Adaptive Sliding Mode Control And Application For Uncertain Nonlinear Systems

The control plant is often nonlinear and uncertain in real engineering. Therefore researches on the control of uncertain nonlinear system have both theoretical and practical interests. Sliding mode control (SMC) shows a strong vigor on controlling an uncertain nonlinear system for its excellent robustness and complete adaptability to matching uncertainties and external perturbations. However, there exist some problems including chattering, excessive control gain, depending on mathematical model, requiring uncertainty to satisfy the matching condition and needing to ascertain the boundary of the uncertainty, which prevent SMC from being applied in engineering. Adaptive control (AC) is another common method to solve the control of uncertain nonlinear system. It can make control system insensitive to un-modeled dynamics, process parameter perturbation and external disturbance, and does not need uncertainty to satisfy the matching condition and ascertain the boundary of the uncertainty. Meanwhile, AC can make system automatically maintain the best work condition when the structure parameters and initial conditions changed or objective function extreme points drifted. But AC is often associated with other robust control methods by reason of own complex design method and susceptible robustness to model error when non-parametric uncertainty exists. So with combining the advantages of SMC and AC, and introducing AC into SMC, this paper studies adaptive sliding mode control method and theory of uncertain nonlinear system systematically as to expand the application range of SMC further and rich the research of uncertain nonlinear system control .Finally the design algorithms of this paper are applied in the ship fin stabilizer uncertain nonlinear system.Simulation results show that the effectiveness of roll stabilization performance, which provides some ideas for ship fin stabilizer control engineer. Our study addresses the following topics:?The research status of classical adaptive, backstepping adaptive and intelligent adaptive with the combination of SMC in uncertain nonlinear system is summarized. The related basic theory of nonlinear system analysis and design is introduced, including differential geometry, feedback linearization and Lyapunov stability theory.?For a class of matched uncertain affine nonlinear system, firstly the conventional SMC method with saturation function is introduced. Then a parameter adaptive SMC is proposed by using bipolar sigmoid function instead of sign function. The controller can not only realize the adaptive changes of switching gain and boundary layer thickness to achieve the compromise of tracking error and chattering, but also weaken the input chattering, obtain high tracking precision and need not to know the boundary of the uncertainties.?For a class of parameter semi-strict feedback unmatched uncertain nonlinear system, a backstepping adaptive SMC suitable for output tracking is proposed combined with backstepping adaptive and SMC. The controller allows parametric and non-parametric uncertainties including matched and unmatched exist simultaneously, furthermore input coefficient uncertanty in matched non-parametric uncertainties is also considered. Therefore it has good robustness. At the same time, arrival time of sliding mode surface can be adjusted and chattering can be reduced further by designing the gain parameter.?For a class of unmatched parameter observable minimum phase uncertain affine system, a dynamic backstepping adaptive SMC strategy is proposed combined with backstepping adaptive and SMC by using dynamic input-output linearization. The characteristic of the method lies in that it does not need to change uncertain nonlinear system into parameter strict or pure feedback form.?For a class of model unknown uncertain nonlinear system, a basic RBF neural network adaptive SMC is proposed. It uses RBF neural network to approximate the system uncertain dynamics, designs the weights adaptive laws, and utilize SMC to guarantee the system robustness. The characteristic of the controller is that it can guarantee system better following the desired trajectory when the approximation error is smaller, that is to say, when initial weight is suitable.Otherwise, the system state boundedness and asymptotic stability can not be guaranteed. According to the shortcomings of the controller, an improved RBF neural network adaptive SMC is proposed .The advantage of the controller lies in that the system can still maintain good control performance by the compensation of supervisory control when the approximation error is larger, so the system state boundedness and asymptotic stability can be guaranteed, furthermore, the weights boundedness are guaranteed by modifying the adaptive laws based on projection algorithm.?For the ship fin stabilizer uncertain nonlinear system, firstly ship rolling mathematical model is introduced. Then according to the influence of random wave, 2-D irregular long-crested wave Longuet-Higgins model is established based on spectrum analysis, and subsequently wave model simulation is made. Finally the control algorithms of chapter 3 and 5 are applied in the design of fin stabilizer controller. The simulation results under two high-sea conditions show that the two algorithms can make the system achieve good rolling performance, fast response speed, high control precision and good robustness.