Analysia And Design Of Repetitive Control System Based On 2D Model

In control system practice, high accuracy tracking or rejection of periodic signals is an important issue. Repetitive control (RC) is known as an effective approach for such control problems. The internal model principle shows that the RC, which contains a periodic signal generator in the control loop, achieves zero steady-state tracking error for reference inputs or complete rejection of disturbances. Due to its simple structure and high control accuracy, the RC has been widely applied in many control systems, and has drawn much attention in various engineering fields.To improve existing results on RC theory and to reveal the true nature of RC systems, this thesis presents theoretical results in the synthesis and desingn of a linear RC system. The main work and innovations are listed as follows:(1) A design method of calculating the largest cut-off angular frequency for a low-pass filter and the gains for a state-feedback controller for RC systems is presented.For a class of unceitain RC control systems with limited bandwidth, an iterative algorithm for calculating the largest cut-off angular frequency of a low-pass filter and the gains of a state-feedback controller, as well as the design method for this class of RC systems arepresented. First, a state feedback controller is employed to robustly stabilize the closed-loop system and the robust stability condition of the system is derived. Next, the design problem is transformed into a generalized eigenvalue minimization problem for calculating the bandwidth for the repetitive controler. Furthermore, the problem of designing a state-feedback controller for a fixed low-pass filter is converted into the design problem of a standard H∞state-feedback controller. Then, an iterative algorithm for calculating the largest cut-off angular frequency of a low-pass filter and the gains of a state-feedback controller is presented. The algorithm produces a combination of parameters that yields a low-pass filter with the widest bandwidth and the repetitive controller with a high control precision under the condition that the robust stability of the closed-loop control system is guaranteed.(2) A continuous-discrete two-dimensional (2D) hybrid model to describe the control and learning actions of an RC system is established.There exists a trade-off between the robust stability and tracking performance in the simultaneous optimization method. To further improve the control performance, we focused on the fact that RC actually involves two independent types of actions:control and learning. Their characteristics are completely different:control is a continuous process within one repetition period, and learning is discrete behavior between periods. Based on the 2D characteristics of information propagation in the RC system, a continuous-discrete 2D hybrid model of a linear RC system is established. The analysis of the properties for the 2D hybrid model, such as transfer function, zeros and poles are also studied. Furthermore, some stability conditions for the 2D hybrid model are presented and the criterion is extended to calculate lower bounds on stability margins of an RC system.(3) A design method of optimal RC based on 2D hybrid model is proposed.To solve the drawbacks of existing RC systems, such as the separate choice and optimization of the dynamic compensator and the low-pass filter, we devised a new type of RC configuration, which contains a feed-forward compensator and a state-feedback controller. We then transformed an integrated design of this RC system into a stabilization problem of a 2D hybrid system. And we obtained an optimal repetitive controller based on LQR by using the optimal control theory for a given performance index. Unliking existing methods, the parameters of the repetitive controller and dynamic compensator can easily be obtained and the control and learning actions can be adjusted independently by tuning the weights in the performance index. (4) A design method of robust RC based on 2D hybrid model is presented.The optimal RC based on a 2D hybrid model can not be applied to a plant with uncertainties. To solve this problem, an effective design method of robust RC based on 2D hybrid model for a linear uncertain system is provided. First, the design problem of a repetitive controller for a linear normal plant is transformed into the design problem of a state-feedback controller for a 2D hybrid model and the corresponding design algorithm is devoleped. Next, the results are extended to a system with time-invariant structured uncertainties. Furthermore, for the case in which the gains of the controller to be designed have additive variations, a design method of non-fragile guaranteed-cost repetitive controller based on 2D hybrid model is presented by introducing a quadratic performance index function and using the LMI techniques. An H∞RC problem is defined when exogenous disturbances exist. Then, the problem of designing an H∞repetitive controller is formulated as the problem of designing an H∞state-feedback controller for a 2D hybrid model. The existence condition and method of designing an H∞state-feedback controller for the 2D model is presented by using a 2D Lyapunov function. Finally, this idea is applied to solve the problem of designing an H∞repetitive controller.(5) A design method of improved RC system based on a 2D hybrid model is proposed.The design methods of RC based on 2D hybrid model are extended to the analyse and design of an improved RC system. A new modified RC configuration for a class of linear system with uncertainties is presented, and a continuous-discrete 2D hybrid model with a delay for this configuration is established. Then, the problem of designing an improved repetitive controller is formulated as a problem of designing a state-feedback controller for the 2D hybrid model with a delay. An existence condition and design method of a state-feedback controller for the 2D model is obtained by using a 2D Lyapunov function. Based on these results, the design problem of improved repetitive controller for a class of linear system described by a 2D hybrid model is developed. The results of this design method showed the practical value in applications.