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Proceedings of the 2011 6th IEEE International Conference on Nano/Micro Engineered and Molecular Systems February 20-23, 2011, Kaohsiung, Taiwan

Virtual Prototyping Simulation for Electrostatically Suspended Rotor Micro Gyroscope Initial Levitation Dangdang Shao1, Wenyuan Chen, Weiping Zhang2, Feng Cui, Qijun Xiao Research Institute of Micro/Nano Science and Technology, Shanghai Jiaotong University 1, Abstract-We use virtual prototyping technique to develop a 3D model for electrostatically suspended rotor micro gyroscope system according to its actual mechanical structure and material properties. System level dynamic simulation results obtained from the established virtual prototyping model provide necessary reference and guidance for micro gyroscope system control. Various PID control methods used to realize rotor initial levitation with different control parameters are evaluated and validated by the analytical model before application. The output motion characteristic curves including force, velocity and displacement of rotor are analyzed. Based on simulation resultsďźŒ we find suitable strategy to realize rotor levitation and obtain superior motion performance. The displacement of rotor in Z direction measured in real working environment shows that the PID control method verified by the virtual prototyping simulation is workable. Rapid initial levitation of rotor provides prerequisite for the follow-up rotating and torque exerting control.


The electrostatically suspended rotor micro gyroscope in this paper is realized based on UV-LIGA fabrication process. The whole electrostatically suspended rotor micro gyroscope system mainly includes upper stator, lower stator, rotor and peripheral control electrodes. Stator and rotor are fabricated independently as shown in Fig.1 and Fig.2.


Electrostatically suspended micro device is an innovative MEMS device and has been widely used in different fields such as automobiles, robotics, astronomy, aviation and aircraft. Compared with traditional mechanical vibration device, which is sensitive to manufacturing tolerances, electrostatically suspended device can eliminate mechanical friction and obtain high precision. Moreover, it has special advantages such as low power consumption, high resolution and low drift deviation [1]. However, because of the small size of suspended micro device, there are several common difficulties in recent research, a. Micofabrication is challenging and the request of machining precision is hard to obtain. b. Weak signal should be carefully detected meanwhile noise interference should be minimized. c. Coupling is likely to occur to multi-axis device, thus bring out more difficulties to signal and processing. To settle the second and third issues described as below, it is necessary to find suitable control method which should be able to control the whole system effectively and efficiently. In current researches, Tohoku University developed a levitated ring-shaped rotational gyro/accelerometer based on PID control strategy [2]. University of Southampton developed an electrostatically levitated disc based on SigmaDelta control strategy [3]. The electrostatically suspended spherical bearing developed by Tsinghua University is based on non-linear control strategy [4].

978-1-61284-777-1/11/$26.00 Š2011 IEEE

Fig.1 Stator of micro gyroscope

Fig.2 Rotor of micro gyroscope

The rotor is levitated by electrostatic force through axial and radial electrodes and driven to rotate by the rotation electrodes to produce angular momentum in order to detect the input angular rate [5]. During micro gyroscope application, successful levitation of rotor is the prerequisite for further rotation. Control voltage is applied to upper and lower stator to levitate the rotor from bottom to null position. After stable levitation, the rotor can be driven to rotate easily.


The control strategy used to realize rotor initial levitation should meet both quick response time and good system stability. In this paper, PID control strategy is applied for this purpose. Due to the difficulties in real device system control, we use virtual prototyping technique to evaluate PID control methods based on different control parameters before real device applications. By tuning control parameters based on the high imitation model, virtual prototyping technique is proved to be quite useful to achieve good control performance. The whole product developing cycle is also shortened but still with reliability and efficiency. II.


A sandwich-like 3D model consistent with the actual gyroscope structure and material properties is established in Fig.3. A nickel rotor, an upper stator, a lower stator and control electrodes are assembled together. The upper and lower stators are both integrated on glass base. The dimensions of the model are set strictly match with the real size of micro gyroscope device.

(b) Fig.4. (a)-(b) Gyroscope Virtual Prototyping Model

The main analyzed objective in this system is the rotor, which should be levitated before rotating. Set the material properties 3 3 of it as Nickel with density 8.9 × 10 kg / m as shown in Fig.5.

Fig.3 Electrostatically Suspended Rotor Micro Gyroscope Structure Model Fig.5 Set Material Density

After setting the 3D model, we load the whole structure to virtual prototyping simulation environment by parasolid kernel as shown in Fig.4.

In the real working environment, we apply an electrostatical force to levitate the rotor based on PID control. The displacement of the rotor is detected by the differential capacitance method and then fed back to the controller to produce the control voltage. Then add the control voltage together with the bias voltage and then apply the sum to the corresponding levitation electrode to make the rotor suspend stably in the null position. The relationship between electrostatic force and applied voltage can be expressed as, Fz =

1 2


V2 ∑ d2


where ε is the vacuum permittivity, A is area of control pairs of rotor, d is the normal gap between the rotor and the electrodes, V is the control voltage and bias voltage. In the virtual prototyping simulation environment, we set the kinematic pair between rotor and stator as ideal slide during the initial levitation process. Another force is also added to the center of mass of the rotor. The force is the object of PID control method which is used to realize



levitation. Set input function for PID controller by adding state equations for displacement and velocity, Dz and VZ respectively, as shown in Fig.6.


Fig.6 Set Input Function

Create PID link by setting the displacement of the center of mass of the rotor as ‘Input’ and the velocity of the center of mass of the rotor as ‘Derivate Input’ (Fig.7), and the force is parameterized as shown (Fig.8).


(c) Fig.9(a)-(c) Rotor Motion Characteristic Curves with PID Control Parameters as P Gain: 5.0E-003,I Gain: 1.0E-010,D Gain: 1.0E-010

Fig.7 Define PID Controller

For the suitable setting of PID control parameters, it should be able to levitate the rotor to the null position successfully in short time period without oscillation. Parameter setting as P Gain=2.0E-003 , I Gain=5.0E-003 , D Gain=2.0E-010 is found to be such a workable solution. The corresponding motion curves of the rotor as shown in Fig.10 indicate that the rotor turns to levitation and becomes stable with a displacement of 4um after about 1s.

Fig.8 Parameterize the Force

We apply several sets of PID control parameters and analyze corresponding motions of the rotor in the model. The output motion characteristic curves including force, velocity and displacement reveal dynamic performance of rotor based on PID control with different control parameters. III.


As shown in Fig.9, when the control parameters are set as P Gain=5.0E-003, I Gain=1.0E-010, D Gain=1.0E-010, the rotor will not be able to reach stable levitation and will keep oscillation around the null position. We can thus conclude that such parameter setting is not workable to realize rotor initial levitation.



in real gyroscope device



An electrostatically suspended rotor micro gyroscope is introduced. PID control method is applied to realize rotor initial levitation. Virtual prototyping simulation is used to evaluate motion performance and validate different PID control parameters before actual usage. Simulation results show quick-response and stability of rotor levitation performance. Later experimental results based on real device demonstrate the feasibility of PID control method obtained from the virtual prototyping simulation.


ACKNOWLEDGMENT This work was supported by National Science Foundation (No.60402003) and National Defense Pre-Research Foundation(No.9140A09020706JW0314).

(c) Fig.10(a)-(c) Rotor Motion Characteristic Curves with PID Control Parameters as P Gain: 2.0E-003,I Gain: 5.0E-003,D Gain: 2.0E-010


Initial levitation experiment results based on real device control validate the PID control method obtained from virtual prototyping simulation, as shown in Fig.11

[2] [3] [4] [5]

Fig.11 Testing Results of Rotor Displacement Z direction


REFERENCE Xiao, Q., Chen, W., Li, S., Cui, F., Zhang, W., “Modeling and simulation of levitation control for a micromachined electrostatically suspended gyroscope”, Microsyst. Technol., 2010, 16, pp. 357-366. Murakoshi, T., Fukatsu, K., and Nakamura, S., “Electrostatically levitated ring-shaped rotational gyro/accelerometer”, Jpn J. Appl. Phys., 2003, 42, Pt. 1 (4B), pp. 2468–2470. Kraft, M., Farooqui, M., Evans, A., “Modeling and design of an electrostatically levitated disc for inertial sensing applications”, J. Micromech. Microeng., 2001, 11, pp. 423–427. HAN, F., Li, D., GAO, Z., WANG, Y., “Nonlinear control of active electrostatic bearings for initial levitation”, J. Tsinghua Univ, 2005, Vol.45, No.11. Cui, F., Chen, W., Su, Y., “Design of electrostatically levitated micromachined rotational gyroscope based on UV-LIGA Technology,” Proceedings of SPIE, 2004, Vol.5461, pp. 264-275.

Virtual Prototyping Simulation for Gyroscope Initial Levitation