Chen Hsieh

All covariance controllers for linear discrete-time systems

The authors characterize the set of covariances that a linear discrete-time plant with a specified-order controller can have. The controllers that assign such covariances to any linear discrete-time system are given explicitly in closed form. The freedom in these covariance controllers is explicit and is parameterized by two orthogonal matrices. By appropriately choosing these free parameters, additional system objectives can be achieved without altering the state covariance, and the stability of the closed-loop system is guaranteed. >

Control of large flexible structures-an experiment on the NASA Mini-Mast facility

The output variance constraint controller design procedure is integrated with model reduction by modal cost analysis. A procedure is given for tuning MIMO controller designs to find the maximal RMS performance of the actual system. Controller designs based on a finite element model of the system are compared with controller designs based on an identified model (obtained using the Q-Markov cover algorithm). The identified model and the finite-element model led to similar closed-loop performance, when tested in the Mini-Mast facility at Langley Research Center, The linear controllers designed tolerated significant Coulomb friction in the joints of the structure, even though robustness with respect to parameter variations was not included in the design.<<ETX>>

Modeling and Micro-Radian Precision Pointing of a Flexible Manipulator With the Existence of Static Friction

Controlling flexible structures has been considered as a well-developed topic in the control field. In this topic, vibration suppression and line-of-sight (LOS) pointing are two of the main research issues. Unfortunately, among all works reported, only a few have really achieved high levels of pointing precision. This is mainly because friction, especially static friction, is hard to deal with. In this research, the LOS control of the flexible beam of a standard hub-beam system is studied. The precision required is 1 s-1. Instead of treating friction as an external noise and trying to compensate for it, the friction phenomenon is represented by a linear spring and is included as part of the system model when the hub sticks. This is, in fact, a good approximation of the hysteretic friction behavior in the presliding phase if the spring stiffness is appropriately chosen. This modification greatly enhances the fidelity of the system model. What is more important is that it makes active controls still available in the stick phase to facilitate the fine tuning of the pointing error. Based on this modified model, it is then not hard to synthesize traditional proportional-integral-derivative and linear quadratic Gaussian controls to get LOS pointing with microradian precision.

Contour Controller Design for Two-Dimensional Stage System with Friction

For multiple-axis stages, it is required to operate the axes simultaneously, such that the resulting trajectory of platform follows a given contour. For most stage systems, friction acts as the major disturbance which degrades the precision of system motion and its effect should be compensated. In this paper, contouring control of a two-dimensional stage system subjected to friction is investigated. A systematic contour controller design based on task coordinate frame is proposed and its effectiveness is studied through theoretical analysis and numerical simulations.

Fast Nanometer Positioning of Heavy Loads Using a Hybrid Driver

Current motion tables can hardly exhibit the capabilities of positioning with nanometer precision and carrying heavy loads simultaneously. This is mainly because that the driver used to drive the table cannot fulfill the requirements needed for driving an ultra precision system without sacrificing the power it can offer. In this research, the concept of a hybrid driver is introduced and tested. This driver is basically a combination of a linear amplifier and an on-off large power supply. Although there are still some defects need to be overcome, preliminary experimental tests have shown that this kind of driver does have potential to carry heavy loads to do fast and long distance positioning with nanometer precision and in-position vibration.