Discrete Sliding Mode Control Of Electrostatic Levitation System

Electrostatic levitation in which electrostatic forces are applied to suspend levitators without contact and friction is superior to traditional electromagnetic levitation in that electrostatic levitation suspends not only electromagnetic levitators but also non-electromagnetic levitators such as conductors and nonconductors. Electrostatic Suspension Gyroscope(ESG) which is acknowledged as a highly precise active inertial navigation instrument is an important application of electrostatic levitation. Due to plant parameter variation and exterior disturbance, controller design is of vital importance to realize stable suspension. Commonly adopted linear control algorithm is inadequate to suppress these uncertainties while sliding mode control algorithm is robust enough to overcome this shortcoming, so discrete sliding mode control of electrostatic levitation system is presented in this dissertation in order to improve the robustness of the levitation system.Discrete sliding mode theory has been applied to electrostatic levitation system in which general discrete state space expressions with parameter variation have been set up based on gyro rotor electrostatic force equation and other annuluses including high-voltage amplifier, position sensor and time delay. Discrete linear disturbance observer designed in discrete domain as a feed-forward compensation is applied to cancel part or all of exterior disturbance forces. Meanwhile, state variable errors in discrete sliding mode observer designed in discrete field tend to zeros in finite number of sampling periods with the existence of parameter variation and exterior disturbance. Discrete sliding mode controller designed in discrete domain consists of integral linear control component which is designed by pole placement method, discontinuous control component and disturbance control component with boundary layer. Meanwhile, continuous lag-lead control algorithm and discrete linear state feedback control algorithm are applied to electrostatic levitation system respectively in comparison with sliding mode control algorithm.All the three control systems mentioned have been simulated respectively by using MATLAB SIMULINK in which dynamical simulation models of three control systems have been set up. In order to testify the strong robustness of sliding mode controller, the properties of three control systems in time domain, frequency domain are compared respectively in consideration of plant parameter variation and exterior disturbance force. Compared with lag-lead controller, sliding mode controller has more satisfactory performance in that its overshoot and settling time in step response have been reduced 40 percent and shortened 60 percent respectively, and the deviations of the rotor from the sphere center in the stimulation of exterior vibration and impulse have been reduced 80 percent and 87 percent respectively, and its resonant peak has been reduced 6.32dB and its damping factor has been increased at high frequency band while keeping the bandwidth still at the range between 600Hz and 800Hz, and its stiffness at lower frequency band(<10Hz) and the lowest stiffness at medium frequency band have been raised about 10 times and 2.85 times respectively. The simulation results show that sliding mode controller has strong robustness in suppressing parameter variation and exterior disturbance.In order to further testify this result, electronic circuit experiment with DSP simulation environment has been carried on, in which three control algorithms have been transferred into instructions of assemble language, and then is simulated.All in all, the robustness of electrostatic gyro levitation system has greatly been improved by applying sliding mode control theory to the system. It is of vital significance to secure the long-time and stable operation of ESG.