[Univ of Cambridge] [Dept of Engineering]

Active control of flexible structures using inertial stick-slip actuators

A P Darby


Future Space mission proposals include many large optical structures which must be capable of maintaining high shape accuracy. Typically, dimensional stability of the order of microns must be maintained over distances of tens of meters. In the past, this stability has been achieved by the use of organic composite materials, such as carbon fibre reinforced plastic (CFRP), which are thermally unresponsive, lightweight and stiff. These materials, however, are both expensive and subject to unknown changes in their properties during their space exposure lifetime. Hence, active control allows the use of more conventional engineering materials and the construction of larger and more ambitious structures.

In a typical application the two main effects to be controlled are vibrations, due mainly to on-board disturbances, such as torque wheels, and quasi-static disturbances, caused by effects such as temperature gradients or initial lack-of-fit of structural members. This dissertation describes a system which provides 6DOF alignment correction of a payload mounted at the tip of a flexible structure, subject to dynamic and quasi-static disturbances, using a Stewart platform arrangement. The six legs of the platform are formed by a new type of actuator. The actuator uses a stick-slip motion, driven by an inertial mass. The dynamics of the actuator are described and its ability to control both dynamic and quasi-static disturbances is examined, experimentally. The inherently non-linear input-output response of the actuator is quantified and modelled.

The flexible structure, used for experimental tests, consists of a pantographic mast. The modal parameters are identified through the use of a numerical model verified by modal tests that have been carried out on the actual structure. Important joint effects are examined and modelled. The modal model is combined with a rigid body model of the Stewart platform to produce a non-linear analytical model of the interaction between the structure and the actuators. This is used to estimate the performance and examine the stability of the closed-loop controlled system.

A linearised model is derived, using a simple bi-linear model of the actuator, to allow linear control techniques to be applied to the system. The quasi-static control problem is solved simply by using a proportional controller based upon a kinematic model of the Stewart platform. The stability of the controller is examined using a dynamic model. The system has been successfully demonstrated on the test structure in which disturbances are introduced via random thermal elongations of several structural members.

For the more difficult vibration control problem, three controller designs are examined. The simple proportional controller is unsatisfactory. However, non-collocated controllers, using the linearised dynamic model, such as LQG and H¥ loop-shaping methods, produce better results, although the performance is less satisfactory than desired. The non-linear model is found to predict reasonably the performance and stability of the closed-loop system when compared with measured experimental results

[Cambridge University | CUED | Structures Group | Geotechnical Group]

This page is maintained by rcb@eng.cam.ac.uk (last update 10 November 2003)