Robert P. Leland

Adaptive control of a MEMS gyroscope using Lyapunov methods

Two adaptive controllers for a vibrational MEMS gyroscope are described. Both controllers tune the drive axis natural frequency to a preselected frequency, regulate the amplitude of the drive axis vibration, cancel out quadrature error due to stiffness coupling, and drive the sense axis vibration to zero for force-to-rebalance operation. The first controller is based on an averaged, low frequency model, and the second is based on the full gyroscope model. Both controllers are successfully simulated for the Berkeley Z-axis gyro. The Lyapunov function used is critical in obtaining a good transient response, especially for the force-to-rebalance and automatic gain control loops. To implement the full model controller with displacement measurements only, and no velocity measurements, the controller is approximated.

Adaptive mode tuning for vibrational gyroscopes

We present an adaptive controller for tuning the natural frequency of the drive axis of a vibrational gyroscope. This is an attractive alternative to a phase-locked loop, since it introduces feedback, which can reduce the effects of imprecise fabrication. We also operate the gyroscope at a fixed frequency, chosen by the designer, which can simplify signal processing.

Adaptive tuning for vibrational gyroscopes

We propose an adaptive control scheme to tune the natural frequency of a microelectromechanical (MEMS) resonator for a vibrational gyroscope to a desired frequency. This is an attractive alternative to the phase locked loop, since it introduces feedback, which can reduce the effects of imprecise fabrication. In particular, we use adaptive control to set the natural frequency of the drive axis.

Adaptive learning defuzzification techniques and applications

Abstract In this paper, adaptive learning defuzzification techniques are studied under the consideration of system performance indices. By treating defuzzification processes as continuous mappings from space [0,1] n to the real line, the concept of the optimal defuzzification mapping can be developed. Since all the continuous defuzzification mappings considered in this paper form a Banach space, approximation to the optimal mapping with some known functions can be expressed as the parametric optimization problem. To find the optimal parameters, adaptive learning of the optimal defuzzification mapping is investigated. Learning laws for the parameters in the defuzzification mapping are derived in one case. Numerical results indicate that the adaptive learning defuzzification method can give superior defuzzification results to some popular defuzzification methods.

A new fuzzy time-series model of fuzzy number observations

Fuzzy time series [4] has been proposed to model dynamic processes whose observations are fuzzy sets or linguistic values, and some applications have been made with satisfactory results [5, 6]. In this paper, a new fuzzy time-series model is proposed by means of defining some new operations on fuzzy numbers. The proposed model is in the form of two theorems that relate the current value of a fuzzy time series with its past.

Adaptive oscillator control for a vibrational gyroscope

We present an adaptive controller for the drive axis of a vibrational gyroscope. A piezoelectrically driven gyroscope is operated as an oscillator circuit, by using a destabilizing positive feedback with automatic gain control. We adapt the feedback loop gain to obtain the desired amplitude for the oscillation and a parameter of the phase shift component in the feedback loop to yield a 90/spl deg/ phase shift. No sinusoidal driving input is required, and naturally occurring noise is the only input. The resulting oscillation is at the drive axis resonant frequency.

Lyapunov based adaptive control of a MEMS gyroscope

We present an adaptive controller to control all modes of a vibrational MEMS gyroscope. Our controller tunes the natural frequency of the drive axis, regulates the amplitude of the drive axis vibration, cancels out quadrature error due to stiffness coupling, and drives the sense axis vibration to zero in force-to-rebalance mode. We use both feedforward and feedback control. We simulate this controller for the Berkeley Z-axis gyro. The Lyapunov function used has a critical effect on the system response time, especially for the force-to-rebalance and automatic gain control loops.

The adaptive control system of a MEMS gyroscope with time-varying rotation rate

This paper presents a new adaptive control system to control both axes of a vibrational MEMS gyroscope. Here we suppose the rotation rate of gyro is an unknown time-varying parameter, rather than a constant as in current literature. A recently reported polynomial approximation is used to identify the time-varying rotation rate. A Lyapunov approach is employed to attain both of the control and adaptive laws. The simulation results based on Berkeleys Z-axis gyroscope model verify the controllers.

Linear quadratic stochastic control of atomic hydrogen masers

Data are given showing the results of using the linear quadratic Gaussian (LQG) technique to steer remote hydrogen masers to Coordinated Universal Time (UTC) as given by the United States Naval Observatory (USNO) via two-way satellite time transfer and the Global Positioning System (GPS). Data also are shown from the results of steering a hydrogen maser to the real-time USNO mean. A general overview of the theory behind the LQG technique also is given. The LQG control is a technique that uses Kalman filtering to estimate time and frequency errors used as input into a control calculation. A discrete frequency steer is calculated by minimizing a quadratic cost function that is dependent on both the time and frequency errors and the control effort. Different penalties, chosen by the designer, are assessed by the controller as the time and frequency errors and control effort vary from zero. With this feature, controllers can be designed to force the time and frequency differences between two standards to zero, either more or less aggressively depending on the application.

Fuzzy stochastic fuzzy time series and its models

In this paper, as an extension of the concept of time series, we will present the definition and models of fuzzy stochastic fuzzy time series (FSFTS), both of whose values and probabilities with which the FSFTS assumes its values are fuzzy sets, and which may not be modeled properly by the concept of time series. To investigate FSFTS, the definition of fuzzy valued probability distributions is considered and discussed. When the FSFTS is time-invariant, several preliminary conclusions are derived.