Nonlinear Systems With Input Saturation And Unknown Information

Almost any system will show certain nonlinearity more or less. While among the practical control systems, the phenomenon of saturation is the most common nonlinearity. Due to the physical restriction of the actuators itself, actuators inevitably suffer from the limitation of executive ability. The saturation obviously weakens the executive ability of the systems. And if this case is not considered during the controllers designing, it certainly will lead to the degradation of the system dynamic performance or unstable state, which has a significant impact on the system normal operation and means the plant can not accomplish the specified assignment, even causes the property damage even casualties. Thus, the study about the input saturation has a crucial theoretical and practical significance. In this paper, two novel control algorithms are proposed for two different nonlinear systems with input saturation and uncertain information. And the integral designing process is shared.This work stems from the study on Speed-high Rail, and makes some contribution to the theoretical analysis and controllers designing for the certain nonlinear systems. In most cases, it is impossible to obtain the accurate mathematical model of the practical system. While, the robust adaptive technology is always used to tackle this condition and can also ensure the system stable with given dynamic performance. Besides, the neural network is also applied to approximate the unknown functions, which has great capacity for approximating and learning. In order to design the controllers briefly, the backstepping technique based on Lyapunov function is introduced by uniting with the dynamic surface control (DSC) technique. The controllers can ensure that all signals of the system are semi-global uniformly ultimately bounded. A well-defined smooth hyperbolic tangent function is chosen to approximate the hard saturation to avoid the non-differentiable feature of the saturation, so that the Backstepping technique can be utilized. The relationship between the tracking error and the controller parameters is discussed, which has profound guiding significance for the simulation.The control schemes proposed in this paper can ensure the stability of the closed-loop system and realize the designing aim of tracking the desired value. The validity of the controllers are proved through theoretical derivation and MATLAB simulation.