Control design of linear dynamic systems with matrix differential equations for aerospace applications.

摘要

In this dissertation, two control design approaches for general matrix second order systems with indefinite and nonsymmetric system matrices using accelerometers are proposed.;The first approach takes advantage of the distributed sensing and actuation of smart structures in which one can use as many actuators as controlled modes. In this case, the design is directly carried out via matrix second order framework.;The second approach is an extended algorithm for designing the controller as well as the estimator in the form of a matrix second order system. In this approach, there are no limitations on the number of sensors and actuators. Baseline controller design is obtained using standard approaches (such as pole placement and LQR) for state space systems by feedback of velocity and displacement. Once a baseline design is available, algorithms for constructing the same closed loop system by feedback of acceleration and velocity or acceleration and displacement are proposed.;Since the information of high order signals (such as acceleration) can be sensed directly, the sensor equation and control laws in a state space framework are modified to meet real situations. In order to deal with different sensors and feedback of various signals in the state space system, the 'Generalized State Space System with State Derivative Measurement' is proposed in this study. In this framework, it is assumed that different sensors are available to directly detect and feed back different types of signals(state derivative and state) to improve system performance without increasing the number of actuators.;For systems in which only the state derivative can be sensed directly, a special case of 'Generalized State Space System with State Derivative Measurement', namely, the 'Reciprocal State Space System' is proposed. It is shown that many available design methods, stability tests, controllability tests and observability tests for standard state space systems can also be applied to the 'Reciprocal State Space System'. Furthermore, the control design of descriptor systems can be handled using this novel framework. The concept and design approaches of the 'Reciprocal State Space System' are supplemental to those of standard state space system. Therefore, more flexibility is obtained to deal with problems of larger scope than before.;Various applications are considered to illustrate the proposed design algorithms. Thus, the dissertation provides contributions that have both theoretical and practical values.