Tham khảo tài liệu 'frontiers in adaptive control part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Function Approximation-based Sliding Mode Adaptive Control for Time-varying Uncertain Nonlinear Systems 141 time sec Figure 17. The approximation of uncertainty CB X 1 ủ m t Figure 18. Behavior of sliding function s t 4. Conclusions In this chapter two sliding mode adaptive control strategies have been proposed for SISO and SIMO systems with unknown bound time-varying uncertainty respectively. Firstly for a typical SISO system of position tracking in DC motor with unknown bound time-varying dead 142 Frontiers in Adaptive Control zone uncertainty a novel sliding mode adaptive controller is proposed with the techniques of sliding mode and function approximation using Laguerre function series. Actual experiments of the proposed controller are implemented on the DC motor experimental device and the experiment results demonstrate that the proposed controller can compensate the error of nonlinear friction rapidly. Then we further proposed a new sliding model adaptive control strategy for the SIMO systems. Only if the uncertainty satisfies piecewise continuous condition or is square integrable in finite time interval then it can be transformed into a finite combination of orthonormal basis functions. The basis function series can be chosen as Fourier series Laguerre series or even neural networks. The on-line updating law of coefficient vector in basis functions series and the concrete expression of approximation error compensation are obtained using the basic principle of sliding mode control and the Lyapunov direct method. Finally the proposed control strategy is applied to the stabilizing control simulating experiment on a double inverted pendulum in simulink environment in MALTAB. The comparison of simulation experimental results of SIMOAC with LQR shows the predominant control performance of the proposed SIMOAC for nonlinear SIMO system with unknown bound time-varying uncertainty. 5. Acknowledgements This work was supported by the National Natural Science Fundation .