Gain Scheduling Control Of Actuator Saturated Systems With Its Applications To Spacecraft Rendezvous

Saturation nonlinearity exists in every practical control system and makes the over-all system inherently nonlinear. Ignoring saturation nonlinearity in the controller design may lead to performance degradation and even instability of the closed-loop system. Con-troller design that takes into account input saturation has been recognized to be a difficult problem. Therefore, the study of control systems with actuator saturation is significant in theory and applications. This thesis studies the gain scheduling state feedback control and gain scheduling output feedback control for the linear system with actuator satura-tion. And the proposed approaches are used to solve the control problems of spacecraft rendezvous. The main results are listed in the following.The design idea of low gain feedback is that design as small as possible control gain to avoid actuator saturation. When the initial conditions are far from the origin, the control gain must be very small. However, as the state converges to the origin gradually, the amplitude of the control gain becomes smaller and smaller. Thus, the convergence rate of the closed-loop system is very slow. To solve this problem, we proposed the continuous static gain scheduling state feedback controller and the discrete static gain scheduling state feedback controller based on parametric Lyapunov equation, invariant sets and gain scheduling technique to guarantee the global stabilization and semi-global stabilization of the closed-loop system, respectively. The proposed gain scheduled approaches improve the dynamic performance of the closed-loop systems significantly by increasing a design parameter representing the convergence rate of the closed-loop system. The proposed approaches are applied into the spacecraft rendezvous and the simulation results show the closed-loop system with continuous static gain scheduling control has better dynamic performance than the discrete static gain scheduling control. However, the discrete static gain scheduling control is easy to implement and more easily accepted by engineers.For linear systems with actuator saturation, by using the parametric Lyapunov e-quation based and Riccati equation based design, we propose the continuous dynamic gain scheduling approaches to increase the design parameter online so as to increase the convergence rates of the closed-loop systems. To apply the proposed gain scheduling approaches, only a scalar differential equation whose right-hand-side is a function of the state vector is required to be integrated online. The closed-loop system is proven to be exponentially stable provided some parameters in the scheduling law are properly chosen. The established gain scheduling approaches are also extended to exponentially unstable linear systems with actuator saturation. Simulation results show that the closed-loop sys-tem with continuous dynamic gain scheduling control has better dynamic performance than the static gain scheduling control.State feedback control is very powerful for the control system whose full information of the state vectors is assumed to be accessible for feedback. Thus, if the state of the sys-tem is measurable, state feedback is the best choice. However, in practice, only the mea-sured output information rather than the full state information is available for feedback. Consequently, output feedback control is more reasonable. By combining the parametric Lyapunov equation approach and the gain scheduling technique, new observer-based dis-crete static gain scheduling output feedback controller and observer-based dynamic gain scheduling output feedback controller are proposed to solve the semi-global stabilization problem for a linear system subject to actuator saturation. By scheduling the design pa-rameters online the convergence rate of the state can be improved. Numerical simulations for spacecraft rendezvous system show the effectiveness of the proposed approaches.The problem of robust control of spacecraft circular orbit rendezvous system sub-ject to input saturation is studied in this paper. On the one hand, the relative model with parameter uncertainties caused by linearization error and saturation nonlinearity is estab-lished based on C-W equation. New robust discrete static gain scheduling controller and robust continuous dynamic gain scheduling controller are designed respectively to solve the robust control problem of spacecraft rendezvous system. By scheduling the design parameters, the convergence rate of the state can be improved. On the other hand, a ro-bust continuous static gain scheduling control is proposed to solve the problem of robust global stabilization of a spacecraft circular orbit rendezvous system with input saturation and input-additive uncertainties. To apply the proposed gain scheduling approaches, only a scalar nonlinear equation is required to be solved. With the designed controllers, the spacecraft orbit rendezvous is accomplished successfully.