Semi-global Exponential Stability Research Articles

Centrifugal compressor surge and speed control

Previous work on stabilization of compressor surge is extended to include control of the angular velocity of the compressor. A low-order centrifugal compressor model is presented, where the states are mass flow, pressure rise, and rotational speed of the spool. Energy transfer considerations are used to develop a compressor characteristic. In order to stabilize equilibria to the left of the surge line, a close coupled valve is used in series with the compressor. Controllers for the valve pressure drop and spool speed are derived. Semiglobal exponential stability is proved using a Lyapunov argument.

Passivity-Based Interaction Controller and Observer for Robot Manipulators

This work presents the design of a passivity-based controller and observer for a robot manipulator interacting with a compliant environment. Regulation of the contact force along the constrained direction and tracking of the end-effector position along the unconstrained directions is achieved; semiglobal exponential stability is proved. The control scheme is implemented in the joint space, and experimental results are illustrated for an open control architecture industrial robot which is endowed with joint position sensors and wrist force sensor, but no joint velocity sensors.

Speed and surge control for a lower order centrifugal compressor model

A model of a variable speed centrifugal compression system is presented. The model is based on the work of Greitzer (1976), but the compressor characteristic is developed by modelling the losses in the compressor. For surge control, a close coupled valve is employed. This valve is placed immediately downstream of the compressor, and the pressure drop over the valve is used as the control variable. This makes it possible to manipulate the shape of the equivalent compressor, consisting of compressor and valve. The speed of the compressor is controlled with a PI-controller. Semi-global exponential stability of the model with the proposed controllers is proven by the use of Lyapunovs theorem.

Re-examining the Nicosia-Tomei robot observer-controller from a backstepping perspective

Many robot controllers require not only link position measurements but also link velocity measurements; however, most robotic systems are only equipped with link position measurement devices. To address this problem, the authors present an observer-based controller for the link position tracking, output feedback control of robot manipulators. The approach is based on an observed integrator backstepping procedure which allows the authors to obtain a semi-global exponential stability result for the link position-velocity tracking error. Implementation of the proposed controller on a two-link direct-drive manipulator produces results which indicate good link position tracking performance and robustness against payload variations.

A partial state feedback controller for tajectory tracking of rigid‐link fiexible‐joint robot using an observed backstepping approach

AbstractThis article presents a partial state feedback controller for a rigid‐link flexible‐joint (RLFJ) robot using an observed integrator backstepping approach. The robot controller requires only link position and actuator position measurements, and eliminates the need for measuring link velocity and actuator velocity. The controller uses two exact knowledge, second‐order nonlinear observers to estimate the link and actuator velocities. The overall control system achieves a semiglobal exponential stability result for the link position and velocity tracking errors as well as the velocity observation errors. A stability proof and simulation results for the proposed partial state feedback controller are included in the article. © 1995 John Wiley & Sons, Inc.

Semi-global exponential stabilization of linear discrete-time systems subject to input saturation via linear feedbacks

In this paper, we show that a linear discrete-time system subject to input saturation is semi-globally exponentially stabilizable via linear state and/or output feedback laws as long as the system in the absence of input saturation is stabilizable and detectable, and has all its poles located inside or on the unit circle. Furthermore, the semi-globally stabilizing feedback laws are explicitly constructed. The results presented here are parallel to our earlier results on the continuous-time counterpart (Lin and Saberi, 1993).

Semi-global exponential stabilization of linear systems subject to “input saturation” via linear feedbacks

It is known that a linear time-invariant system subject to “input saturation” can be globally asymptotically stabilized if it has no eigenvalues with positive real parts. It is also shown by Fuller (1997) and Sussmann and Yang (1991) that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws. In this paper we show the existence of linear state feedback and/or output feedback control laws for semi-global exponential stabilization rather than global asymptotic stabilization of such systems. We explicitly construct linear static state feedback laws and/or linear dynamic output feedback laws that semi-globally exponentially stabilize the given system. Our results complement the “negative result” of Fuller (1977) and Sussmann and Yang (1991).