the stability of the closed loop system. Finally, simulation results signify the robustness and effectiveness of the proposed control schemes and the comparison of root mean square error under different fractional orders and integer order are given to demonstrate the better performance of proposed controller.
Highlights
Microgyroscope has many applications in military and civil fields such as navigation, automobile and traffic etc. due to their superior features in angular velocity measurement
The mathematical model of z-axis microgyroscope is described, and the preliminary of fractional calculus is introduced, for solving the trajectory tracking problem of microgyroscope system with unknown model uncertainties and external disturbances, an adaptive fractional fuzzy sliding mode controller based on backstepping design is proposed based on Lyapunov theory
In order to achieve the dynamics of the MEMS, some assumptions have been made: 1) the motion of the proof mass is limited to x and y axis as shown in Fig 1; 2) the microgyroscope rotates at a constant angular velocity; 3) the centrifugal forces is neglected
Summary
Microgyroscope has many applications in military and civil fields such as navigation, automobile and traffic etc. due to their superior features in angular velocity measurement. An adaptive sliding mode controller based on backstepping technique was proposed for robotic manipulator in [37] which estimates the system uncertainties and external disturbances by the adaptive laws. The superior characteristic of this designed controller is that a fractional order term is adopted in the sliding manifold which generates an extra degree of freedom and makes the design of control law more flexible, the performance of the closed loop system has been improved a lot compared to the traditional SMC whose sliding surface is based on integer order calculus of the state variables. 2. Based on backstepping fractional sliding mode control scheme, a fuzzy logical system is designed to deal with the unknown uncertainties and external disturbances which weakened the chattering phenomenon.
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