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Tham khảo tài liệu 'robust control theory and applications part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Robust Fuzzy Control of Parametric Uncertain Nonlinear Systems Using Robust Reliability Method 387 2 Robust reliability based design of optimal controller Firstly if Theorem 3.3 is used by solving a optimization problem corresponding to 64 with a 1 the gain matrices as follows for deriving the controller are obtained K1G -20.8512 -13.5211 -3.2536 K 2G -21.2143 -13.1299 4.3799 . The norm of the gain matrices are respectively K1g 25.0635 and K2G 25.3303 . So there exist relations K1J 326.1639 13.0135 K1G l K2l 488.2767 19.2764 K2G . To examine the effect of the controllers the initial values of the states of the Lorenz system are taken as x 0 10 -10 -10 r the control input is activated at f 3.89s all as that of Lee Park and Chen 2001 the simulated state trajectories of the controlled Lorenz system without uncertainty are shown in Fig. 2. In which on the left- and right-hand sides are results of the controller of Lee Park and Chen 2001 and of the controller obtained in this paper respectively. Simulations of the corresponding control inputs are shown in Fig. 3 in which the dash-dot line and the solid line represent respectively the input of the controller of Lee Park and Chen 2001 and of the controller in the paper. Time sec Fig. 3. Control input of the two controllers dash-dot line and solid line represent respectively the result of Lee Park and Chen 2001 and the result of the paper The simulated state trajectories and phase trajectory of the controlled Lorenz system are shown respectively in Figs. 4 and 5 in which all the uncertain parameters are generated randomly within the allowable ranges. 388 Robust Control Theory and Applications Fig. 4. Ten-times simulated state trajectories of the controlled chaotic Lorenz system with parametric uncertainties all uncertain parameters are generated randomly within the allowable ranges and on the left- and right-hand sides are respectively the results of controllers in Lee Park and Chen 2001 and in the paper 40- 20- 0- -20 J .
