J.S. Gibson

Time-optimal control of robotic manipulators along specified paths

The minimum-time manipulator control problem is solved for the case when the path is specified and the actuator torque limitations are known. The optimal open-loop torques are found, and a method is given for implementing these torques with a conventional linear feedback control system. The algorithm allows bounds on the torques that may be arbitrary functions of the joint angles and angular velocities. This method is valid for any path and orientation of the end- effector that is specified. The algorithm can be used for any manipulator that has rigid links, known dynamic equations of motion, and joint angles that can be determined at a given position on the path.

Saturation-Induced Instability and Its Avoidance in Adaptive Control of Hard Disk Drives

This paper presents an investigation of the design and implementation of minimum-variance adaptive controllers for computer hard disk drive (HDD) read-write track following. A common characteristic of minimum-variance controllers, adaptive or not, is that they rely on prediction filters with large high- frequency gains to predict broadband disturbances, and this often produces control-signal saturation and eventual loss of stability. Two methods are introduced here to address this issue. The first method, suitable for online adaptive control, uses frequency weighting to constrain the high-frequency gain of the prediction filter. The second method, suitable for tuning fixed-gain controllers, employs an adaptive scheme iteratively over a finite duration. Both methods were implemented on a commercial hard disk drive, and experimental results demonstrate their effectiveness.

Vector-channel lattice filters and identification of flexible structures

A novel derivative of a least-squares lattice filter is presented and applied to the identification of flexible structures. The vector-channel lattice given, derived in an infinite-dimensional history space, without matrix manipulations or geometric arguments, can constrain the autoregressive (AR) coefficients for several outputs to be the same. Numerical results for a simulated flexible structure compare the vector-channel lattice to the standard lattice filter. These results show that the frequencies and damping ratios for the most significant modes can be identified adaptively with lattice filters. >

Frequency-Weighted Minimum-Variance Adaptive Control of Laser Beam Jitter

This paper introduces a frequency-weighting method for adaptive disturbance rejection. The method constrains the high-frequency gain of the prediction filter in a minimum-variance adaptive controller. In an experimental application, the method is used to control a microelectromechanical system fast steering mirror to suppress laser beam jitter. The paper analyzes the effect of sensor noise on the performance of the adaptive control system and demonstrates that sufficient levels of high-frequency noise and/or disturbance combined with control saturation produce a spiking phenomenon in the output error. The experimental results show that the frequency weighting eliminates the spiking.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

An abstract approximation framework is developed for the finite and infinite horizon discrete-time linear-quadratic regulator problems for systems whose state dynamics are described by a linear semigroup of operators on an infinite-dimensional Hilbert space. The schemes included in the framework yield finite-dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Optimal Suppression of Laser Beam Jitter by High-Order RLS Adaptive Control

This paper demonstrates high-performance adaptive control for a laser-beam steering system, which exhibits high-order unknown jitter dynamics. The adaptive controller, which is based on a recursive least-squares finite-impulse-response lattice filter, has the distinguishing feature that variable and high-order adaptive filters can be realized in the real-time implementation. Varying the order of the adaptive controller produces both fast adaptation and optimal steady-state performance in the experiment, without the large transients often produced by fixed-order recursive least-squares adaptive controllers. The steady-state performance of the high-order adaptive controller approximates closely the theoretically achievable minimum-variance steady-state performance, which is derived from the identified plant and jitter dynamics. Experimental results also illustrate the capability of the adaptive controller to adapt rapidly to changing jitter characteristics.

Adaptive identification of a flexible structure by lattice filters

This paper presents adaptive parameter identification results for a complex flexible structure with many closely packed natural frequencies. Least-squares lattice filters, which are recursive in both time and order, are used to estimate the number of excited modes, natural frequencies, and damping ratios from input/output data. One-step-ahead output prediction also is generated by the lattice filters. The paper compares results from several experiments on the same structure, including one experiment during which the mass of the structure changes.

A new method for synthesizing multiple-period adaptive-repetitive controllers and its application to the control of hard disk drives

This paper introduces a new method for synthesizing multiple-period repetitive controllers. The main innovations in the synthesis procedure presented in this article are two. The first one is that this technique yields a solution compatible with the integration of the computed multiple-period repetitive controller into a minimum-variance adaptive control scheme. The second innovation is that the solution is period-recursive, reducing the complexity of controller synthesis considerably when compared with other methods available in the literature. To exemplify the synthesis procedure, a multiple-period repetitive controller is designed and integrated into an adaptive-repetitive control scheme used in the track-following control of a commercial hard disk drive. Experimental results show the effectiveness of the presented approach.

Variable-order adaptive control of a microelectromechanical steering mirror for suppression of laser beam jitter

We present an adaptive control scheme for laser-beam steering by a two-axis microelectromechanical systems (MEMS) fast steering mirror. Disturbances in the laser beam are rejected by a µ-synthesis feedback controller augmented by the adaptive control loop, which determines control gains that are optimal for the current disturbance acting on the laser beam. The variable-order adaptive controller is based on an adaptive lattice filter that implicitly identifies the disturbance statistics from real-time sensor data. Experimental results demonstrate that the adaptive controller significantly extends the disturbance-rejection bandwidth achieved by the feedback controller alone. The experimental results also illustrate the value of the variable-order capability of the adaptive controller.

Feedforward adaptive noise control with multivariable gradient lattice filters

This work presents a novel feedforward adaptive noise control (ANC) algorithm based on multivariable gradient lattice filters to control acoustic noise or vibration globally. In addition, a gradient-based lattice for AR and FIR models and its transpose lattice for the multivariable ANC algorithm are derived. The filter has different forward and backward reflection coefficient matrices to provide a faster convergence than the gradient lattice algorithm when using the same reflection coefficient matrices. Experimental results demonstrate the effectiveness of the proposed algorithm in controlling broadband acoustic noise in an enclosure.