Controller Design And Analysis For Singularly Perturbed Systems Subject To Actuator Saturation

Multiple time-scale characteristics widely exist in the field of chemical process, robot, aerospace engineering, power system etc. Early methods for multiple time-scale systems usually ignore the fast dynamics and design controllers based on the reduced slow subsystems, which may lead to degradation of system performance and cannot meet the requirement. Then singular perturbation theory is introduced to cope with this kind of systems, which can reduce the computational burden and avoid the illconditioned numerical issues. On the other hand, Actuator saturation is a common phenomenon in the practical control systems, which has already led to a series of accident. Thus controller design and analysis of systems with actuator saturation have attracted much attention.Since the traditional singular perturbation theory can not be applied to nonsmooth systems, analysis and design of singularly perturbed systems(SPSs) with actuator saturation are hard tasks in control theory. This thesis focuses on the controller design and stability analysis of the SPSs with actuator saturation, and the main results are summarized as following:1. Sability analysis of continuous-time singularly perturbed systems subject to actuator saturation systemsStability bound and basin of attraction are the key indexes of singularly perturbed systems with actuator saturation. This thesis studies on the methods of estimating the stability bound and basin of attraction of continuous-time singularly perturbed systems with actuator saturation. First, by using the Lyapunov function and invariant set principle, a set invariance condition is proposed. Then based on the proposed set invariance condition, a one-dimensional search algorithm is established to get the best estimate of the stability bound with guaranteed basin of attraction. Finally, a convex optimization problem is formulated to maximize the basin of attraction with a guaranteed stability bound. The proposed methods are independent of the singular perturbation parameter and thus avoid the ill-conditioned problem. Since the obtained estimations of the basin of attraction and stability bound are independent of the singular perturbation parameter, the proposed results are more general and robust than the existing approache.2. Fast sampling control of singularly perturbed systems with disturbance and actuator saturationBased on the fast sampling model, the problems of controller design and stability analysis are considered. First, for the given disturbance upper bound and the expected stability bound, by using the Lyapunov function and invariant set principle, a fast sampling controller design method is proposed such that the closed-loop system is bounded stable for the allowable disturbance and singular perturbation parameter. Then, for predefined stability bound, a fast sampling controller design methods is proposed to optimize the disturbance tolerance ability of the system. At last, for given stability bound, a fast sampling controller design method is proposed to maximize the disturbance rejection ability of the system.3. Slow sampling control of singularly perturbed systems with disturbance and actuator saturationBased on the slow sampling model, the problems of controller design and stability analysis are considered. First, for the given disturbance upper bound and the expected stability bound, by using the Lyapunov function and invariant set principle, a slow sampling controller design method is proposed such that the closed-loop system is bounded stable for the allowable disturbance and singular perturbation parameter. Then, for predefined stability bound, a slow sampling controller design methods is proposed to optimize the disturbance tolerance ability of the system. Furthermore, a fast sampling controller design method is proposed according to the expected stability bound such that the disturbance rejection is optimized. Finally, a comparison is made between the fast sampling control and slow sampling of the singularly perturbed systems with disturbance and actuator saturation.