tailieunhanh - RECENT ADVANCES IN ROBUST CONTROL – NOVEL APPROACHES AND DESIGN METHODSE Part 12

Tham khảo tài liệu 'recent advances in robust control – novel approaches and design methodse part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Synthesis of Variable Gain Robust Controllers for a Class of Uncertain Dynamical Systems 319 Timett Fig. 1. Time histories of the state X1 t Fig. 2. Time histories of the state X2 t The results of the simulation of this example are depicted in Figures 1-3 and Table 1. In these Figures Case 1 and Case 2 represent the time-histories of the state variables X1 t and X2 t and the control input u t generated by the proposed controller and Desired shows the desired time-response and the desired control input generated by the nominal system. Additionally Jk e t k 1 2 in Table 1 represent the following performance indecies. J1 e t j eT t e t dt J 2 e t sup e t 1 t From Figures 1-3 we find that the proposed variable gain robust state feedback controller stabilizes the uncertain system in spite of uncertainties. Besides one can also see from Figures 1 and 2 and Table 1 that the proposed variable gain robust state feedback controller achieves the good transient performance and can avoid serious chattering. 320 Recent Advances in Robust Control - Novel Approaches and Design Methods Fig. 3. Time histories of the control input u t Summary In this section a design method of a variable gain robust state feedback controller for a class of uncertain linear systems has been presented and by numerical simulations the effectiveness of the proposed controller has been presented. Since the proposed state feedback controller can easily be obtained by solving the standard algebraic Riccati equation the proposed design approach is very simple. The proposed variable gain robust state feedback controller can be extended to robust servo systems and robust tracking control systems. 3. Variable gain robust output feedback controllers In section 2 it is assumed that all the state are measurable and the procedure specifies the current control input as a function of the current value of the state vector. However it is physically and economically impractical to measure all of the state